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HANDBOOK OF AUTOMATION,
COMPUTATION, AND CONTROL
Volume 3
SYSTEMS AND COMPONENTS

JOHN WILEY & SONS, INC.
New York • London

HANDBOOK OF AUTOMATION,
COMPUTATION, AND CONTROL
Volume

3

SYSTEMS AND COMPONENTS

Prepared by a Staff of Specialists

Edited by

EUGENE M. GRABBE
SIMON RAMO
DEAN E. WOOLDRIDGE
Thompson Ramo Wooldridge Inc.
Los Angeles, California

Copyright

©

1961 by John Wiley & Sons, Inc.

All Rights Reserved. This book or any part
thereof must not be reproduced in any form
without the written permission of the publisher.
Library of Congress Catalog Card· Number: 58-10800
Printed in the United States of America

CONTRIBUTORS

G. S. AXELBY, Westinghouse Electric Corporation, Baltimore, Maryland
(Chapter 22) .

C. W. BAILEY, Consolidated Electrodynamics Corporation, Pasadena, California
(Chapter 24)

E. V. BERSINGER, Radio Corporation of America, Van Nuys, California
(Chapter 19)

P. S. BUCKLEY, E. I. du Pont de Nemours and Company, Inc., Wilmington,
Delaware (Chapter 7)

N. COHN, Leeds and Northrup Company, Philadelphia, Pennsylvania
(Chapter 17)

M. E. CONNELLY, Massachusetts Institute of Technology, Cambridge, Massachusetts (Chapter 1)

P. E. A. COWLEY, Shell Development Company, Emeryville, California
(Chapter 9)

R. O. DECKER, Westinghouse Electric Corporation, Pittsburgh, Pennsylvania
(Chapter 25)

D. P. ECKMAN, Case Institute of Technology, Cleveland, Ohio (Editor, Part D)
L. J. FOGEL, Astronautics Division, General Dynamics, San Diego, California
(Chapter 2)

A. S. FULTON, Thompson Ramo Wooldridge Inc., Canoga Park, California
(Editor, Part F; Chapters 1Band 23)

E.F. HOLBEN, Conoflow Corporation, Philadelphia, Pennsylvania (Chapter B)
E. M. GRABBE, Compagnie Europeimne d' Automatisme Electronique, Paris,
France (Chapter 14)

T. R. JAMES, General Mills, Inc., Minneapolis, Minnesota (Chapter 3)
v

CONTRIBUTORS

vi

D. L. JOHNSTON, Urwick-Orr and Partners, Hertfordshire, England (Chapter 4)
R. E. KALMAN, International Business Machines, Baltimore, Maryland
(Chapter 12)

A. G. KEGEL, Westinghouse Electric Corporation, Baltimore, Maryland
(Chapter 22)

C. G. LASPE, Thompson Ramo Wooldridge Products Company, Beverly Hills,
California (Chapter 11)

I. LEFKOWITZ, Case Institute of Technology, Cleveland, Ohio (Chapter 13)
J. LYMAN, University of California, Los Angeles, California (Chapter 2)
R. O. MAZE, Minneapolis-Honeywell Regulator Company, Minneapolis, Minnesota (Chapter 21)

J. M. MOZLEY, The Johns Hopkins Hospital, Baltimore, Maryland (Chapter 7)
G. F. PITTMAN, JR., Westinghouse Electric Corporation, Pittsburgh, Pennsylvania (Chapter 25)

J. E. RIJNSDORP, Royal Dutch Shell, Amsterdam, Holland (Chapter 70)
J. ROSENBERG, University of California, Los Angeles, California (Chapter 6)
J. S. SABY, General Electric Company, Cleveland, Ohio (Chapter 26)
J. A. SARGROVE, Automation Consultants and Associates, Ltd., London, England
(Chapter 4)

A. J. SCHENK, Jervis B. Webb Company, Detroit, Michigan (Chapter 5)
M. A. SCHULTZ, Westinghouse Electric Corporation, Pittsburgh, Pennsylvania
(Chapter 76)

W. E. SHOUPP, Westinghouse Electric Corporation, Pittsburgh, Pennsylvania
(Chapter 16)

L. M. SILVA, Beckman Instruments, Inc., Anaheim, California (Chapter 15)

A. P. STERN, General Electric Company, Syracuse, New York (Chapter 27)
M. E. STICKNEY, Lockheed Aircraft Corporation, Sunnyvale, California
(Chapter 20)

T. M. STOUT, Thompson Ramo Wooldridge Products Company, Beverly Hills,
California (Chapter 11)

.

J. WALKER, Librascope, Burbank, California (Chapter 24)
W. G. WING, Sperry Gyroscope Company, Great Neck, New York (Chapter 28)

FOREWORD

The proliferation of knowledge now makes it most difficult for scientists
or engineers to keep ahead of change even in their own fields, let alone in
contiguous fields. One of the fields where recent change has been most
noticeable, and in fact exponential, has been automatic control. This
three-volume Handbook will aid individuals in almost every branch of
technology who must constantly refresh their memories or refurbish their
knowledge about many aspects of their work.
Automation, computation, and control, as we know them, have been
evolving for centuries, but within the last generation their impact has
been felt in nearly every segment of human endeavor. Feedback principles were exploited by Leonardo da Vinci and applied by James Watt.
Some of the early theoretical work of importance was contributed by Lord
Kelvin, who also, together with Charles Babbage, pointed the way to the
development of today's giant computational aids. Since about the turn of
the present century, the works of men like Minorsky, Nyquist, Wiener,
Bush, Hazen, and Von Neumann gave quantum jumps to computation and
control. But it was during and immediately following \Vorld vVar II that
quantum jumps occurred in abundance. This was the period when theories
of control, new concepts of computation, new areas of application, and a
host of new devices appeared with great rapidity. Technologists now find
these fields charged with challenge, but at the same time hard to encompass. From the activities of World \Var II such terms as servomechanism,
feedback control, digital and analog computer, transducer, and system
engineering reached'maturity. More recently the word automation has
become deeply entrenched as meaning something about the field on which
no two people agree.
Philosophically minded technologists do not accept automation merely
as a third Industrial Revolution. They see it, as they stand about where
the editors of this Handbook stood when they projected this work, as a
manifestation of one of the greatest Intellectual Revolutions in Thinking
that has occurred for a long time. They see in automation the natural
consequences of man's urge to exploit modern science on a wide front to
vii

viii

FOREWORD

perform useful tasks in, for example, manufacturing, transportation, business, physical science, social science, medicine, the military, and government. They see that it has brought great change to our conventional way
of thinking about the human use of human beings, to quote Norbert
Wiener, and in turn about how our engineers will be trained to solve
tomorrow's engineering problems. They even see that it has precipitated
some deep thinking on the part of our industrial and union leadership
about the organization of workers in order not to hold captive bodies of
workmen for jobs that automation, computation, and control have swept
or will soon sweep away.
Perhaps the important new face on today's technological scene is the
degree to which the broad field needs codification and ·unification in order
that technologists can optimize their role to exploit it for the general good.
One of the early instances of organized academic instruction in the field
was at The Massachusetts Institute of Technology in the Electrical Engineering Department in September 1939, as a course entitled Theory and
Application of Servomechanisms. I can well recollect discussions around
1940 with the late Dr. Donald P. Campbell and Dr. Harold L. Hazen,
which led temporarily to renaming the 'course Dynamic Analysis of Automatic Control Systems because so few students knew what "servomechanisms" were. But when the GI's returned from war everybody knew,
and everybody wanted instruction. Since that time engineering colleges
throughout the land have elected to offer organized instruction in a multitude of topics ranging from the most abstract mathematical fundamentals
to the most specific applications of hardware. Textbooks are available on
every subject along this broad spectrum. But still the practicing control
or computer technologist experiences great difficulty keeping abreast of
what he needs to know.
As organized instruction appeared in educational institutions, and as
industrial activity increased, professional societies organized groups in the
areas of control and computation to meet the needs of their members to
tell one another about technical advances. Within the past five years
several trade journals have undertaken to report regularly on developments in theory, components, and systems. The net effect of all this is
that the technologist is overwhelmed with fragmentary, sometimes contradictory, redundant information that comes at him at random and in
many languages. The problem of assessing and codifying even a portion
of this avalanche of knowledge is beyond the capabilities of even the most
able technologist.
The editors of the Handbook have rightly concluded that what each
technologist needs for his long-term professional growth is to have a body
{Jf knowledge that is negotiable at par in anyone of a number of related

FOREWORD

ix

fields for many years to come. It would be ideal, of course, if a college
education could give a prospective technologist this kind of knowledge.
It is in the hope of doing this that engineering curricula are becoming
more broadly based in science and engineering science. But it is unlikely
that even this kind of college training will be adequate to cope with the
consequences of the rapid proliferation of technology as is manifest in the
area of automation, computation, and control. Hence, handbooks are an
essential component of the technical literature when they provide the
unity and continuity that are requisite.
I can think of no better way to describe this Handbook than to say that
the editors, in both their organization of material and selection of substance, have given technologists a unified work of lasting value. It truly
represents today's optimum package of that body of knowledge that will
be negotiable at par by technologists for many years to come in a wide
range of disciplines.
S. BROWN
Dean, School of Engineering
Massachusetts Institute of Technology
GORDON

PREFACE

Accelerated advances in technology have brought a steady stream of
automatic machines to our factories, offices, and homes. The earliest
automation forms were concerned with doing work, followed by the controlling function, and recently the big surge in automation has been
directed toward data handling functions. New devices ranging from
digital computers to satellites have resulted from military and other government research and development programs. Such activity will continue
to have an important impact on automation progress.
One of the pressures for, the development of automation has been the
growing complexity and speed of business and industrial operations. But
automation in turn accelerates the tempo of whatever it touches, so that
we can expect future systems to be even larger, faster, and more complex.
While a segment of engineering will continue to mastermind, by rule of
thumb procedures, the design and construction of automatic equipment
and systems, a growing percentage of engineering effort will be devoted to
activities that may be classified as problem solving. The activities of the
problem solver involve analysis of previous behavior of systems and equipment, simulation of present situations, and predictions about the future.
In the past, problem solving has largely been practiced by engineers and
scientists, using slide rules and hand calculators, but with the advent of
large-scale data processing systems, the range of applications has been
broadened considerably to include economic, government, and social activities. Air traffic control, traffic simulation, library searching, and language
translation are typical of the problems that have been attacked.
This Handbook is directed toward the problem solvers-the engineers,
scientists, technicians, managers, and others from all walks of life who are
concerned with applying technology to the mushrooming developments in
automatic equipment and systems. It is our purpose to gather together
in one place the available theory and information on general mathematics,
feedback control, computers, data processing, and systems design. The
emphasis has been on practical methods of applying theory, new techniques

xii

PREFACE

and components, and the ever broadening role of the electronic computer.
Each chapter starts with definitions and descriptions aimed at providing
perspective and moves on to more complicated theory, analysis, and applications. In general, the Handbook assumes some engineering training and
will serve as an information source and refresher for practicing engineers.
For management, it will provide a frame of reference and background ma:terial for understanding modern techniques of importance to business and
industry. To others engaged in various ramifications of automation systems, the Handbook will provide a source of definitions and descriptive
material about new areas of technology.
It would be difficult for any·one individual or small group of individuals
to prepare a handbook of this type. A large number of contributors, each
with a field of specialty, is required to provide the engineer with the desired
coverage. With such a broad field, it is difficult to treat all material in a
homogeneous manner. Topics in new fields are given in more detail than
the older, established ones since there is a need for more background' information on these new subjects. The organization of the material is in
three volumes as shown on the inside cover of the Handbook. .Volume 1
is on Control Fundamentals, Volume 2 is concerned with Computers and
Data Processing, and Volume 3 with Systems and Components.
In keeping with the purpose of this Handbook, Volume 1 has a strong
treatment of general mathematics which includes chapters on subjects not
ordinarily found in engineering handbooks. These include sets and relations, Boolean algebra, probability, and statistics. Additional chapters
are devoted to numerical analysis, operations research, and information
theory. Finally, the present status of feedback control theory is sum:"
marized in eight chapters. Components have been placed with sys..:.
tems in Volume 3 rather than with control theory in Volume 1, although
any discussion of feedback control must, of necessity, be concerned with
components.
The importance of computing in research, development, production, real
time process control, and business applications has steadily increased.
Hence, Volume 2 is devoted entirely to the design and use of analog and
digital computers and data processors. In addition to covering the status
of knowledge today in these fields, there are chapters on unusual computer
systems, magnetic core and transistor circuits, and an advanced,treatment
of programming. Volume 3 emphasizes systems engineering.' A part of
the volume covers techniques used in important industrial applications by
examining typical systems. The treatment of components is largely concerned with how to select components among the various alternates, their
mathematical description, and their integration into systems. There is

xiii

PREFACE

also a treatment of the design of components of considerable importance
today. These include magnetic amplifiers, semiconductors, and gyroscopes.
'Ve consi<;ler this Handbook a pioneering effort in a field that is steadily
pushing back frontiers. It is our hope that these volumes will not only
provide basic information on new fields, but will also inspire work and
further research and development in the fields of automatic control. The
editors are pleased to acknowledge the advice and assistance of Professor
Gordon S. Brown and Professor Jerome S. 'Yiesner of the Massachusetts
Institute of Technology, and Dr. Brockway McMillan of the Bell Telephone Laboratories, in organizing the subject matter. To the contributors
goes the major credit for providing clear, thorough treatments of their
subjects. The editors are deeply indebted to the large number of specialists in the control field who have aided and encouraged this undertaking by reviewing manuscripts and making valuable suggestions. Many
members of the technical staff and secretarial staff of Thompson Ramo
Wooldridge Inc. and the Ramo-'Yooldridge Division have been especially
helpful in speeding the progress of the Handbook.
EUGENE

M.

GRABBE

SIMON RAMO
DEAN E. VVOOLDRIDGE

August 1961

CONTENTS

A.

SYSTEMS ENGINEERING
Chapter 1.

1.
2.
3.
4.
5.
6.
7.
8.
9.

Chapter 2.

1-01

Systems Design
Scope of Control System Applications
1-01
Educational Requirements
1-02
Formulation of the Design Problem
1-03
System Functions
1-06
Detailed System Design
1-10
Detailed Unit Design
1-21
Unit and System Tests
1-24
1-24
Final Design
Conclusion
1-26
References
1-26

The Human Ca'mponent

2-01

1. General Comparison of"Humans and Machine
Components
2-01
2. Design Problems Specific to 'Human
Components
2-04
3. Information inputs to the Human Component
2-05
4. Control Operation
2-10
5. Human Transfer Functions
2-11
6. Practical Human Factors Design
2-13
References 2-15

B.

MANUFACTURING PROCESS CONTROL
Chapter 3.

Automatic Machines

1. Types of Processes
3-01
2. Classification of Automatic Mechanisms
3-03
3. Transporting and Positioning Mechanisms
3-04
4. Work Performing Mechanisms
3-13
5. Machine Programming
3-15
xv

3-01

CONTENTS

xvi

6. Automatic Inspection
3-22
7. Typical Examples
3-24
References
3-29

Chapter 4.

Automatic Inspection and Control
1.
2.
3.
4.

5.
6.
7.
8.

Chapter 5.

Chapter 6.

5.
6.
7.
8.

5-01

Conveyor Systems
5-01
Problems of Conveyor Controls
5-02
Multiple Drive Conveyor Requirements
5-05
Basic Electrical Controls
5-09
Conveyor Control Circuits
5-14
5-17
Synchronized Conveyor Systems
Control Systems for Synchronization
5-20
Selective Dispatching Systems
5-23
References
5-27

Numerical Control of Machines
1.
2.
3.
4.

C.

Purpose
4-01
4-01
Limitations of Human Inspector
Characteristics of Fault Statistics
4-02
Sensing Elements for Inspection
4-05
Inspection and Control System Qesign
4 ..05
Manipulation of Time Scale
4-09
Displays and Recording Systems
4-10
Electrica I Component Testing
4-11
References
4-12

Materials Handling
1.
2.
3.
4.
5.
6.
7.
8.

4-01

6-01

Types of Control Systems
6-01
Information Requirements
6-12
6-13
Numerical Codes and Their Selection
Storage Media Applicable to Numerical
Control
6-18
Incremental and Absolute Control Logic
6-19
Transducers
6-21
6-23
Servo System Considerations
Programming (Preparation of Control Tapes or
Cards)
6-28
References
6-31

CHEMICAL PROCESS CONTROL INSTRUMENTATION
Chapter 7.

Instrumentation Systems
1. Trends and Limitations in Systems Engineering
7-01
2. Control Functions
7-03
3. Pneumatic Control Systems
7-10

7-01

CONTENTS

xvii

4.
5.
6.
7.
8.

Electric and Electronic Control Systems
7-17
Hydraulic Control Systems
7-18
Pneumatic Components
7-18
Electric and Electronic Components
7-61
Self-Actuated Controllers
7-75
9.. Control Panels
7-79
References
7-81

D.

CHEMICAL PROCESS CONTROL SYSTEMS
Chapter 8.

Design Procedures .
1.
2.
3.
4.

Chapter 9.

Chapter 10.

Introduction' and Terminology
8-01
Specification of Quality Control
8-02
Operational Factors
8-02
System Desigh
8-05
References
8-20

Process Test Methods
1.
2.
3.
4.
5.
6.

6.
7.
8.
9.
10.
11.
12.

9-01

Introduction and Terminology
9-01
Tuning a Control Loop
9-02
Step Function Testing
9-03
Impulse Function Testing
9-09
Frequency Response Testing
9-11
Statistical Methods for the Measurement of Process
Dynamics
9-13
9-14
References

Single and Multiple Loop Controls
1.
2.
3.
4.
5.

8-01

Introduction and List of Symbols
10-01
Block Diagram of Single Loop Control
10-03
Reduction of Sinusoidal Deviations
10-04
Transfer Function of the Controller
10-05
Dynamic Behavior for Some Typical
10-06
Processes
Responses to Step and Constant Rate
10-17
Disturbances
Adjustment of the Controller Actions
10-20
Feed-Forward Control
10-27
Cascade Control
10-28
Use of Analytical Instruments for Process
Control
10-34
Multivariable Control Systems
10-35
Special Subjects
10-40
References
10-40

10-01

xviii

CONTENTS
Chapter 11.

1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
Chapter 12.

E.

12-01

Introduction
12·01
Application Considerations
Design Procedures
12·04
Examples
12·07
Special Purpose Computer
Future Systems
12·09
References
12·09

12·03

12·07

13·01

Computer Control .

1.
2.
3.
4.
5.
6.
7.
Chapter 14.

Introduction
11·01
11-02
Nonlinearities in Measurement Instruments
Nonlinearitles in the Process
11·06
Nonlinearlties in Control Equipment
11·09
Nonlinear Control Devices
11·11
Classification of Process Nonlinearities
11·12
Effects and Treatment of Nonlinearities
11·15
Adjustment of Controller Constants
11·16
Use of Local Feedback Loops
11-25
Compensation for Nonlinearities
11-26
References
11·28

Sampled.Data Control

1.
2.
3.
4.
5.
6.
Chapter 13.

11·01

Nonlinearities

The Trend to Computer Control
13·01
Control Based on Computed Functions
13·03
Optimizing Control
13·04
Analytical Methods of System Optimization
13·06
Direct Methods of Optimizing Control
13·10
Optimizing by Computer Control
13·16
Applications of Computer Control
13·17
References
13·29

Data Processing
1. Introduction
14·01
2. Monitors and Data Logging Equipment
14·08
3. Process Control Computer Equipment
14·13
4. Planning for Computer Control
14·17
References
14·22

14·01

INDUSTRIAL CONTROL SYSTEMS
Chapter 15.

15·01

Transmission Systems

1.
2.
3.
4.

Introduction
15·01
Information
15·04
Transmission Systems
15·09
FM Demodulation and System Errors

15·27

xix

CONTENTS
5. AM Detection and System Errors
6. Pulse Transmission
15-69
References
15-89
Chapter 16.

15-49

Nuclear Reactor Control

l6-01

1. Introduction
16-01
2. Reactor Control System Requirements
16-05
3. The Reactor as a Servomechanism Component
16-07
4. Power Level Automatic Control
16-21
5. Example of the Design of a Reactor Automatic
Control Loop
16-24
References
16-29
Chapter 17.

Control of Interconnected Power Systems .
1.
2.
3.
4.
5.
6.
7.
8.
9.

F.

Introduction and Scope
17-01
Interconnected Power Systems
17-03
The Generation Control Problem
17-08
System Governing
17-17
Supplementary Regulation
17-24
Area Regulation
17-29
Regulation as a Function of Bias Setting
Economy Dispatch
17-64
Control Executions
17-103
References
17-124

17-01

17-50

COMPONENT SELECTION
Chapter 18.

Basic Principles

18-01

1. Objectives
18-01
2. General Requirements
18-03
3. Performance Factors and Definitions
Chapter 19.

Reliability
1.
2.
3.
4.

Chapter 20.

18-05

Importance
19-01
Failures
19-02
Redundancy
19-06
Reliability Prediction
References
19-16

19-01

19-12

Measuring Elements and Sensors
1.
2.
3.
4.
5.

Introduction
20-01
System Requirements
20-02
Transducer Characteristics
20-02
Displacement Measurement
20-05
Pressure and Force Measurement
20-12

20-01

CONTENTS

xx
6.
7.
8.
9.
10.
11.

Chapter 21.

Amplifiers
l.
2.
3.
4.
5.
6.
7.

Chapter 22.

Chapter 24.

23-01

Introduction
23-01
Adders
23-02
Integrators and Differentiators
23-05
Multipliers and Dividers
23-05
References
23-15

Continuous End Point Analyzers .
1.
2.
3.
4.
5.
6.
7.
8.
9.

22-01

Introduction
22-01
Actuator Specifications
22-04
Actuator Measure'!1ents
22-12
Selecting Actuators
22-17
Electric Actuators . 22-27
Fluid Actuators
22-31
Mechanical Actuators
22-46
References
22-55

Computing Elements
1.
2.
3.
4.

21-01

Introduction and Definitions
21-01
General Properties
21-02
Modulators and Demodulators
21-13
Electronic Amplifiers
21-23
Electromechanical Amplifiers
21-41
Rotary Amplifiers
21-45
Pneumatic and Hydraulic Amplifiers
21-47
21-49
References

Actuators
1.
2.
3.
4.
5.
6.
7.

Chapter 23.

Speed Measurement
20-17
Acceleration Measu rement
20-18
Flow Measurement
20-19
Liquid Level Measurement
20-23
20-24
Temperature Measurement
Nuclear Radiation Measurement
20-25
References
20-27

Introduction
24-01
Optical Analyzer~
24-02
Mass Spectrometer Analyzers
24-17
Gas Chromatography Analyzers
24-26
Specialized Analy:z;ers
24-28
Viscosimeters
24-40
Thermal Conductivity Analyzers
24-43
Dielectric Constant Analyzer
24-45
Vapor Pressure Analyzers
24-46
References
24-48

24-01

CONTENTS
G.

xxi

DESIGN OF COMPONENTS
Chapter 25.

1.
2.
3.
4.
5.
Chapter 26.

Introduction
26-01
Principles of Operation of Semiconductors
26-02
Diode Characteristics
26-16
Amplification by Semiconductor Diodes
26-26
Transistor Characteristics
26-30
Transistor Types
26-43
References
26-64

Basic. Circuit Considerations and Symbols
Temperature Effects and Bias Stabilization
Low-Frequency Amplifiers
27-23
High-Frequency Amplifiers
27-42
D-C Amplifiers
27-56
Oscillators, Modulators, Mixers, Detectors
Switching Circuits
27-71
Power Supplies
27-97
References
27-104

Gyroscopes

1.
2.
3.
4.
5.
6.

INDEX

26-01

27-01

Transistor Circuits .

1.
2.
3.
4.
5.
6.
7.
8.

Chapter 28.

Introduction
25-01
Magnetic Amplifier Fundamentals
25-02
Magnetic Amplifier Components
25-12
Magnetic Amplifier Design
25-19
Commonly Used Circuits
25-28
References
25-39

Semiconductor Devices

1.
2.
3.
4.
5.
6.
Chapter 27.

25-01

Magnetic Amplifiers

Introduction
28-01
General Dynamic Principles
28-02
Types of Gyroscopes
28-05
Design Characteristics
28-15
Gyroscope Applications
28-22
Gyroscope Testing
28-35
References
28-40

27-01
27-15

27-61

28-01

SYSTEMS ENGINEERING

A.

SYSTEMS ENGINEERING
1. Systems Design, by M. E. Connelly
2. The Human Component, by J. Lyman and L. J. Fogel

A

SYSTEMS ENGINEERING

Chapter

1

ISystems Design
M. E. Connelly

1. Scope of Control System Applications
2. Educational Requirements
3. Formulation of the Design Problem
4. System Functions
5. Detailed System Design
6. Detailed Unit Design
7. Unit and System Tests
8. Final Design
9. Conclusion
References

1.01,
1·02
1·03
1·06
1·10
1·21
1·24
1·24
1·26
1·27

1. SCOPE OF CONTROL SYSTEM APPLICATIONS

A control system is defined as an integrated complex of devices that
governs or regulates a process or an operation. In many cases, it is difficult to delineate sharply between the system being controlled and the
control system. Often the two are so interdependent that they must be
designed as a composite unit, in which case the,distinction becomes academic. Control systems mayor may not require human participation.
In addition, they mayor may not be responsive to the state of the process
or operation under control.
.
The scope of control system applications is extremely diversified and is
expanding rapidly as more industrie/:l become aware of the possibilities
of control techniques. These possibilitief3 may be listed briefly as follows:
Reduction in manpower required.
Greater production capacity.
1·01

SYSTEMS ENGINEERING

1-02

Increased production flexibility.
Lower production costs, higher efficiency.
Improved quality control, product standardization.
Shorter lead times, inventory reduction.
Safety.
Elimination of monotonous human operations.
Improved performance: power amplification, fast response, accuracy, rapid
coordination of multiple factors.
Operation under adverse conditions.
Increased equipment utilization.
Easier production control.

In some applications, such as the control and guidance of high-speed
missiles, there is no alternative to the use of automatic devices if the required performance is to be achieved. When faced by a multiplicity of
operations or the need for rapid response, human operators simply do
not measure up to the task. In other cases, operations or processes
have been automatized because it was the most satisfactory or the most
efficient way to achieve a given result. The introduction of control techniques has in some measure freed production from the limitations of the
human operator and has opened new possibilities for product and process
simplification.
To indicate the wide variety of fields in which control systems are being
utilized, Table 1 lists a few representative applications. Several complex
systems are treated in detail in the chapters that follow (Refs. 1 to 9).
1. REPRESENTATIVE CONTROL SYSTEM ApPLICATIONS
Automatic Machines. Numerically controlled milling machines, automatic electronic assembly lines, self-regulated rolling mills, engine block production lines,
program-controlled lathes, automatic inspection and quality control devices, material-handling automata, packaging and bottling machines
Communications. Dial telephone systems, test range communications
Transportation. Automatic railroad freight-sorting yards, pipeline controls,
power distribution control, air traffic control systems, autopilot and landing
devices, navigation aids, ship stabilizers
Process Control. Chemical plants, nuclear controls, petroleum refineries, distilleries
Military. 'Fire-control systems (airborne, shipboard, and ground-based), missile
stabilization and guidance, air defense control systems, training simulators
Research and Development. Diffraction grating rulers, x-ray positioners, ironlung regulators, synthetic human organs (heart, kidney), automatic spectrometers
TABLE

2. EDUCATIONAL REQUIREMENTS

In order to cope with the control system problems that arise in such
fields as those listed in Table 1, the system designer must master avariety
of skills. Since it involves the techniques of a number of the engineering

SYSTEMS DESIGN

1-03

and scientific disciplines, control system design demands a broad understanding of basic physical principles and a thorough working knowledge
of practical components. To emphasize this requirement, a list of representative topics that might be included in the training of system designers
is presented in Table 2. The breadth of these studies and the extensive
TABLE

2.

REPRESENTATIVE BACKGROUND FOR CONTROL SYSTEM DESIGN

Mathematics
Vector analysis
Laplace transform and Fourier
analysis
Functions of a complex variable
Differential and integral equations
Probability and statistics
Numerical analysis
Advanced algebra
Information theory
Operations research and game
theory

Basic Science
Classical and statistical mechanics
Thermodynamics and heat
Optics
Electromagnetic theory
Atomic, molecular, and nuclear
physics
Geophysics
Astrophysics
Acoustics

Engineering
Circuit theory and network
synthesis
Applied electronics
Feedback control
Energy conversion
Hydraulics
Pneumatics
Principles of radar
Machine design
Chemical engineering
Measurement and instrumentation
Switching circuits
Digital computing techniques
Analog computing techniques
Pulse circuits
Nonlinear mechanics
Aerodynamics
Metallurgy
Hea t engineering
Solid state devices

scope of control system applications illustrate that, in order to do even a
very little in the field, one must know a great deal. Moreover, this strong
academic background must be supplemented by a high degree of practical,
mechanical ability.
In general, however, each control system problem is unique and the
background demanded of the designer varies accordingly. It is hardly
likely that anyone control engineer is expert on all the subjects listed in
Table 2.
3. FORMULATION OF THE DESIGN PROBLEM

Design procedures for control systems vary from problem to problem
and any suggested approach, such as the one that follows, can be treated
only as a rough guide that must be modified to suit specific control situations. Procedural patterns in control work recur frequently enough,
however, to warrant the presentation of a generalized design procedure.
Problem Definition. The first task facing the designer is to define
his problem precisely or even to perceive that a problem exists. The

1-04

SYSTEMS ENGINEERING

statement of the problem may be specific or may be so indeterminate
that it can be expressed only in statistical terms. For example, the problem might be to perform a fixed set of operations, as in a bottling machine,
or to maintain a sequence of specified conditions, as in a chemical process.
Other control systems are called u:pon to adapt themselves to a variety
of changing circumstances, in which case the statement of the problem involves the determination of the range of these conditions. In many cases,
future, as well as present, requirements must be specified. The planning
of military systems is extremely difficult in this respect in that every
weapons system requires an estimate of what the enemy capabilities will
be several years in the future. The problem, in this case, is a matter of
speculation.
Most nonmilitary control problems can be formulated with some degree
of precision, although even here it is not uncommon for design specifica.tions to be based on estimated requirements. The capacity of an automat~c freightyard, for example, would depend on the railroad's expected
future traffic situation.
Typical of the data that the designer tries to establish at the outset are
inputs, outputs, overall performance requirements, environment, economic
factors, and time schedules. These are the basic ingredients of the
problem.
Operations Research. The relatively new discipline of operations
research can be used to advantage at this stage of the planning, particularly in translating a. vague, functional requirement into quantitative
terms. As an illustration, in designing an air traffic control system for a
metropolitan area one would naturally have to specify the capacity of the
system (see Ref. 1). From aircraft manufacturing data, Federal Aviation
Agency route plans, military and airline traffic estimates, and from current airport operational ~ata, an estimate could be made of the future
traffic situation. If the expected average rate of aircraft arrivals to the
area is QA, and the average rate at which the airport facilities can land
plan·es is QL, it is possible to compute the probability Pn that n aircraft will
be waiting to land when servicing has reached an equilibrium. By the
queueing theory of operations research (see Vol. 1, Chap. 15, Operations
Research, Sect. 5, Waiting Time Models)
(1)

The mean number of planes waiting to land will be
(2)

~=

:t nP
n=O

n

=

QA/QL
•
1 - (QA/QL)

SYSTEMS DESIGN

1-05

Figure 1 shows the variation of the mean number of planes waiting
to land, W, with the ratio Q~t!QL. Before undertaking such an analysis,
one might intuitively assume that a landing capacity QL equal to the
average rate of arrival Q"l would be adequate. However, from Fig. 1 it
is clear that a much greater landing capacity is required to prevent the
incoming traffic from saturating the system. In cases such as this, a
quantitative analysis can often rescue the intuition from major blunders.
Unfortunately, the converse is occasionally true. A poorly conceived
analysis may also lead common sense astray.
Mean
number 8
of

aircraft
waiting 6
to land

1

4

W

2

QA

_

QL

-

Avg. arrival rate
Avg.landing rate -

FIG. 1. Queued aircraft as a function of the ratio of arrival rate to landing capacity.

Setting Limits. In formulating a problem, care must be exercised to
avoid expanding it beyond its efficient limits. In lieu of a thorough study
of the real requirements for a system, there is also. a temptation to set
excessively stringent specifications in the hope that all possible contingencies will be adequately covered. On the other hand, a more serious
error is to understate the problem. Similarly, the partial treatment of a
problem often has only limited usefulness. For example, the design of a
traffic control system to coordinate the arrival of 200 aircraft into an
area per hour would be of little use if a landing system having a capacity
of 20 planes per hour were r~tained .. These two problems must be treated
as an integrated whole. In fact, the modern emphasis on the overall systems approach to complex problems originated in the proven inadequacy
of piecemeal attacks.
Importance. It would be difficult to overemphasize the importance of
a well-conceived statement of the problem in control system design.
Often this statement more or less completely determines the nature of the
design, the cost, and the ultimate effectiveness of the system. In many

SYSTEMS ENGINEERING

1-06

cases, additional effort spent on this initial planning can prevent a control
system from being stillborn.
4. SYSTEM FUNCTIONS
Simple Sequence Control. Having defined the problem, the designer
next outlines the operations necessary to cope with it. In some applications, where the problem might consist simply of a sequence of functions
to be performed, these two steps are closely related.
EXAMPLE. A typical functional sequence can be listed for the automatic
machine tool shown in Fig. 2. This machine automatically loads, rough

FIG. 2. Rough boring unit for engine blocks.

(Courtesy T. C. Cameron, Sundstrand
Machine Tool Co.)

bores, chamfers, transfers, and unloads engine blocks. At the same time
it performs the auxiliary functions of lubrication and chip removal. The
functional cycle is as follows:
1.
2.
3.
. 4.

The transfer bar lowers to engage work. .
The transfer bar advances and moves each part to the next station.
The locating pins in each fixture rise .
The clamps lower to secure the part.

1-07

SYSTEMS DESIGN

5. The transfer bar raises, then returns; simultaneously all heads start
rapid approach.
6. Heads feed individually.
7. Heads return rapidly individually.
8. The locating pins drop, and the clamps rise.
9. The cycle is repeated if a new part is available and the finished
part has been removed from the unload station.
A system of limit switches, solenoid valves, clamps, locating pins, and
transfer devices positions the engine blocks in sequence and actuates the
feed and withdrawal of the machine heads. A limit switch is required at
the .end of each motion and at any point in the cycle where a machine
member stops, starts, or changes rate. From the time sequence of these
functions, the designer can draw up a cycle diagram showing the order in
which the operations take place. Figure 3 illustrates such a diagram for
the rough bore machine (see Ref. 6).
Control Logic. Although the rough bore cycle can be interrupted by
malfunctions or by manual intervention, this machine generally illustrates
a large class of special purpose control systems for which the operation is
a simple sequence of specified steps. The logic controlling such machines
can be considerably more complex than the elementary example just cited,
and operations based on position, time, and arbitrary combinations of
conditions can be instrumented by using switching circuits. Control systems can even be designed with the ability to choose between alternate
modes of operation depending on the circuplstances. In Boolean notation, one can express a typical decision as follows. (See Vol. 2, Chap. 17.)
(3)

(A

+ B)·C = D,

(4)

(A

+ B)·a

= E.

In words, these equations state that if condition A or condition B exists
and if condition C also exists, then response D will be activated. However, if condition A or condition B exists and condition C does not exist,
then response E will be activated. The switching circuit for implementing this decision is shown in Fig. 4. vVhen complex logical nets are built
up using basic and-or elements, these switching circuits can often be
greatly simplified by algebraic manipulation of the Boolean equations.
(See Vol. 2, Chap. 17 for a table of Boolean equivalences.) To illustrate
this point, note the simplification of the following Boolean equation.
(5)

AB

+ AB

= A(B

+ B)

= A.

The corresponding switching circuits are also shown in Fig. 4.
Programmed Control. lVlore flexible control systems than the fixed

Station 1

Station 3

Station 2
lS-9

lS-Sl
Station loaded

lS-23

lS-16
SV_16]
SV-18 Head

SV-9I Head
SV-ll
lS-lO

SV-231
SV-25 Head

lS-17
SV-lO
SV-ll

I
SV- 9 1

SV-16

I
1

I

SV-30]
SV-32 Head

lS-30

SV_37]
SV-39 Head

Station 8

Station 7
lS-37

SV-24
SV-2S

I

SV-23 I

lS-52
Station loaded

SV-38
lS- 38 1
SV-39 lS-47 I
SV-37 I
SV-46 I
SV-40 lS-391
SV-49 lS-48 I
lS-41 _~..J
lS-50 _~...J ....
Chamfer)tool
Chamfer)otool
SV-41
lS-40 SV-50

I

I

lS-ll ~

I
lS-181

lS-251

lS-32 I

.J

I

I

I

SV-47
SV-48

SV-31
SV-32

I

SV-30 I

6

00

lS-46

SV_46!
SV-48 Head

lS-31

lS-24
SV-17
SV-18

Station 6

Station 5

Station 4

~S ... 49

(J)

-<
VI
~

m
~

13
lSSV-12

SV-51l~ling

Clamp

l'

Clamp
SV-21 lS-22

Clamp
SV-14 lS-lS

Clamp
SV-7 lS-8
lS-6
)
pms
lS-7 SV-8

lS-20 - + - SV-19

lS-14 SV-lS
locating
pins

Unc1!mp

t

SV-13
lS-12

t

Clamp
SV-35 lS-36

Clamp
SV-28 lS-29

lS-2}
SV-26

1'

34
lSSV-33
.

,

VI

Clamp
SV-44 lS-45

43
LSSV-42

m

Z

C->

Q

Z
m
m

lS-21 SV-22

Unc~mp

lS-28 SV-29

t

SV-20
lS-19

Unc~mp

t

SV-27
lS-26

lS-3S SV-36

Unc1~mp

t

SV-34
lS-33

lS-44 SV-45

Uncla~p

t

SV-43
lS-42

Unclamp
Starting position
- - Rapid traverse
--- Feed
lS limit switch operating where shown in cycle
SV Solenoid valve energized to cause motion shown
o

FIG. 3.

lS-3
SV-l
lS-2

t

SV-4"
40

Transfer cycle

»

SV-3

Cycle diagram showing machine sequence controls.

t

lS-l
SV-2
lS-4

(Courtesy T. C. Cameron, Sundstrand Machine Tool Company.)

;:c

Z
Q

1-09

SYSTEMS DESIGN
Supply
voltage

n
Relay
coil

(A +B)·C=D
(A+B).C=E
E
Relay
coil

Is equivalent to

A

FIG. 4. Simple switching logic circuits.

logic machines just discussed are possible if the sequence of operations is
controlled by a program of instructions which can be read or set into the
system. In these cases, the system must be designed to accommodate a
range of instructions and performance requirements. By simply revising
the program, one can change the functions of the system.
Continuous Control. In contrast to the fixed logic and programmed
control systems above, there is a more sophisticated class of controls
that continuously and automatically adjust themselves to the state of the
process or operation being controlled. Process controls in which the
state of the process is monitored and in which these data are used to regulate the· operations of the process are typical of this class. An autopilot
that must stabilize the orientation of an aircraft in space under such conditions as atmospheric turbulence is a second illustration. In this case,
the autopilot function is to detect deviations of the aircraft heading and
orientation from the desired state and to actuate the control surfaces of the
aircraft so as to reduce this deviation to zero.
In the process industry, the basic functions have been classified, and
Table 3 lists these so-called unit operations and unit processes. It is
common practice to exercise control over each of these operations individually, rather than attempt the integrated control of multiple functions.
See Chap. 3, Automatic Machines; Chap. 7, Instrumentation Systems;
and Chap. 10, Single and Multiple Loop Controls.

1-10

SYSTEMS ENGINEERING
TABLE

3.

UNIT FUNCTIONS IN PROCESS CONTROL

Combustion
Oxidation
Neutralization
Silicate formation
Causticization
Electrolysis
Double decomposition
Calcina tion
Dehydration
Nitration
Fluid flow
Heat transmission
Evaporation
Distillation and
sublimation
Gas absorption

Esterifica tion
Reduction
Ammonolysis
Halogenation
SuI phonation
Hydrolysis
Alkylation
Friedel-Crafts
Condensation
Humidification and
cooling
Drying
Adsorption
Solvent extraction and
dialysis
Polymeriza tion

(Ref. 7)

Diazotiza tion and
coupling
Fermentation
Pyrolysis (cracking)
Aroma tiza tion
Isomeriza tion
Acylation
Oxo reaction
Mechanical separatIOn
Size reduction
Size enlargement
Mixing
High-pressure
techniques
Movement and storage
of materials

Criteria for Control. In the design of many complex control systems,
the desired functioning of the system may not be at all obvious. In the
case of the air traffic control problem previously cited, for example, the
designer must decide what the most efficient sequence of functions would
be, let us say, to maximize the rate of landing aircraft. Confronted by a
problem of this complexity, intuition alone is usually inadequate, and recourse to the formal mathematical techniques of operations research may
be necessary. The mathematical model here would have to consider incoming and outgoing routes, altitudes, aircraft speeds and endurance,
local geographic features, Federal Aviation Agency regulations, and
waiting procedures, all under a variety of weather and traffic conditions.
A single functional sequence would be inadequate under such circumstances, and the control system would have to be capable of several alternate modes depending on the situation.
In every case, stating the functional requirements for a system implies a quantitative specification of how well these functions must be performed. These functional specifications are the basis for the unit and
component specifications to be established later in the design.
5. DETAILED SYSTEM DESIGN

System Block Diagram

Having established what the control system is to do, the designer next
translates this concept into a system block diagram. This is essentially
the creative stage in the history of the design. There are innumerable
ways to solve a given control system problem, and the designer must de-

SYSTEMS DESIGN

1-11

cidc which of these approaches seems to offer the simplest means of
achieving the required performance. There is an element of truth in the
statement that almost any result can be achieved by the brute force deployment of hardware, hence to some extent the success of the designer
can be measured by the relative simplicity of his design. Practically,
from the point of view of reliability alone, an unnecessarily complex system often defeats its own purpose.
Block diagrams exist at various levels of detail. They can be used to
divide the functions of the system into logical subsidiary operations, to
indicate the flow of information throughout the system, or to represent the
system dynamics schematically. A typical preliminary system block diagram for the numerically controlled milling machine developed at the
Massachusetts Institute of Technology is shown in Fig. 5 (see Ref. 8).
Other block diagrams are presented throughout this volume.
The system block diagram is normally in a state of constant evolution
and becomes more detailed and specific as the unit designs develop. Each
diagram incorporates a host of major engineering decisions, particularly
with respect to the alternative techniques for performing various operations.
System Simplifications. In addition to specifying the essential features of the design, the system block diagram reduces a single, large problem to a set of simpler unit problems, each of which can be assigned to
an individual or group for solution. In this fashion, the detailed design
of the various units can proceed in parallel, and the design responsibility
can be shared by a number of engineers. The interrelation between these
units and the setting of unit design criteria consistent with the overall
system specifications remain the responsibility of the systems designer.
Design Decisions. In the selection of the key techniques and components for the system, the designer had best have on hand what can
only be described as an ample bag of tricks. A file of catalogues of commercial equipment and a library of technical books and journals constitute only part of the requirement. There is no substitute for ingenuity
and actual experience with the techniques for performing a multitude of
operations (see Ref. 9). Typical decisions that might be made at this
stage of the system design are listed in Table 4.
Economics. Generally speaking, all control systems must pay their
own way, that is to say, the benefits must be worth the cost. Even military systems must demonstrate that they produce more offensive or defensive capability per dollar spent than alternative systems. Normally,
these economic factors are considered before a design is initiated, but
quantitative data on the system are usually sketchy at the beginning, and
a reevaluation of the system concept and the economic factors is often

Checking~i~~s________ ~--,
- - - - - '"

('
I

,

~-------<

-+

Central control

I

I--("')

en

!!!.

lit

0tI;:!.
:J ,

0(')
;00;(')

0
.-+

~~ :J

en 0

"0

a

iii"

qIl)

::I

en

(')

':J

en

Ol(')
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a.;:l. Ol
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('):J
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ct2.

3' ?"
~ OtI"O

"0

16

!!!.C

c:: 0tIiii"
iii" :JCD
CD Olen
en iii"

Clock system

!!!.

!!!. ~

a.0tI Ol
Ol:J :J
.-+Ol a.
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0

3
3Ol

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1[lOtI
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C

iii"
CD
en

I~

Iiii"
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Control register
pulses
r

-1

("')

ig

Automatic
data supply
system

Manual data
supply system

~

r---

~

3
3
nl

:J

a.

"0

C

Checking signals
I
I

I
I

!

y Axis
Pulse-code-to-analog
servomechanism

iii"
CD
en

y Axis
Machine drive
servomechanism

Synchro
data

(J')

-I

Relative
cutter
position

I

m

Z

m

~

Z
Q

Checking signals

I

I
I

I

z Axis
Pulse-code:..to-analog
servomechanism

(J')

zm

_----,-------- -------,

~

m
~

9

L

I
I
....

(J')

-<

I

I
I

I

Machine drive
servomechanism

Relative
cutter
position

---~-~------- ----~-,

I
0

x Axis
,.

Retract signal

J

I
/...

Command
~ulses;
("')

Synchro
data

i

I
I

I

I

I\,)

I

x Axis
Pulse-code-to-analog
servomechanism

I

.....

I

I

Synchro
data

z Axis
Machine drive
servomechanism

t
Synchronizing pulses
-

FIG. 5. Numerically controlled milling _machine-simplified block diagram.

Relative
cutter
position

SYSTEMS DESIGN
TABLE

4.

1-13

REPRESENTATIVE DESIGN DECISIONS

System Type.
Manual
Analog

Automatic
Digi tal
Continuous data
Sampled data
Continuous control
Discontinuous
Fixed function
Adjustable function
60 cps
400 cps

Semiautomatic
Analog-digi tal
control
Programmed
dc

Data Representation. Voltage, phase, frequency, current, charge, magnetic state,
pulses, visual indication, aural indication, count, time interval, impedance, force,
torque, density, radioactivity, volume, deformation, flow, electromagnetic intensity, pressure, temperature, displacement, velocity, acceleration, angular rotation,
angular velocity, angular acceleration, relay state
Power levels, impedance levels, scale and conversion factors
Components.
Electromechanical devices
Electronic devices
Mechanical devices
Pneumatic devices
Hydraulic devices
Electrical devices
Regular, miniature, sub-miniature tubes, transistors, magnetic circuits
Transducers
Analog-digital converters
Indicators
System plate, filament, bias, and reference power supplies
Input-Output Devices. Manual, typewriter, plugboard, punched tape, magnetic
tape, punched cards, film, models, magnetic drums, cathode ray tubes, meters,
neon tubes
Digital Computer Design. Memory capacity, access time and type, serial or parallel,
synchronous or asynchronous, radix, word length, fixed point or floating point,
single address or multiple address, coding, operating speeds, standard program
orders, number range, marginal checking, parity checks
Formulation of Dynamic Equations. Mathematical model, choice of variables, axis
system, approximations.
Optimum filtering in the presence of noise
System Configuration (example for fire-control system). On or off carriage, gun-drive
or antenna-drive tracking, gun-line or tracking-line computation, rectangular or
polar coordinates, stabilized or nonstabilized platform
Grounding and shielding system, cable and connector diagrams, fuses and circuit breakers, clock frequencies, carrier and modulation frequencies, pulse repetition rates, compatibility with existing systems, malfunction detectors, space,
weight, power allowances, pulse timing sequences and waveforms, optimum coding, specifications of realistic unit design criteria
Communications. Messages, data, remote control
Process Control Design. Batch or continuous production, yield, flow diagrams,
material and energy balance, quality control, specifications, disturbances (type,
ldcation, magnitude), choice and location of measurement devices and controllers,
choice of measured and controlled conditions, waste disposal, corrosion protection,
transfer lags, buffer storage requirements, ambient conditions, starting and shutdown procedures, process monitors, economic factors, requirements for fuel, power,
wa ter, and raw materials
General. Schedules, personnel, deliveries, costs, reports, contracts

1-14

SYSTEMS ENGINEERING

in order after the initial systems design has been completed. At this
stage, estimates of cost, performance, manpower requirements, and depreciation have considerably more authority than estimates made at the
outset of the design.
This is the proper time also, before extensive development has started,
to decide which features of the design are worthwhile and which are
superfluous. In addition, the basic compromises that must be made are
more apparent when the initial system design is available. One desired
requirement, say high accuracy, may have to be traded off against another requirement, such as fast response. Cost, maintenance, and manpower requirements are constraints that affect every system feature. To
illustrate a typical compromise of engineering economics, one can consider
a process for which the yield increases with operating temperature, but so
does the rate of deposit formation. The designer must decide whether the
plant should be designed for high yield and short life, or lower yield and
longer life.
Dynamic Analysis

When the principal units of a system have been chosen and their characteristics established, it is then possible to carry out a dynamic analysis
of the system. Frequently major components are fixed beforehand, and
the remaining components must be selected for compatibility. In many
cases, the dynamic idiosyncrasies of the fixed elements must be compensated for in the characteristics of the auxiliary equipment. For example,
the aircraft to be used with a given autopilot design may be specified,
consequently the autopilot parameters must be adapted to the dynamics
of this specific aircraft. Achieving satisfactory system dynamics is difficult enough, but when the principal dynamic element is fixed, as it is in
the case of the autopilot-aircraft combination, a high degree of analytical
skill is required.
Dynamic Block Diagrams. In dynamic analysis, a form of the system
block diagram that exhibits the dynamic features of the system is very
helpful. Such a diagram for the lateral autopilot of an airplane is shown
in Fig. 6. Note that the transfer function of each dynamic element has
been expressed in Laplace transform notation. Usually it is necessary
to write the integro-differential equations describing an operation or
process and to convert these equations into transfer functions for use in
the block diagram.
To complete the illustration of the autopilot system, the differential
equations describing the lateral motion of the aircraft itself are necessary.
For small perturbations about a level, steady-state flight condition, these
can be written as follows (see Ref. 10).

SYSTEMS DESIGN

(0)

1-15

Roll
pVSb 2

pV 2Sb

4Ixx

2Ixx

+ C1r--r + C1M1 - - · oR,
pV 2Sb

pV 2Sb

pVSb 2

(7) Yaw r = CnQR - - - oR + Cn {3 -21 (3 + G -1-- r
lIr

21 zz

(8)

4 zz

zz

Y force

Roll rate gyro

Control valve
k3
VJ

.~

E
co

c

>,

"0

Control valve
ka

Rudder
actuator

-~

72-,+1

FIG. 6. Autopilot dynamic block diagram.

Vertical
gyro

1-16

(9)

SYSTEMS ENGINEERING

Euler heading tj; = r,

(10)

Euler roll

(11)

Sideslip

it> = p,
~ = rw - r,

where the symbols used in the equations may be defined as follows:
p = roll component of body axis angular rate,
r = yaw component of body axis angular rate,
rw = yaw wind axis component of wind axis angular rate,
V = aircraft velocity,
S = wing area,
b = wing span,
lxx, 1 zz = moments of inertia about roll and yaw axes, respectively,
p = air density,
m = aircraft mass,
{3 = sideslip angle,
oA = aileron deflection,
oR = rudder deflection,
y; = Euler heading angle (wind axes),
cp = Euler roll angle (wind axes),
C = Aerodynamic coefficients (usually nonlinear functions of one or
more variables).

The equivalent block diagram for the aircraft dynamics alone is shown
in Fig. 7. Combining Fig. 6 and Fig. 7 gives the overall system block
diagram from which it is possible to analyze the response of the system to
representative inputs under a variety of noise conditions.
Techniques for Dynamic Analysis. Several theoretical techniques
are available for the dynamic analysis of systems of moderate complexity.
The designer should be particularly familiar with the following techniques, all of which are treated in detail in Vol. 1: Nyquist plots, Bode
asymptotes, Nichols charts, root locus plots, signal flow diagrams, polezero analysis, correlation functions and spectral density, Laplace transforms, Fourier analysis, classic differential equation theory, phase plane
analysis, describing functions, and sampled data analysis using the z
transform (see Vol. 1, Part E, Feedback Control, and Ref. 11).
Simulation. For a system as complex as the autopilot-aircraft combination, hovvever, the simulation of the dynamic equations on an analog
or digital computer is the most practical approach. Although specific
and simplified characteristic modes of a system's operation might be
analyzed through hand calculations, most complete system analyses require a computing facility-the more complex the problem, the larger the
facility. Such simulation studies can be used to determine the optimum

SYSTEMS DESIGN

2

2

s

where
l:J.(s) =

-

P VSb
Clp 4Ixx s

pVSb 2
-Cnp 4I

-g

tz

S

C
-

pV 2Sb

pV 2Sb 1
l{j 2Ixx;

-C"{J pV2Sb!
'2I zz S

p 1' 2 S 1
V - Cy{J~~

Cl{J 2Ixx

C np

1-17

s

=

complex
variable

l:J.ik(S)

=

cofactor
of l:J.(s)

j

=

row

k

=

column

p YSb 2
- Cl r 4Ixx s

p V 2Sb
2J zz -

C"r

p VSb 2
,il" S

+s

2

Py 2 S

C,IJ{J

2m

FIG. 7. Block diagram for lateral dynamics of an aircraft.

to

system parameters and to indicate the need for auxiliary compensation
correct for undesirable dynamic features.
Actual system components
I
often are incorporated in the simulation setup. The techniques of simulation are treated at length in Vol. 2, Chap. 2, Programming and Coding;
Chap. 17, Logical Design; and Chap. 23, Nonlinear Electronic Computer
Elements.
Alternate Formulations of Dynanlic Equations. Not all formulations of a given dynamic problem are of equal complexity. The lateral
equations just given, for example, employ an axis system fixed to the aircraft for roll and yaw and an axis system fixed by the relative wind for y
force. Alternative formulations could be devised employing other axis
systems, but these are 'generally more complicated than the one given.
The designer should select-the axis system, the variables, and the form of
the equations that express the essential dynamic features of the system,

1-18

SYSTEMS ENGINEERING

yet offer the greatest computational simplicity. Dynamic analysis can
be a complicated business and every effort must be made at the outset to
eliminate superfluous terms. In the aircraft lateral equations, for example, it was possible to neglect cross-coupling and product of inertia
terms because motion was restricted to small perturbations. Under such
constraints, numerous trigonometric approximations may also be allowable.
Importance of Dynamic Analysis. The dynamic analysis of a system
is helpful in determining realistic design criteria for the various units
making up the system. The unit designer must know not only the inputs
and outputs of his unit, but also the allowable static and dynamic errors
under representative signal-noise conditions. In this regard a system
simulation or analysis can determine the unit dynamic response necessary
to achieve satisfactory overall performance. The situations chosen may
represent the worst cases that the system is expected to encounter, or may
represent a statistical sample of representative cases.
Process Control Dynamics. A few comments may be made at this
point concerning process control dynamics, a subject which is in a relatively primitive state because of the great difficulty in describing the unit
operations analytically. Designs are largely carried out on an empirical
basis, with past experience playing an important role. Transfer characteristics are approximated as simple lags for the most part, in lieu of more
complete knowledge of the process or plant dynamics.
Rapid measurement of certain quantities, such as the homogeneity of
a mix or the exact chemical composition of the product, may be difficult
or impossible to achieve. As a consequence, these quantities may not
only have to be measured indirectly but also controlled indirectly. Dynamically a process control system is often considered successful if it can
keep deviations within prescribed bounds for severe disturbances. The
time scale of these phenomena may be several orders of magnitude away
from that encountered in other control fields with time constants measured
in hours or even days (see Ref. 12).
System Error Study
Error Criteria. At the outset of a design, a decision must be made on
what constitutes an acceptable system error. This specification might
take the form of a probability plot such as the normal distribution shown
in Fig. 8. This error criterion implies a large statistical sample of systems
and situations.
The designer assigns an error specification to each unit of the system
such that the overall error distribution at least meets the designated
standard. Two common error distributions utilized in unit specifications

SYSTEMS DESIGN

(J'

1-19

= Standard deviation

o
FIG.

Error

f:_

8. Normal error distribution.

are the normal plot, shown in Fig. 8, and the rectangular distribution,
shown in Fig. 9 (see Ref. 1).
If the total system error can be taken as the sum of the output errors
due to each unit, the total error due to n units would be
~T

(12)

= 6

+ b + ... + ~n.

If the errors are independent, the standard deviation of the total error dis-

tribution is equal to the square root of the sum of the squares of the individual standard deviations. That is
(13)

This relation is true regardless of the nature of the individual distributions
as long as these errors are independent. For most systems, the total error
~T approaches a normal distribution having a standard deviation (J'T. The
Probability
density
(J'

tp(E)

-T

o

= Standard deviation = ~

:I
i

+T Error

FIG. 9. Rectangular error distribution.

E~

SYSTEMS ENGINEERING

1·20

standard deviation of a probability density function
value is defined by

P(~)

having a zero mean

(14)

Assignment of Errors. In assigning error specifications to subsidiary
units, the system designer is bound by two constraints:
1. The square root of the sum of the squares of the unit standard deviations must not exceed the desired standard deviation for the system error.
2. The assignment of errors must show a decent regard for what can
reasonably be achieved within the constraints of the existing state of the
art, cost, and development time. It is not facetious to state that a prime
object is to minimize the grumbling of the unit designers.
To illustrate this technique, Table 5 assigns errors to various units of a
TABLE

5.

ASSIGNMENT OF UNI'!' ERRORS IN A FIRE-CONTROL SYSTEM

Error
Tracking error
Range error, converted
to equivalent firecontrol error
Computer errors
Ballistic correction error
Servo dynamic errors
Alignment and data
transmission errors
Ammunition dispersion
Total standard deviation = [1

Distribution
Normal
Rectangular
Normal
Rectangular
Normal
Rectangular
Normal
32 22
1

Standard
Deviation, mils
1
2

3
2

1
1
2

+ 22 + + + + 1 + 22] 72 = 4.9 mils

hypothetical fire-control system whose overall error was specified to be
less than five mils standard deviation. Special care must be exercised in
deciding which errors are biases and which are random distributions.
Optimizing. For systems of moderate complexity in which noise
dominates the selection of appropriate system dynamics, analytic techniques are available for optimizing these dynamics. Generally, a mathematical statement of the expected information signal as well as the noise
input must be formulated, and an appropriate optimizing criterion, such
as the minimization of the root-me an-square error, must be selected. The
principal difficulty in such analysis is to select a correct mathematical
model for the situation and to select the optimum optimizing criterion.
N either of these steps can be described as straightforward or unambiguous
for most cases (see Ref. 11).

SYSTEMS DESIGN

1-21

Special System Problems

In the course of the detailed system design, a number of problems arise
that must be treated on a systems basis. Typical of these is the problem
of interaction between units of the system. A common source of trouble
is the effect of power or reference supply loading by one unit on the operation of other units using the same supplies. The familiar motorboating of audio amplifiers is a simple example of such interaction.
Complex SysteITIs. In a complex system, innumerable opportunities
exist for interaction. Radiation from power-level signals frequently is
picked up by associated circuits, particularly if impedance levels are
high. The manner in which units are interconnected is also a major design problem. Long connecting leads can introduce phase shift, time delays, pickup, and ohmic loss if care is not exercised by providing low impedance driving sources and adequate shielding. Mechanical defiectiOlis
and vibrations caused by one part of a system can adversely affect the
performance of other units, as in the case of tube microphonic effects.
Grounding System. In many control systems, the haphazard design
of the grounding system and failure to pay attention to the ordinary
decencies of shielding and circuit location have led to interminable difficulties. Several common errors are:
1.
2.
3.
4.
5.
6.

Use of a common ground buss for power, plate supply, and signals.
Indiscriminate use of the chassis as a ground.
Insufficient or indiscriminate shielding.
Creation of ground loops.
Poor location of circuits.
Inattention to impedance levels.

Figure 10 illustrates some of these faults in practice.
6. DETAILED UNIT DESIGN

Specifications. The unit designer must translate the specifications for
his unit into a practical piece of equipment. The form of these specifications may be such that they have to be converted to more usable parameters like bandwidth, velocity constant, damping ratio, maximum slewing
rate, and maximum torque before the actual design can proceed. A careful study of the accuracy requirements placed on the unit is also important at the outset, for these will affect the choice of components.
Practical Problems.
The basic theories of feedback control 'and
digital design have been treated in Vol. 1 and Vol. 2, and no repetition of
this material is necessary here. However, a few of the practical problems
of unit design can be discussed with advantage at this point.
The first step in unit design is customarily the formulation of a ~lock

1-22

SYSTEMS ENGINEERING

GServo
motor

'------- - - -

---~>----------'

(a)

'V

Signal
Signal ground
Tied to chassis
or bus
Induced voltage

= d/dt

(b)

Adjacent E
signal
1

Zs
Coupled
El (Xc + Zs) nOise
voltage

(c)

Shielding capacitance
to signal lead (Xc)

(d)

FIG. 10. Common interconnection problems: (a) common ground, (b) ground loop,
(c) high-impedance levels, (d) phase shift introduced by shielding.

SYSTEMS DESIGN

1-23

diagram indicating the basic techniques by which the operation is to be
performed. Next, the principal components such as transducers, servo
motors, and power devices are selected. This choice usually involves a
thorough survey of commercially available components of the desired
type and even comparative testing of these components in the laboratory.
It is important to choose these major items early in the design because
extensive delivery delays are possible.
In many respects, the procedure for unit design corresponds to that
for system design on a smaller scale (see Ref. 13). A representative list of
problems that must be considered by the unit designer is presented in
Table 6.
TABLE

6.

REPHESEN'l'A'l'IVE UNIT DESIGN PROBLEMS

Amplifier Design. Saturation levels, gain, feedback, stability, power and voltage
levels, phase, tube and transistor selection, impedance levels, coupling, drift,
quadrature rejection, automatic gain control, noise, balancing, magnetic circuit
design, decoupling
Choice of servo motors, tachometers, potentiometers, synchros, gyroscopes,
transducers, resolvers, relays, choppers, valves, indicators
Synthesis of compensation networks and filters
Unit ground system and shielding

Power Supply Requirements.

Capacity, regulation, ripple

Sta'tic and dynamic analysis

No1tlinearity Effects. Backlash, coulomb friction, potentiometer wire stepping,
stiction, hysteresi~, cogging, saturation, potentiometer loading, motor characteristics
Design of Mechanical Assemblies and Automata.
supervision of machine shop, inspection, assembly

Layout, detailing, checking,

Pulse Circuit Design. Multivibrators, flip-flops, blocking oscillators, delay
circuits, gates, pulse shapers, comparators, counters, diode logical circuits, boxcar
generators, sweep circuits, frequency dividers, sampling circuits
Selection of Motors and Transmissions. Single-phase, two-phase, three-phase,
dc, series, shunt, compound, armature-controlled, field-controlled, induction, synchronous, Ward-Leonard, amplidyne, rototrol, hydraulic, pneumatic
Switching circuit design
Marginal checking, test points, test instruments, alarms, panel indicators
Manual control provisions
Fusing and circuit breakers, interlocks, fail-safe devices
Design of modulators and demodulators
Noise
Hydraulic and pneumatic pressures, relief valves
Component tolerances, component tests
Unit schematics, electrical and mechanical layouts, parts lists, reports

1-24

SYSTEMS ENGINEERING

7. UNIT AND SYSTEM TESTS

Every experienced engineer is acquainted with the utter perversity of
nature. For this reason, unit and system designs are usually verified experimentally in the laboratory or in pilot plant operation before the final
system is produced. Almost inevitably, a host of shortcomings appears
in the course of these tests, many of which originate in incompatibilities
and interactions between units of the system. A deliberate attempt
should be made at this stage not only to determine the basic operating
characteristics of each unit and the system as a whole but also to subject
the equipment to a wide variety of severe conditions. A unit that gives
weak performance or a unit for which the adjustments are critical should
be redesigned. In addition, a systematic simplification of the various
units is often attempted during the breadboard tests. Generally, the
probability of successful system operation increases with a decrease in the
numher of components employed, although redundant components are
sometimes deliberately fldded with the express purpose of improving reliability.
Static and ,dynamic performance can be established during these tests,
and the system and unit parameters adjusted for optimum performance,
although in some cases optimum performance may be difficult to define.
In refinery operations, for example, a variety of crude oil types and
catalysts may be utilized, with products ranging from aviation gas and
fuel oil to wax and asphalt. The significant parameters of the process
may number in the hundreds. Specifying optimum performance for such
a system is rather difficult.
A chronic hazard in control system design is over-optimism in estimating
the time, care, and patience necessary to put even a well-designed system
into working order. In many cases, the test and evaluation of a system
is an operation comparable in magnitude to the design, and the test
facilities, as in the case of missile programs, may be far more elaborate
than.the system itself. The problems of data instrumentation and data
reduction for large-scale systems tests are extensive. A modern trend in
this regard is to employ statistical methods in the design and analysis
of test experiments (see Ref. 1).
Standard test and calibration procedures for the system can also be
evolved at this stage of the development. In the final system, built-in
test equipment tailored to these procedures can often save substantial
maintenance and checkout time.
8. FINAL DESIGN

The ~onstruction and test of a breadboard system is fundamentally intended to establish the basic soundness of the system concept. In the

SYSTEMS DESIGN

1-25

interest of expediency, the execution of such systems is generally informal.
The final unit, however, must make its way in the humid, vibrating and
fungus-laden world, consequently more sophisticated packaging is required. The final system must generally incorporate a multitude of essential virtues ranging from rustproofing to gopher shields. To indicate the
scope of the packaging problem, a partial list of such considerations is
presented in Table 7.
TABLE

7.

REPRESENTATIVE PACKAGING PROBLEMS

Military specifications (MIL specs)
Mounting, mechanical strength, vibration and resonance
Space allocation
Ventilation, lighting, heating
Ease of operation and maintenance, accessibility
Facilities for personnel
Test equipment, test points, name plates
Junction boxes, system wiring, color codes, terminal strips, connectors
Special Packaging. Mobile, airborne, underwater, explosion-proof
Graphic instrument panels (process controls)
Automatic data logging
Intercommunication circuits
Electrical outlets
Malfunction Indicators. Excess error, alarms, fuse lamps
Environment Factors. Ambient temperature, shock, humidity, altitude, attitude,
accelerations, pressure
Human engineering (matching machine to operator)
Safety
Reliability
Standardization of parts, interchangeable plug-in units, spares
Finishes, appearance
Rustproofing, fungus-proofing, weather-sealing, dustproofing
Instrumen ta tion
Noise levels and acoustics
Insulation
Lubrication
Preliminary mockups
Weight
Cost
Tolerances

vVhen completed, of course, the final system must be thoroughly
checked for performance under a variety of conditions and any new deficiencies must be corrected. The ultimate user will most likely require a
field test or demonstration of the system before acceptance, as well as
complete operating and maintenance manuals, schematics, and parts lists.
On complex systems, field service personnel may remain with the lmit

1-26

SYSTEMS ENGINEERING

for months after delivery for maintenance purposes, additional debugging,
and training of customer personnel. Some control systems are purchased
with provisions for permanent field service.
A record of system malfunctions kept during the development phase
and during the first months of system operation will aid in the design of
succeeding models by uncovering poorly designed or unreliable components. To achieve reliable operation with a large system demands
exceptional reliability from the individual components. Many of today's
control systems, such as the air defense complex, demand a degree of
reliability per operation several orders of magnitude better than that of
a dial telephone system.
The system records should also indicate the economics of the system's
operation, if possible. This involves maintenance and operating costs,
spoilage, down-time and productivity. Such a study will either demonstrate the economic virtues of the design or will warn the designer not
to make the same mistake again.
9. CONCLUSION

The advantages that result from the application of control techniques
to industrial and military problems have been summarized and the broad
scope of such applications indicated. The background required for successful control systems design has been suggested, and a generalized design procedure presented. Practical problems frequently encountered
in such designs have been listed in tabular form.
Although the control system design procedure has been presented as a
step-by-step sequence, it must be emphasized that the various stages of
design and test interact with each other in innumerable ways. Design is
itself a feedback process, and some steps may be repeated several times
before a satisfactory system results. In particular, the designer often discovers that the original realistic design criteria are unrealistic and must
be modified.
The remainder of Vol. 3 will examine specific control system designs in
detail and will present further information on components frequently employed in control work, including the ubiquitous human operator.

REFERENCES
1. H. H. Goode and R. E. Machol, Systems Engineering, McGraw-Hill, New York,
1957.
2. R. R. Everett, C. A. Zraket, and H. D. Benington, SAGE-A data processing
system for air defense, Proc. East. Jt. Camp. Can!., 148-155, Dec. 1957.

SYSTEMS DESIGN

1-27

3. E. Bloch, The engineering design of the Stretch computer, Proc. East. Jt. Compo
Con!., 48-58, Dec. 1959.
4. L. Ridenour, Radar System Engineering, MeGraw-Hill, New York, 1947.
5. H. E. Vaughn, Research model for time-separation integrated communication,
Bell System Tech. J., 38, 909-932 (1959).
6. T. C. Cameron, Four steps to practical machine tool control, Control Eng., 3,
No. 1,56-62 (1956).
7. George Brown, et al., Unit Operati()ns, Wiley, New York, 1950.
8. J. O. McDonough and A. K. Susskind, A numerically controlled milling machine,
Joint AIEE-IRE-ACM Compo Coni., 133-137, Dec. 1952.
9. J. Truxal, Control Engineers' Handbook, McGraw-Hill, New York, 1958.
10. M. Connelly, Simulation of aircraft, MIT Servomechanisms Laboratory Report 7591-R-l, Feb. 1958.
11. J. Truxal, Automatic Feedback Control System Synthesis, McGraw-Hill, New
York, 1955.
12. D. Eckman, Automatic Process Control, Wiley, New York, 1958.
13. D. T. N. Williamson, Design of a high performance amplifier, Wireless World,
53, 118-121 (April 1947); 161-163 (May 1947).
14. Educational needs in systems engineering-panel discussion, 1958 I.R.E. N ational Convention Record, Pt. 4.

A

SYSTEMS ENGINEERING

Chapter

2

The Human Component
J. Lyman and L. J. Fogel

1. General Comparison of Humans and Machine Components

2-01

2. Design Problems Specific to Human Components

2-04

3. Information Inputs to the Human Component

2-05

4. Control Operation

2-10

5. Human Transfer Functions

2-11

6. Practical Human Factors Design

2-12

2-15

References

1. GENERAL COMPARISON OF HUMANS AND MACHINE COMPONENTS

Human Operations. The unique ability which makes the human operator particularly suited to control operation as part of a servo system is
that he can program and reprogram his computation while the process is
in progress to account for transient and nonstationary characteristics in
the perceived data.
This reprogramming may be looked upon as a decision which occurs at
a particular level within a hierarchy of decisions relevant to the intended
purpose. This hierarchy can be grossly characterized as follows:

1. Decision that determines the general computation program which
will be used to process the received data so as to accomplish the intended
purpose in an optimum manner, e.g., a flight plan.
2. Decision that selects data from the information displayed in the environment.
2-01

SYSTEMS ENGINEERING

2-02

3. Decision that determines the state of the system from the perceived
inf orma tion.
4. Decision that determines the manner of control action which will
minimize some function of anticipated error.
These classifications are not mutually exclusive, but they are distinctly
ordered. They must be performed in an ordered sequence to lead to effective system control. Each decision in this sequence depends on the relationship between the human and equipment components of the task. The
nature of this relationship is shown in Fig. 1.
Measuring Unit

\
\

\
\

Correlating
Unit

\
\
~\

(9~\

~\

'1:\
\
\
\

\
\

Control Unit

FIG. 1. Human and technical links in a control cycle.

Humans and Machines. The successful operation of the total system
depends on establishing the highest possible degree of compatibility between those parts of the task under design control and the functional
properties of the human over which the designer has little influence. As
an initial step it becomes necessary for the engineer to know what some
of these properties are in terms of functions in which machines excel as
compared with those in which humans excel. He can then select the proper
part of the task for the man and avoid assigning duties to him that a machine can do better, recognizing any compromise he is making. To assist
in this process a comparison of the functions of men and machines is presented in Table 1. It should be emphasized that as technical sophistication improves, history has shown that machines can economically take
over more of the functions in which man appears to excel. Accordingly,
the designer must be constantly alert to developments that can be substituted for human functions.

THE HUMAN COMPONENT
TABLE

1.

2-03

FUNCTIONAL ADVANTAGES AND DISADVANTAGES OF MEN AND MACHINES

Data Sensing
Man

Machines

Can monitor low-probability events
for which, because of the number possible, automatic systems would not be
feasible.

Program complexity and alternatives
limited so that unexpected events cannot be adequately handled.

Under favorable conditions absolute
thresholds of sensitivity in various
modes are very low.

Generally not as low as human thresholds.

Can detect masked signals effectively
in an overlapping noise spectrum on
displays such as radar and sonar.

May not be useful when noise spectra
ovcrla p detection of signal.

Able to acquire and report information
incidental to primary activity.

Discovery and selection of incidental
intelligence not feasible in present designs.

Not subject to jamming by ordinary
methods.

Generally subject to disruption by
various interference and noise sources.

Data Processing
Little or no perceptual constancy or
ability to recognize similarity of pattern in either the spatial or temporal
domain.

Able to recognize and use the information, redundancy (pattern) of the real
world to simplify complex situations,
e.g., recognition of airport through
stages of ground contact, approach,
and landing.
Reasonable reliability in which the
same purpose can be accomplished by
different approach (corollary of reprogramming ability).

May have high reliability at increased
cost and complexity. Particularly reliable for routine repetitive functioning.

Can make inductive decisions in situations not previously encountered; can
generalize from few data.

Virtually no capacity for creative or
inductive functions.

Computation is weak and relatively inaccurate; optimal theory of games
strategy cannot be routinely expected.

Can be programmed to use optimum
strategy for high-probability situations.

Channel capacity limited to relatively
small information throughput rates.

Channel capacity can be made as large
as necessary for task.

Can handle variety of transient overloads and some permanent overloads
without disruption.

Transient and permanent overloads
may lead to disruption of system.

Short-term memory relatively poor.

Short-term memory and access times
excellent.
(continued)

2-04

SYSTEMS ENGINEERING
TABLE

1.

FUNCTIONAL ADVANTAGES AND DISADVANTAGES

OF MEN AND MACHINES-( Continued)

Data Transmitting

Man

Machines

Can tolerate only relatively low imposed forces and generate relatively
low forces for short time periods.
Generally not good at tracking though
may be satisfactory where situation requires frequent reprogramming; can
change to meet situation. Is best at
position tracking with changes under
3 radians per second.

Can withstand very large forces and
generate them for prolonged periods.

Performance may deteriorate
time; usually recovers with rest.

with

Relatively high response latency.

Good tracking characteristics may be
obtained over limited set of requirements.

Behavior decrement relatively small
with time; wear maintenance and
product quality control necessary.
Arbitrarily low response latencies
possible.

Economic Properties
Relatively inexpensive for available
complexity and in good supply; must
be trained.

Complexity and supply limited by cost
and time; performance built in.

Light in weight and small in size for
function achieved; low power requirement, less than 100 watts.

Equivalent complexity and function
would require radically heavier components and enormous power and cooling
resources.
Maintenance problem becomes disproportionately serious as complexity
increases.
Expendable and unconscious of personal existence; will perform without
distraction from problems arising outside of task.

Easy to maintain with minimum of "in
task" extras.
N onexpendable and interested in personal survival; emotional.

2. DESIGN PROBLEMS SPECIFIC TO HUMAN COMPONENTS

Once the task has been defined, it is necessary to consider the environment in detail to insure that the assignment can and will be fulfilled. The
important physical aspects are shown in Fig. 2, but the environment has
not been completely specified without th~ information .input and output
coupling to and from the man (Ref. 20). The task must be analyzed
into decisions, and assurance provided to the operator that the required
information can and will be received as it is needed. He must also have

2-05

THE HUMAN COMPONENT
Environment
Atmospheric

Thermal

~

If?
Sensory
display
Man

Machine
Motor
output

2Jfl

Visible
radiation

4>

Ionizing
radiation

,

Mechanical

FIG. 2. Environmental and machine links to the human.

efficient means for coupling his control actions to the system. Specific
hardware design problems requiring data on humans fall into the following
ca tegories :
1. Problems of the general working environment such as optimum heatmg, lighting, and ventilation in relation to human physiological parameters.
2. Problems of size, shape, and arrangement in which human characteristics limit the physical form of controls and spaces.
3. Problems of information input in "which human encoding properties
limit channel capacity in terms of speed and sensitivity of response and
the nature of the stimulating energy which can be applied to the senses.
4. Problems of motor output (including voice) in which human neuromuscular characteristics limit the static and dynamic properties of control movements and the useful power that is available.

In this presentation attention will be directed primarily to categories 3
and 4.
3. INFORMATION JNPUTS TO THE HUMAN COMPONENT

Displays and instruments are devices which enable adequate control by
virtue of the information they transmit. The operator is a channel for
processing and transmitting this information from the display to the controls. The controls are monitored by means of an information channel
from the operator to the machine. The channel capacity of the human

2-06

SYSTEMS ENGINEERING

and its optimum utilization through proper encoding of the information
to be transmitted by the human to the controls is an orienting viewpoint that aids in making appropriate design decisions.
Vision
Perceptual Capacity. Vision is the most important and widely utilized
input channel. In considering the visual acuity and physical characteristics of the human eye, it has been estimated that about 4.3 million bits
per second can be received by the retina (Ref. 16). However, this is not
perception, the usable acceptance of data. Empirical studies have revealed that the maximum amount of information which can be accepted
by a human observer when he attempts to locate a point on a straight
line (e.g., an indicator scale) is about 3 bits (Ref. 9). As the number of
coordinates is increased, there is an increase in the message carrying capacity of the stimulus, but this does not appear to be linear. Thus two
coordinates of a dot on a plane transmit about 4.4 bits and the eight
coordinates of one-to-four dots on a plane about 7.8 bits (Ref. 17). The
importance of the type of encoding is further suggested by the fact that
apparently maximum perceptual capacity is approached during the reading of printed English text. This figure is about 50 bits per second (Ref.
3) .
Other Limitations.

The time operating characteristics of the eye impose certain communication channel limitations. Dark and light adaptation (Ref. 13) of the light-sensitive material of the retina must be considered in any evaluation of the communication constraints caused by the
physical environment. Furthermore, the stimulus brightness is perceived
in relation to its previous intensity level. This function is approximated
logarithmically over the usual range of values (Refs. 23, 28). The eye
scans the visual field in a series of irregular discrete steps. This saccadic
motion limits the fixation time to about 90% of the observation time interval (Ref. 3). This motion is not random and, although little is known
about the causal relations, it appears quite efficient as a preliminary pattern discrimination filter (Ref. 19).
Filter Action. Perceived data are recognized as part of a time-series
and experiments have shown (Ref. 10) that the human operator apparently cannot perceive data without some reference to previous and possible future data. The observer appears to postulate a structure on the
incoming message and proceeds to verify or deny the hypothesized pattern. The hypothesized pattern introduces a certain amount of redundancy and thus can only diminish the channel capacity. His perceptual
operation thus becomes a filter operation which examines the redundancy
of the received data in comparison to that of the hypothesis. For ex-

THE HUMAN COMPONENT

2-07

ample, target detection would result when the amount of the particular
type of redundancy became sufficiently close to that of the estimated message structure as the latter is programmed in the human's memory.
Averaging. The human operator has an even more subtle filter action, he apparently performs a moving time average on the received data.
This corresponds to a spectral transformation which varies as a function
of the interval of averaging so that he can select the shape of the desired
signal spectrum and increase the signal-to-noise ratio even if the signal
and noise spectra overlap (Ref. 6).
To illustrate, consider the simplified example, where equal importance
is attributed to data over the entire range of the averaging time. (Actually
the importance weighting is probably exponential with maximum importance given to the latest received data.) Let the signal and noise spectra be independent and added together to form the received message.
Such a linear moving time average may be shown to perform a spectral
transformation of the form
sin 2 (Tw/2)
(1)

T(w)

(Tw/2)2

where w is the radian frequency and T is the time interval of averaging
observation. This transformation may be plotted for values of w as shown
in Fig. 3. Note that instantaneous averaging introduces a unitary transfer, no modification; while as T approaches infinity, the transfer function
approaches a unitary impulse. The signal-to-noise ratio of the averaged

T

w

FIG. 3. Spectral transformation of linear moving timc averagc.

SYSTEMS ENGINEERING

2-08

signal may be written in the following form

i

oo

T(w)Ss(w) dw

S/N= _ _
o _ _ _ __

(2)

f.oo(l - T(w))S,(w) dw

so that the maximum signal-to-noise ratio is· achieved when the shape of
the transformation best approximates that of the signal spectrum 8 s as
shown in Fig. 4. This corresponds to an optimal interval of time averag1.0
Signal spectrum

SiN

Transformation for T

= > max SIN

.--Noise spectrum

_______ E _ _ _ _ _ _ _ ---,

I
I
I

o

27r

w
FIG. 4. Spectra and transformation of signal and noise.

ing. Some displays already perform such an averaging process and practice allows the human to take this into account by a modification of the
signal "inertia." A cathode ray tube screen provides this kind of noise
filtering of input data. Too large a persistence would filter out the signal
as well as the noise and thus would greatly reduce the value of the display.
Audition

N ext to VISIOn, audition is the main primary input channel. It is
temporal more than spatial in its perceived dimensionality and being
omnidirectional for input signals it is particularly suited to applications
where a high "attention getting" value is required by the task.
The physical information capacity of the ear has been estimated to be of
the order of tens of thousands of bits per second (Ref. 15). However, as
in vision the maximum rate of information perception is probably quite
small, being nearer to dozens than thousands of bits per second. Experiments (Ref. 22) on the identification of stimuli on the auditory dimensions of pitch and loudness show about three bits per single dimensional
stimulus (e.g., frequency) and up to about five bits for multiple stimuli

THE HUMAN COMPONENT

2-09

in both dimensiollH. Binaural localization (Ref. 18) of the direction of a
sound source can provide a small amount of additional information along
another coordinate.
The time resolution of the received data limits the information rate of
auditory perception. Consider the identification of a single frequency
tone. The spectrum of an instantaneous impulse is flat and provides no
pitch identity. As the reception time proceeds, the equivalent spectrum
gathers in a more and more sharply defined peak at the appropriate frequency, until it is identified. The listener appears to accrue the individual cycles of energy and compare the period to that stored in the
memory for the expected frequency. As this process proceeds, the level
of confidence increases with the corresponding level of the redundancy
until the required significance level is reached and identification takes
place. This suggested mechanism is heuristic and appears to agree with
the observed empirical evidence (Ref. 25) that indicates increased pitch
luss for sounds of low frequency displayed for the same small interval as
those of higher frequency. Further, it seems to help account for the decreased reaction time of a listener when presented some higher frequency
(Ref. 7).
Other Senses
Kinesthetic. The human is equipped with a kinesthetic channel which
displays information generated by the vestibular canal and the many
proprioceptors distributed in the muscles, tendons, and tissues in and
around joints throughout the body. This force and motion sensing system
becomes an important consideration in relation to control operation for
it gives a spatial reference for the relation of the operator's body and its
parts to the location and reactive forces ("feel") of the control. During
accelerations of -the controlled system (e.g., flight) the information from
this source as to the state of the system may become unreliable and be
inconsistent with that from other sources, tending to disorient the operator
(Ref. 26). Its relative discrimination of spatial position is less accurate
than vision, and it may be overridden when more accuracy of control is
required.
Olfactory. The human operator associates a general meaning with
eaeh of the sensory channels. This inherent meaning is maximum for
channels where the diversity of data meanings is minimum. For example,
the initial meaning carried by any new odor inside an aircraft cockpit isemergency warning. Only after the smell has been properly identified
can this inherent meaning be rejected. Practical use has been made of
this by adding artificial odor to illuminating gas to ensure identification
of a dangerous leak in the home. Although the olfactory sense channel is

2-10

SYSTEMS ENGINEERING

not suited to a high average information rate (Ref. 24), it can carry a
large amount of information at particular times when it is excited by the
low probability occurrence it monitors.
Taste. The taste sense· channel is closely linked to the olfactory sense.
Its initial activation period is short, but it adapts rapidly and returns to
its original state relatively slowly. This prevents a rapid information
flow rate. There are four basic taste dimensions: sweet, bitter, sour, and
salty. This can again be utilized to form an attribute space within which
redundancy comparison and identification can take place.
Skin Senses. The skin senses, consisting of touch, heat, cold, and pain
can provide effective communication channels, e.g., Braille. In the usual
servo control loops, the human operator uses the tactile sense to identify
the meaning of a particular control by the shape of a knob or handle
when vision is occupied elsewhere. Various codings have been suggested
for "blind feeling" (Refs. 12, 27). As with olfaction these senses seem
well suited to utilization for appropriate high-surprise value data.
4. CONTROL OPERATION

In terms of decision by the operator the most important reason for displaying information is to tell the operator how to apply force and move
controls-which one, what direction, how much, and for how long in order
to maintain some criterion state in the system. The aim of good display
design practices is to minimize computations by the operator and supply
only the required information and not more. In transferring this information to the control the interaction of operator and the physical control
characteristics determines the net effectiveness of input information utilization. Friction, inertia, and compliance of the control members as well
as control-display amplification ratio and control-to-display transfer
function are all matters which the designer must consider. Assuming that
optimum values for these physical factors are possible in a given system
design, the limitations that the operator imposes for transferring informa.;..
tion to the controls are determined by his storage capacity, his motor
output capacity, and the effects of overloading channel capacity.
Storage Capacity. A control operation decision requires comparing
the redundancy of input information with a recalled pattern. It has been
estimated that total human storage capacity falls somewhere in the range
of 108 to 1015 bits (Refs. 8, 21), but the maximum amount is not what is
relevant to a control decision; it is the effectiveness of access that is important. If the large storage capacity is considered, the access time for
a human is relatively rapid, apparently of the order of a few milliseconds,
and seems to result from the memory of conditional probabilities between
events rather than an address to the separate events themselves.

THE HUMAN COMPONENT

2-11

Motor Output Capacity. Once the inputs have been processed through
the operator's central correlational processes his output to the controls is
determined by the performance capacity of his muscles and the associated visual and proprioceptive feedback mechanisms. Empirical data
indicate the following approximate output rates of information transmission by the human (Ref. 1) : Piano playing, 22 bits/sec; typing, 17 bits/
sec; impromptu speaking, 26 bits/sec; reading aloud, 24 bits/sec. On
the basis of known data it appears probable that humans are not capable
of transmitting more than about 26 bits/sec. Optimum performance
seems to be somewhat less than this and 10 to 12 bits/sec has been suggested as the information handling capacity that is optimum for a variety of motor tasks (Ref. 5).
Channel Overloading. Irrelevant as well as relevant information is
transduced by the operator and his properties as a living organism are
such that any increase in the amount of information tends to take its toll
in terms of distractions, fatigue, inaccuracy and the imposition of a stressful condition which makes the operator introduce subjective noise ann
clutter into the displayed data (Ref. 4). When functioning near channel
capacity, it is usual to find that each error the operator makes tends to set
off a train of succeeding errors on account of the additional data provided by recognition of the first error and a consequent further reduction
in remaining channel capacity. This effect further emphasizes the importance of designing the task environment so as to minimize unnecessary
loads on the channel capacity of the operator.
5. HUMAN TRANSFER FUNCTIONS
A great deal of effort has been devoted to finding an adequate mathematical model for the human operator in a simple closed-loop system.
The universally recognized nonlinearity and time varying characteristics
of the human have made this a formidable task. The effective reprogramming property that characterizes the human permits him to modify
his transfer function and alter his gain to suit the control task with which
he is confronted, integrating or differentiating as required. The type of
information encoding in the display, and the degree of information transformation or reencoding necessary by the operator determine the extent
of load on the operator's channel capacity and thus his effectiveness in the
system.
As a practical matter it has been pointed out (Ref. 2) that in the simple
tracking situation the transfer function required should be as simple as
possible and whenever practical, the operator should act only as a simple
amplifier and never have to deal with a bandpass greater than 3 radians/
sec. Since this is often not f.easible and, if it is, the human may as well be

SYSTEMS ENGINEERING

2-12

replaced by an amplifier, it has become customary to treat the problem
with some linear time invariant approximate transfer function that will
help account for at least some of the empirical facts. One such approximation for the control of visual displacement ratios in the complex frequency domain is as follows:
C(8)

(3)

U(8)

where e-

T8

TN

= the reaction time delay with

=

TL =

TJ =

K =

T having values ranging from
0.2 to 0.5 sec for random stimuli. (Reaction time appears to
be approximated by 0.3 In (n + 1), where n is the number
of equiprobable choice possibilities in each control decision.)
If the perceived stimulus becomes predictable, the human
operator may begin to generate an output which replicates
the input and is synchronIzed with it. When such is the
case T becomes negligible. Any phase discrepancy is not due
to the reaction time delay. On the other hand, T may be
greater than 0.5 sec, depending upon the interpretation
complexity of the perceived data.
the neuromuscular lag. TN is normally between 0.1 and
0.16 sec for the arm.
the lead time constant and has been observed to have values
between 0.25 and 2.5 sec; however, these values are not the
limit of its range. This constant is a function of both the
dynamic response of the controlled system and the bandwidth of the visual stimulus. This linear factor in the numerator prQyides a 6 db/octave rise in the gain characteristic
from the break point identifie~,.by w = l/T L which may be
looked upon as the added imp()rt~nce the higher frequency
components receive as they imply Imminent "anticipatory"
information.
the system lag time with observed values between 5 and 20
sec; it can have any value, dependent upon the dynamics of
the controlled system and the stimulus bandwidth. This
"integrating" factor provides a smoothing of the input data
so as to allow the output spectrum generated to approximate
better the response spectral characteristic of the physical
system. The closer this term approximates pure integration, the greater relative importance the operator has attributed to the "drift components" of the stimulus.
the gain, adjusted by the human operator to allow proximity to the point of marginal stability. For tasks requiring
greater sensitivity and accuracy, he would raise the gain.

THE HUMAN COMPONENT

2-13

6. PRACTICAL HUMAN FACTORS DESIGN

The foregoing treatment of the human as an information channel is
greatly oversimplified in terms of man's complexity. No attempt has
been made to deal with individual differences, motivational factors, and
the learning process, all of which must be included in practical design
considerations. In spite of these limitations, however, three general principles of practical importance emerge from what has been said:
1. The task must be analyzed in detail to assign the human component
where he will be most effective in terms of functions which he can perform
better than machines.
2. Information at each stage of the process from display to control must
be encoded so as to minimize reencoding steps, that is, displays and controls should be "compatible" in the sense that inputs and outputs through
the human link are similar in their pattern characteristics, e.g., if an
indicator turns clockwise the control knob should also turn clockwise.
3. The information transmitted through the human should be limited to
only that which is essential to his assigned function.
Steps in Human Factors Design Problems

Because the sources of human data are manifold and relatively unfamiliar to the engineer, it is necessary that some systematic approach be
set up to formulate this aspect of a given engineering problem and permit
a solution in terms of actual hardware. Steps which parallel those of
other engineering considerations are as follows:
Step 1. Answer these questions:
(a) How is the information the human must receIve encoded? (i.e.,
words, pictures, warning signals, etc.)
(b) Through what sensory channels is the information to come?
(c) vVhat kind of perceptual decisions must be made (i.e., /'yes-no"
type, qualitative "plus or minus" type, or quantitative "read a number"
type; simple or complex judgments) ?
(d) Through what motor channels do the responses to the information
occur?
(e) What kind of motor outputs must be made (i.e., fine movements,
coarse movements, simple or complex coordinations, relative importance
of speed and accuracy, etc.)?
(f) What is the general situation in which the design will be used (i.e.,
illumination level, etc.-a general description of the environment)?
(g) What is the general condition of the human component in the
normal operation of the design (i.e., state of health, age, sex, length of
time expected to operate, position during operation, etc.) ?

2-14

SYSTEMS ENGINEERING

These questions, specifically answered, will set up the problem with respect to the human factors in most cases.
Step 2. Go to some general reference covering the area in which you
are interested (see reference list below). Use the index and bibliography
in these references to lead you to the specific material which has bearing
on your problem. As this field of technology is new and is developing at
a rapid pace in some cases you may not find what you want and it may be
necessary to consult with human factors specialists. They will frequently
be able to indicate the status of information which is not yet in general
reference works.
Step 3. After you have gathered the information which seems to apply
and are ready for the design stage, layout a tentative design and check
it in relation to specifications imposed by the human factors you have discovered. You may, of course, be required to make a number of compromises before you have a workable design. It almost goes without saying
that the compromises will have to be in the direction of either eliminating
human elements or improving the extra-human components so that the
human "bottleneck" can function at a more efficient level. Selection and
training of the human components will probably help to overcome some
of the factors that require compromise, but cannot be counted on as a way
to correct mistakes of judgment during the design phase.
Step 4. Where circumstances permit, before going into full scale production of a design, a pilot model should be built (just as in cases where
the human factors are not specifically considered) and thoroughly tested
under conditions as close as possible to those of normal use. Here auxiliary tests using as many humans as many times as possible will allow you
to make the final modifications that will yield an optimally effective
design.
Annotated List of Basic Data Sources
Baker, C. A., and W. F. Grether. Visual presentation of information. WADC
Technical Report 54-160, Wright-Patterson AFB, Dayton, Ohio.
Detailed and comprehensive design data for visual displays. Available from
Office of Technical Services, Department of Commerce, Washington 25, D. C.
Chapanis, A., W. R. Garner, and C. T. Morgan. Applied Experimental Psychology.
Wiley, New York, 1949.
The first textbook of "engineering psychology," this book still retains its position
as a standard source book; it is recommended both as a reference and as a readable
introduction to the field.
Dallavalle, J. M. The industrial environment and its control. Pitman Publishing
Corp., New York, 1948.
A general text coverjng the thermal atmospheric, illumination, and noise environments from the standpoint of industrial hygiene. Many data for engineering control of these environments are given.

THE HUMAN COMPONENT

2-15

Ely, Jerome H., et al. Design of controls. WADC Technical Report 56-172, WrightPatterson AFB, Dayton, Ohio, November 1956.
Detailed and comprehensive practical design data. Available from Office of
Technical Services, Department of Commerce, Washington 25, D. C.
Ely, Jerome H., et al. Layout of workspaces.
WADC Technical Report 56-171,
Wright-Patterson AFB, Dayton, Ohio, September, 1956.
Detailed and comprehensive practical design data. Available from Office of Technical Services, Department of Commerce, ·Washington 25, D. C.
Ely, Jerome H., et al. Man-machine dynamics. W ADC Technical Report 57-582,
Wright-Patterson AFB, Dayton, Ohio, Nov. 1957.
Detailed and comprehensive practical design data. Available from Office of Technical Services, Department of Commerce, ·Washington 25, D.C.
McCollum, 1. N., and A. Chapanis. A Human Engineering Bibliography. San Diego
State College Foundation, San Diego, 1956.
A coverage of human engineering material organized by subject with a system of
cross references.
McCormick, E. J. Human Engineering. McGraw-Hill, New York, 1957.
A recent textbook which is valuable for becoming acquainted with the field and
which contains many useful techniques and data.
McFarland, Ross A. Human Factors in Air Transport Design. McGraw-Hill, New
York, 1946.
A detailed coverage of both physiological and psychological factors.
Tufts College. Institute of Applied Experimental Psychology, Report No. 199-1-2,
Handbook of Human Engineering Data for Design Engineers, 1953.
An extensive coverage of the experimental literature in the field. This is a basic
reference work which is recommended for use as an aid in evaluating the applicability
of the results of specific experiments to practical situations.
Woodson, Wesley, E. Human engineering guide for equipment designers. University of California Press, Berkeley, 1954.
A practical handbook which is strong on human sizing data; contains a bibliography of several hundred titles.

REFERENCES
1. Bio Systems Group, Human performance in information transmission, Report
R-62, Control Systems Laboratory, University of Illinois, Urbana, Ill., Oct. 1955.
2. H. P. Birmingham and F. V. Taylor, A design philosophy for man-machine
control systems, Proc. f.R.E., 42, 1748-1757 (1954).
3. C. Cherry, On Human Communication, Technology Press and Wiley, New
York, 1957.
4. J. Deese, and R. Lazarus, The effects of psychological stress upon perceptual
motor performance. Research Bulletin 52-19, Air Force Human Resources Research
Center, 1952.
5. P. M. Fitts, The information capacity of the human motor system in controlling
the amplitude of movement, J. Exptl. Psychol., 47, 381-391 (1956).

2-16

SYSTEMS ENGINEERING

6. L. J. Fogel, A communication theory approach toward the design of aircraft
instrument displays, I.R.E. Convention Record, 1955, Pt. 5, pp. 15-30.
7. ·W. R. Garner, The effect of frequency spectrum of temporal integration of
energy in the ear. J. Acoust. Soc. Am. 19, S08-S15 (1947).
S. B. H. Geyer, and J. W. Johnson, Memory in man and machine, Gen. Elec. Rev.,
60, 29-33 (1957).
9. W. H. Hake and W. R. Garner, The effect of presenting various numbers of
discrete steps on scale reading accuracy, J. Exptl. Psychol., 42, 358-366 (1951).
10. H. W. Hake and R. Hyman, Perception of the statistical structure of a random
series of binary symbols, J. Exptl. Psychol., 45, 64-74 (1953).
11. A. Hald, The Decomposition of a Series of Observations, J. Jorgensen and Co.,
Copenhagen, 1945.
12. Tufts College, Institute of Applied Experimental Psychology, Report No. 1991-2, Handbook of Human Engineering Data for Design Engineers, 2nd edition, 1951.
13. H. Helson, Adaptation-level as frame of reference for prediction of psychophysical. data. Am. J. Psychol., 60, 1-29 (1947).
14. W. E. Hick, Man as an element in a control system, Research, 4, 112-118 (1951).
15. H. Jacobson, Information and the human ear, J. Acoust. Soc. Am., 23, 463-471
(1951).
16. H. Jacobson, The informational capacity of the human eye, Science, 113, 292293 (1951).
17. E. T. Klemmer and F. C. Frick, Assimilation of information from dot and
matrix patterns, J. Exptl. Psychol., 45, No.1 (1953).
18. W. E. Kock, Binall1'al localization and masking, J. Acoust. Soc. Am., 22, SOl804 (1950).
19. M. Luckiesh and F. K. Moss, The Science of Seeing, D. Van Nostrand Co.,
Inc., Princeton, N. J., 1937.
20. John Lyman, Characteristics of the Human Operator. In Symposium on
Frontiers of Man Controlled Flight, H. Haber, Editor. Institute of Traffic and
Transportation Engineering, University of California at Los Angeles, '1953.
21. W. S. McCulloch, Finality and Form, C C Thomas, Springfield, Ill., 1952.
22. 1. Pollack, The information of elementary auditory displays, J. Acoust. Soc.
Am., 25, 165-169 (1953).
23. s. S. Stevens, Decibels of light and sound, Phys. Today, 8, 12-17 (1955).
24. S. S. Stevens, Editor, Handbook of Experimental Psychology, Wiley, New
York, 1951.
25. W. W. Turnbull, Pitch discrimination as a function of tonal duration, J. Exptl.
Psychol., 34, 302-376 (1944).
26. W. E. Vinacke, Illusions experienced by aircraft pilots while flying, J. Aviation
M ed., 18, 30S-325 (1947).
27. W. E. Woodson, Human Engineering Guide for Equipment Designers, University of California Press, 1954.
28. R. S. Woodworth, Experimental Psychology, Holt, New York, 1938.

MANUFACTURING PROCESS
CONTROL

B.

MANUFACTURING PROCESS CONTROL
3. Automatic Machines, by T. R. James
4. Automatic Inspection and Control, by J. A. Sargrove and D. L. Johnson
5. Materials Handling, by A. J. Schenk
6. Numerical Control of Machines, by J. Rosenberg

B

MANUFACTURING PROCESS CONTROl

Chapter

3

Automatic Machines
T. R. James

1. Types of Processes

3-01

2. Classification of Automatic Mechanisms

3-03

3. Transporting and Positioning Mechanisms

3-04

4. Work Performing Mechanisms

3-13

5. Machine Programming

3-15

6. Automatic Inspection

3-22
3-24

7. Typical hamples

3-29

References

1. TYPES OF PROCESSES

The emphasis in this chapter will be on automatic mechanisms for material shaping and assembly processes.
Definitions. Batch Process. An operation in which a quantity of
material 01' parts undergoes a chemical and/or physical change taking
place in one operation throughout the quantity of material under treatment. Steps are fill, operate, and discharge. Example. Deburring parts
in a tumbler.
Continuous Process. An operation or series of operations in which the
material or parts are fed in at one point; move through the equipment,
undergoing the chemical and/or physical change, the condition of the material or parts being related to its position in the equipment; then are discharged at the end of the treatment channel. Example. Baking bread in
the type of oven equipped with a traveling deck.
3-01

3-02

MANUFACTURING PROCESS CONTROL

Machine. A piece of equipment for processing material or parts, having moving elements to facilitate the processing. Example. Sewing machine.
Automatic Machine. A machine which processes material or parts
without routine human assistance. Example. Nail making machine.
In many machines, a portion of the operation is automatic. A sewing
machine automatically produces the stitch, but the work must be guided
by hand. Automation of a process machine usually takes place a few
steps at a time for economic reasons.
Advantages and Disadvantages of Continuous Processing.

1. High volume is possible with less labor and equipment. Production
planning and quality control are usually simpler. Both are therefore less
costly. If a bottleneck occurs, the effect is seen at once and corrected.
Better daily and monthly forecasts can be made when the rate of output
is constant. In chemical or physical processing where heating or cooling
is needed, process time can usually be reduced. Continuous processing
usually produces a better product.
2. Automatic continuous processing presents some obstacles; however,
long runs of the same product are needed to pay for expensive machines.
A substantial change in the product may mean rebuilding or scrapping
the whole process line.
l\1uch equipment must be operated simultaneously. Startups may require skillful and rapid adjustment of the machinery to avoid wasting
material. In some processes, a satisfactory yield of an acceptable product
cannot be obtained until the system reaches an approximate equilibrium.
One problem is too great a variety of products for the use of single
purpose machines or tools. However, in some cases, machines can be
made more versatile with certain types of readily changeable automatic
programming control.
3. Failures. A shortcoming of continuous processing is the loss caused
by the breakdown of process machinery or its control system. One failure
stops the whole machine. However, this hazard can be held to a minimum
with good design which is simple and substantial. Instruments to detect
incipient trouble should be used with automatic correction, if possible,
and operator warning. Along with good design in th~ first place, a preventive maintenance program is needed to assure success. This means (1)
anticipating troubles, (2) keeping the equipment in top condition, and
(3) training crews in the operation, inspection, and repair of all machinery, equipment, and control devices.
4. Too large a number of operations, even with the most favorable
conditions, should not be attempted on a single machine. A line of ma-

AUTOMATIC MACHINES

3-03

chines is usually more practical with some storage between to take care
of short interruptions automatically without loss of time by all machines.
5. A general comparison of automatic and batch processes is given in
Table 1. (This list represents only an average as not strictly true in all
cases.)
TABLE

1.

AUTOMATIC CONTINUOUS VS ilATCH PROCESSES

Batch
Ease of starting
Operation labor
Automatic control
Product control
Minimum investment
Investment per unit
of capacity
Automatic feed and
discharge

Good
High
Practical
Fair
Moderate

Continuous
Difficult
Low
Practical
Good
High

Moderate

Low

Expensive

Practical

2. CLASSIFICATION OF AUTOMATIC MECHANISMS

Automatic System. An automatic system is an arrangement of automatic mechanisms so that a process operation can be performed with a
minimum amount of hand labor and mental strain. The ideal automatic
system consists of:

1. A device for accepting the raw material in bulk and feeding it into
the machine properly oriented and at a controlled rate.
2. Mechanisms for performing operations on the material to give useful
results.
3. Transfer mechanisms to move the material from one operation to
the next and finally to discharge the product from the system.
-4. Means for properly programming the feeding device, the operation
and transfer mechanisms.
5. Controls that compensate for effects caused by unusual deviations
in the raw material and/or the motions of the machine, or that notify the
operator that manual intervention is required.
Automatic Assem,bly. This process will include packaging as well as
fastening parts together, since there is a similarity in the mechanisms
used.
Classification of Operations. In automatic processes, the various
operations can be divided into two main groups: (1) those that transport
and position the material or parts, and (2) those that perform the operations that furnish the desired results. The latter operations either change
the shape of the parts or fasten them together.

3-04

MANUFACTURING PROCESS CONTROL

3. TRANSPORTING AND POSITIONING MECHANISMS

Continuous Material Feeding Devices. In many cases, the material
used is in the form of bar stock, wire, or narrow sheet stock called strip,
which usually is handled in rolls. For feeding material of this type, a
device that will engage the surface of the material and move it the required amount each cycle is used. A pair of spring-loaded rolls intermittently driven by a ratchet and an adjustable crank is the most usual device for sheet stock. However, this method is not readily applicable to
feeding bar stock to rotating machines. Usually, the feeding of automatic
lathes is accomplished by advancing the stock with a chuck that revolves
with the machine and is capable of being given an adjustable motion
of the stock lengthwise.
Feeding Devices for Individual Parts. In other cases, the material
may be in the form of castings or partially finished pieces from rolled
material. The steps in feeding parts are usually (1) the separation of
single parts from the general mass, (2) the orientation of parts, and (3)
the passing of the parts at the desired time to the operation. Often, the
same device performs more than one of these steps.
Separation and Orientation. Successful means for orientation have
usually caused a random motion of the parts, but allow parts that happen to be properly oriented to fall into grooves or pockets. Rotational or
oscillating movement of the equipment is generally used. By the use of
gravity, mechanical motion of the pockets, or vibrational conveyance, the
parts are usually separated in the same operation. The principal of vibrational conveyance is to cause the friction between the parts and the
surface on which they rest to be greater than the acceleration forces in
the direction of travel, but less than these forces in the opposite direction.
Orientation is usually accomplished by:

1. Holding one end of the object while the other end continues to progress.
2. Moving pockets the shape of the parts under a mass of the objects so
that only those happening to be caught in the right orientation will be
caught by the pockets, or moving the mass over and having the opening
so shaped that only those parts having the right orientation will fall
through, or moving the parts along a linear trough and allowing the excess
parts to fall off.
3. Conveying a round piece by gravity or vibration until a flat side or
projection prevents rotation and the part now slides. A trough formed by
two rollers may be used.
4. Turning the part after picking it up for the final feeding operation
until a lug strikes a stop or an indentation is engaged by a pin, the grip
then slipping during the rest of its rotation.

AUTOMATIC MACHINES

3-05

Parts that need orientation only along one axis, such as resistors and
paper capacitors, are easiest to handle. Parts such as nuts and screws are
not overly difficult as the heads can be used for orientation. Objects that
require orientation for electrical reasons should not be symmetrical with
regard to a centerline at right angles to the direction of orientation.
Transfer to Operation. In some cases where belts, gravity chutes,
or vibratory conveyors are used, all that may be required to feed parts to
the operation is a timed gate.

1. The feasibility of the simple gate feeder can be determined by building a mockup of the proposed chute or conveyor, closing the exit end,
filling with the parts, and opening the exit. If the conveying means does
not jam, the first problem has been solved.
2. The next problem is the design of a conveying means that permits
the feeding of a single part at the entrance with the conveying means
empty without jamming. If this can be done, the problem is eliminated.
Figure 1 shows three electronic component chutes as a further explanation.
3. Another problem is the effect on the orientab'on device if the chute
overfills. This problem usually occurs at the entrance of the chute. If
the parts are oriented in the same relation to their direction of travel as in
the feed conveying means, backup into the orientation device is not likely
to cause trouble. If parts are oriented in another direction, and the
answer is not clear cut, build a mockup of the gravity chute for conveying
the parts. Test by repeated overfilling and emptying. If the parts empty
freely, a backup into the orientation device will probably do no harm.
If parts do not empty freely, jamming will almost certainly occur at the
conveying means entrance. Funneling of the entrance will only make
matters worse.
If the first two problems mentioned above have been dealt with satisfactorily but the last problem has presented difficulties, means of stopping
and starting the orientation device in response to the quantity in the
gravity chute will clear up the feeding problem.
If the first and last problems have been solved, the second problem can
be avoided by operating the chute full, stopping the feed gate by electronic means if the chute starts to empty, and starting again by the same
means when the chute fills again.
Feeding Devices for Flowable Material. Granq.lar or powdered material can be fed by opening and closing slides, a rotary valve, a vibratory
conveyor, a screw, a belt conveyor, a chain conveyor, or a rotary conveyor.
In most instances, discrete uniform quantities are required at either
exact or approximate time cycles. In some cases, measurement by volume,

3-06

MANUFACTURING PROCESS CONTROL

Should not be
fed when empty

Section A-A

(a)

(b)

FIG. 1. Electronic component chutes: (a) resistors,
ramie, button type).

(c)
(b)

sockets,

(c)

capacitors

(ce~

AUTOMATIC MACHINES

3-07

such as the space between two slides, or the amount to fill a pocket, will
suffice. Sometimes the final container itself is used to measure the
amount. Vibration, plunger pressure, and oscillation of the air pressure
between atmospheric and a partial vacuum, or combination of any of the
above, are often used to secure a uniform fill. Scale weights, either
manual or automatic, are used as a check, and the volume is readjusted in
accordance with average weights.
In some cases, especially where quantities are large, the first fill is by
volume and is slightly under the required amount, and the remainder is
made up at one to two additional succeeding stations by being dribbled
in slowly while the receiver is on a scale that will cut off the flow at a predetermined weight.
If good accuracy is required, especially if the quantities are small,
weight alone is generally used. The weighing may be done either in a
hopper type scale or in the container. In either case, the rate of flow is
high at first and is slowed to a dribble to eomplete the weighing.
Liquids, even where accuracy is necessary, can always be fed by
volume. Piston displacement will measure even highly viscous liquids or
plastic materials, such as bread dough and thermoplastics, with sufficient
accuracy for most purposes. As in the case for volume feeders of granular material, occasional weighing of samples is used as a check on the
volume feed.
Transfer Mechanisms. The three general types of transfer mechanisms are listed below:
1. A mechanism which intermittently or, in some cases, continuously
advances all parts in a process an equal distance during any given time
interval.
2. A mechanism which transports parts from one operation to the next
operation as fast as received, with a continuous motion.
3. A mechanism which operates in synchronism with the preeeding and/
or following operation and actually grips the part as an individual piece
when moving it to the next operation, or to either of the two transfer
mechanisms described above.
Intermittent Cycle Transfer. In some operations, the transfer mechanism need be only a trough of suitable construction. This is the case
where parts have at least one fairly flat surface at right angles with two
other opposite part surfaces, and the parts are strong enough so that one
can be pushed with another. A reciprocating plunger is then used to push
the parts along. A continuously moving belt, with fingers to stop the
pieces at each station, is another example of this type of transfer mecha-

3-08

MANUFACTURING PROCESS CONTROL

nism. An intermittently moving chain carrying flights may be used instead of a belt.
Accurate positioning in the horizontal plane, if required, may be obtained by one surface of a part being pushed against a side rail, while a
portion of one of the end surfaces rests against a retractable stop. Another method is to use two locating holes in the part. Then, at the station the transfer mechanism inserts a pin in each of these holes. Parts
not easily aligned or kept in alignment by guides are sometimes put on a
special adapter or pallet for conveying and positioning by this type of
transfer mechanism.
A bar on which pushing flights are mounted is also used as this type of
transfer mechanism. This bar is given a lengthwise reciprocating motion
to move parts, and either a sidewise or angular motion to move the flights
clear of the parts on the return stroke. Good positioning accuracy without stops is obtained by this method if the speed is kept low enough to
prevent coasting of the parts after the conveyor stops. Figures 2-4 illustrate these linear types of transfer mechanisms.
An intermittently driven rotary table makes a transfer device requiring
only accurate positioning of the table to position accurately at all stations. The table is at a disadvantage from the standpoint of inertia when
compared with a chain conveyor. The chain or other straight type of
conveyor also has the added advantage of accessibility to both sides of
the line for the feeding of parts and materials and for adjustment and
maintenance. Nevertheless, rotary tables are often the best solution
where accurate positioning is needed.
For very heavy work, the parts are mounted on cars which are pulled
from station to station and held in position by locking pins at the station
while the operations are in progress.
Continuous Transfer. These may be belts, chains with flights that
form a flat surface, or gravity chutes. In some cases, parts are blown
through tubes with air. These conveyors should maintain the orientation
of the parts, but synchronism of delivery is not required. Such conveyors
are generally used between machines in a line and, should the machine
to which the parts are being fed be stopped to correct trouble, a bank of
parts is built up in the conveyor, rather than shutting down the line.
Since the parts arc already oriented, only a simple gate feeder is required.
Single Operation Transfer. Transfer mechanisms of this type may
take either a positive grip on the article or hold it by partial encirclement
for the required time.
Single paddles or fingers, either reciprocating or mounted on a revolving
shaft are used to remove articles from an operation and feed them to the
next one.

3-09

AUTOMATIC MACHINES

Intermittent drive
Fixed guide

(a)

Work stations

Part feeder

Flight'
(b)
Chain

Transfer mechanism, fixed cycle type: (a) top view, (b) side view.

FIG. 2.

Work stations

Guide

\

(a)

\\

-Single revolution clutch

~Stop-released

on completion
of slowest operation
(b)

FIG. 3.

Transfer mechanism, variable cycle type: (a) top view, (b) side view.

MANUFACTURING PROCESS CONTROL

3-10

(a)

Fixed cycle
flights

FIG. 4.

Transfer mechanism, single station type: (a) top view, (b) side view.

In other cases, a positive grip on the part is used. One company
markets a machine employing an arm with a swing and lift motion to
pick the pieces from a rotary table and place them in a die. For lightweight pieces with a fiat surface, a vacuum cup is used to grip the piece.
Pieces that cannot be handled by vacuum are gripped by vacuumoperated fingers. These fingers, two stationary and one movable, are arranged so that their positions can be adjusted to fit the work piece.
Figure 5 is an illustration of this machine. For large work difficult to

AUTOMATIC MACHINES

3-11

FIG. 5. Punch press fceder, vacuum pickup.

remove by hand or by any of the foregoing methods, an air-operated
mechanical arm is available that can be preprogrammed to grip the piece,
remove it from the press, turn it over, or change its orientation if desired,
and then place it on a conveyor belt. Figure 6 is an illustration of this
arm.
Storage Devices for Processes Requiring Extra Time. Some parts
of automatic processes such as cooling for sand casting, proofing of bread
dough, and drying and curing of plastics may require too long a time at a
station or series of stations, without resulting in an impractical machine.
In these cases, the situation can often be saved by the use o,t a long
belt conveyor between machines. Sometimes if parts are to be held together for an adhesion process, an additional upper belt weighted with
rollers is used. To save floor space, it is usually best if the shortest dimension of the part can be parallel to the direction of travel and the belt
speed low enough so that the parts almost touch each other. If further
l'eouction of floor space is needed, a wider belt may be used and the parts

3-12

MANUFACTURING PROCESS CONTROL

,,
I

Lifting air cylinder

I

,I
I
I
,
I
___ ,I
,I

"
II
II

I'

I'
I'

I:"
II

II
II
II
II
,
,I
l- ____ .JJ
I

~Press

/'

,

Arm swung upward,,~.~ /

frame

I

:'-,- --- -- -

0/

-

--. ---

I
I
I

I
I

Limit switch

I

I

I
I
I

I

I
I
I

I

I
I

Arm in lowered
position

I
I

I

I

Arm stroke
I
adjustment cam :

Angular adjustment
of jaw
Jaw length and radial
adjustment

FIG. 6. Sahlin iron hand.

AUTOMATIC MACHINES

3-13

may be placed several abreast during the operation. If the latter plan is
needed, it will simplify the transfer if the belt is at right angles to both
the preceding and following lines. Parts can then be allowed to accumulate until the desired number abreast is obtained and then pushed by a
single stroke onto the belt.
Storage Devices to Minimize Production Loss Due to Down Time.

In the operation of a line of machines, minor malfunctioning or tool replacement causes a certain amount of down time on the individual machines. Unless there is some storage between machines, all machines in
the line must shut down when one is down. If there are more than two
or three machines in the line, the loss of production is often considerable.
Automatic storage between the machines is usually desirable to reduce
these short down-time losses of single machines. Here the problem is
different from that for process storage, as the parts in storage should
travel quickly between machines if the receiving machine has no supply.
Parts that are not damaged by a belt sliding against their lower side
are usually simply held back by a gate on a belt conveyor ahead of the
receiving machine. To utilize this kind of storage, the parts must also be
of such shape that they will not jam between the guides of the conveyor
or override preceding parts. A vibratory conveyor may in some cases be
less likely to jam than a belt conveyor, and its smooth metal bottom may
be less damaging to the parts. In other cases, an inclined gravity chute
may be the best answer, even if the parts must be elevated before entering
the chute. In the case of small parts, it is sometimes most practical to
have a hopper and another feeder between machines. This type of storage will allow one machine to be down for a longer time than a chute
or a conveyor without shutting down the line.
4. WORK PERFORMING MECHANISMS

Some operations may be performed in series at a single station as on an
automatic turret lathe. In other instances only a single operation may be
performed at a station, as in packaging where a work station is required
for each step as unfolding a box blank, gluing the bottom, and filling.
Machining Equipment

Commonly used equipment includes lathes, milling machines, drills,
boring machines, gear cutting machines, and grinders.
Lathes. Three types used for automatic machining operations are:
1. Single Spindle. The single spindle is used for one or two specialized
operations. There may be several of these in line.
2. Single Spindle with Turret Support Tools. Several operations may
be performed without moving the piece being machined. The tools are

3-14

MANUFACTURING PROCESS CONTROL

installed in the turret and are brought in and out of action, step by step.
3. Multiple Spindle. These spindles move from work station to work
station. Here, only a few tools are used at each station.
The tools used on automatic lathes are the same type used for manually
controlled operations, but more care must be taken in selecting longwearing materials and shapes. It is also possible to supply a means of
changing tools without making adjustments each time to compensate for
tool length.
Milling, Drilling, and Boring. These operations are usually at stopping points of a transfer system in adjustable positions and at angles
which will allow the transfer to be in the direction of line of travel to
keep the system simple. Again, the tools are conventional, but are
selected for long-wearing qualities. Carbide-tipped drills are often used
even on softer metals for durability.
Gear Cutting. Gear blanks are generally formed in a separate operation, since they may be made at higher speeds than the teeth can be cut.
Cutting teeth is a special operation of milling or shaping. The equipment
may be basically automatic, but it requires not more than two stations
for forming gear teeth. At the first station, most of the cutting is completed. The second station is reserved for the finishing operation, which
is usually of a type termed "shaving."
Grinding. Two types of surfaces are ground, circular and flat. Circular surfaces may be ground by methods similar to those used in lathes or,
if of uniform diameter, between two grinding wheels. Flat surfaces are
generally ground as in a milling station arrangement, although two
parallel sides are often ground at once between the flat faces of two
wheels. Parts for grinding are semifinished previously, and generally
this operation does not involve high cutting forces, which makes it feasible to simplify the feeding and holding of parts. Circular parts with only
'one diameter to be ground accurately may be passed between two wheels,
the work being supported by a single track. If the parts are comparatively short, a gravity chute, curved to become level as it passes between
the wheels, is a satisfactory feeding means. Parts with two parallel
surfaces to be ground may be pushed between two surface grinding wheels,
with each part pushing the piece in line ahead of it through the machine.
Stamping and Forming. Tools for automatic punch press and stamping operations are conventional. Standard dies are often used, since even
for manual operation the dies are designed for a large number of repeat
operations. When many operations are to be performed, the strip stock
is fed into the initial ~tation and the parts are moved from station to station by transfer devices installed between stations. Frequently, the parts

AUTOMATIC MACHINES

3-15

in press work must be removed from the transfer device at a station and
placed in the dies.
Automatic forging operations are more complicated than those for cold
forming. Progress has been made, though, by using electric induction heat~
ing of the parts. A machine is now offered which automatically feeds
blanks and turns out small finished forgings. Certain types of forming
operations, such as rolling, drawing, and extrusion lend themselves readily
to automatic, continuous operation without the need of intermittent transfer devices. For rolling and drawing operations, the drawing rolls may
be considered to be the transfer devices and the dies and forming rolls
the work stations. For extrusion, a plunger or screw is the transfer device, with the die serving as the work station.
Casting and Molding. Automatic sand mold forming is usually done
in several steps. At the first work station, the flasks are filled with sand
by gravity. In the following stages, the flask is rammed or vibrated,
then parted, and in the next step the pattern is removed.
Sand and permanent mold castings are poured' by gravity. Die castings are made in metal molds which are pressure filled.
Molding plastics may readily be done automatically, particularly when
large quantities a1~e l1se~l. .~ This is true for both thermoplastic and thermosetting. The raw materiai'is usually granular in form and requires only
moderate temperatures and pressures.
(a) Thermoplastics are fed from a hopper or bin into a melting
chamber. The molten plastic is injected into the dies with a plunger. A
multiple cavity die is easily handled. The metal dies are good heat conductors, so it is possible to open the die for removal of the part in a very
short length of time.
(b) Thermosetting material is fed in measured quantities into the dies
which are mounted on a turntable at the first work station. In successive
stations, the filled dies are closed and subjected to heat and pressure for a
given length of time. Since the parts become rigid during the heating
process, it is possible to eject the parts immediately after the heating
cycle is completed.
5. MACHINE PROGRAMMING

Automatic machines must, of course, be designed so that the operations
are performed in the proper sequence, and the correct time must be allowed for each operation.
Synchronous Method. The machine is designed either with all moving
parts directly and positively driven from the same power source or, if
more than one power source is used, all sources are controlled by one
central mechanism to synchronize the operations. Mass production auto-

3-16

MANUFACTURING PROCESS CONTROL

matic machines performing operations not requiring an allowance for
time variation are usually of this type, as it is the simplest kind of control
mechanism.
If, however, some of the operations are likely to vary in time because
of variations in the material or tools, it may be wise to start an operation
by a signal given on completion of the preceding operation. For the
purpose of brevity in discussion, this will be called the sequential method.
Recent advances in the art of automation to make it applicable to
moderate, rather than mass production quantities, have been accomplished by the application of much additional engineering skill to make
automatic machines more versatile and more readily changeable from one
product to another. In some cases, a mere change in the size of parts of
the machine, either by adjustment or interchange, has multiplied the use
to which a machine could be put at only a moderate increase in the cost
of the machine.
Flexible Programming. To make an economic success of automatic
machines when their scope was enlarged to include items of which only
moderate quantities were produced, a greater variety in products with
frequent changes in programming was needed, resulting in machines with
variable programming readily selected by the user. This type of programming is treated in later sections.
Synchronous Programming. A typical automatic machine using
this type of programming consists of a transfer mechanism of th"e intermittent type and work stations located at approximately equal intervals
along the travel of the transfer mechanism.
For operation of the work stations by the synchronous programming
method, a direct positive drive by the means of gearing, chain drives, and
shafting from the same power source that operates the transfer mechanism may be used. In other cases, the work stations may be operated
electrically, pneumatically, or hydraulically, these means being programmed by cams positively driven by the motive source of the transfer
conveyor.
The transfer mechanism, whether in the form of a rotary table or
straight-line chain, may be driven and programmed automatically by
one of several different means: (1) ratchet and pawl, (2) Geneva drive,
(3) variable pitch worm drive, and (4) cam and differential gear drive.
Servo Transfer Mechanisms. Intermittent transfer may also be secured
by controlling the drive mechanism from a central machine control by a
cam-operated valve or switch. Often compressed air or hydraulic means
are used for such transfer mechanisms because the resulting mechanism
is simpler than if an electric motor were used. This type of transfer is not
suitable for a large number of operations per minute as some allowance
has to be made for variations in transfer time.

AUTOMATIC MACHINES

3-17

Sequential Programming. For sequential programming, transfer
mechanisms are of the servo type except that instead of being operated by
a central control, the cycle is started by a switch or valve moved by the
previous operation.
An example of this type of programming is used in the filling and closing of flour bags. Since an operator places the bags on the filler tube, it is
desirable not to depend on a predetermined cycle time for the filling operation. Therefore, the filling cycle is initiated by tripping an electric
switch as the bag goes on the tube. In the next step, the time required
for the auger to compress the desired amount of flour into the bag varies
considerably, not only with the type of flour but also with the length of
time the flour has stood in the bin since being milled. Therefore, the
next operation, which consists of adding a small amount of flour slowly
until the correct weight is reached, is also initiated by the filled bag tripping a switch as it passes onto the weighing scales.
Because of the variability of the time cycle of the filling and weighing
operations, the machine stations that close the tops of the bags after filling must also be designed to accept bags on irregular time schedule.
Flexible Programming. vVhile nearly all automatic machines in the
high production field can be changed to accommodate some variation in
the size of the product, and many can be varied to produce a variety of
products, these changes generally require both the changing of parts and
some time-consuming adjustments before being ready to produce the new
product. However, much progress has been made in this direction and
some machines are now available in which a template change or a new
punched card or tape in the control device is all that is needed to reprogram the machine.
Flexible Control hy Mechanical Adjustments. In order to be economically feasible in the small lot field, a type of programming that can
be quickly changed is needed.
If the machine performs only one simple operation such as boring a
single hole, a convenient means of adjusting the bore diameter and feed
rate will serve the purpose. Interchangeable cams are used if several
operations are needed. However, some of the more complex' automatic
lathes now have sufficient adjustability so that special cams are not
needed for each product. Pieces with several surfaces to machine, however, still require considerable time to set up for a new part.
Flexible Control by Template. For some operations, the following
of a template, which may be, in many cases, an accurately made sample
part, is often the best answer.
Milling. Contour milling in either two or three dimensions can be
accomplished by connecting the template follower mechanically to the
milling machine carriages. For two-dimensional milling, the work car-

3-18

MANUFACTURING PROCESS CONTROL

riage usually is moved. In some machines, connections can be made to
rotate cylindrical work. Only one motion in the horizontal plane is then
needed, this being along the line of the cylinder's axis.
For three-dimensional milling by direct ':mechanical connection, generally only the tool head is moved. Th~ee motions are required for this
type of operation, but these need not be straight-line motions or at right
angles to each other. In fact, arcuate motions often simplify the .design
and reduce guidance friction.
A follower of the same radius as the milling cutter is invariably used
to simplify the making of the template.
Similar mechanisms can be used for lathe work on soft materials like
wood but, in general, because of the high tool pressure and because of
difficulty in controlling depth of cut, this method has not been used for
metal turning.
Even in the case of milling, especially in metals, the tool pressure is
high enough to cause operator fatigue and enough deflection in. the mechanic~l connections to make high accuracy impossible. Therefore,' servomechanisms, usually with electric sensors, are used which maintaip. a certain pressure on the template follower. The follower is supported on the
stationary part of the machine along with the tool mount. The template
and work are both attached to the mova~le .part of the machine. Figure
7 explains the follower and servo operation.
Lathe Work. For lathe work, template-actuated servos have been
quite successful. Generally for this kind of operation, the longitudinal
feed is preset and remains the same for the whole operation, the servo
controlling only the depth of cut. Cuts, at right angles to the centerline of
the work, can be secured either by stopping the longitudinal feed, or by
settingtlle cross-feed at an angle of perhaps 45° and withdrawing the
cross-feed enough faster than the longitudinal feed to produce a right
angle cut. By this hitter means, cuts at any angle can be followed. The
same means also serve for following curved contours. One manufacturer
uses an electronic tracing finger similar to. that used in milling. Contacts
in this finger control both the tool cross-feed carriage and the main tool
carriage through mftgnetic clutches.
In the case of lathes, direct hydraulic semling has proved practical. A
differential valve operated by the follower: is .used. The valve follower
assembly is supported on the lathe tool carriage. A very minute difference in the valve plunger position is sufficient to operate the hydraulic
carriage drive in the direction required to null the valve. Accuracies of
within 0.0001 in. of the template diameter are' claimed for this type of
servo.
An air gage sensing element, based on the. change in back pressure as

AUTOMATIC MACHINES

3-19

TemPlateyj

~-j
hopper
I

Refill
hopper

I

.... .. .. ... . . .. I......., .
....
..
. ..

-------------~---------------

e •••
,

•

(c)

~

Discernible interval
/ \ of repetition ~

--·-r--Lr-~·-r·---r-J'--i----T--1i

------~-1'-•
•••• • '

••••

.

- - LI _ _ 11__ -i- -..;..- -11, I

ft' • . • • • • '.

•

'.

-+-,

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(d)

Sporadic""",

~.

/Sporadic

---------------.£-------------•

i·

't.

• • ,0

'

.... ' ....... .

.a •• ••• • • • • • • • • • •

(e)

·~Sporadic

FIG. l-(Continued)

stances a high-velocity low-mass process is more readily controlled than
a slow ponderous one.
There are a number of interesting special cases that arise.
Asynchronous Faults. A multihead production machine might develop
a single faulty station and, rather than reject every piece produced, one
can design the inspection system so that it causes this one faulty station
to be put out of use automatically or its identity signaled, the production
being permitted to continue from the other stations.
Legal Limits. A normal gaussian distribution about a mean value is
normally acceptable for technical requirements, but legal definitions such as
weights of commodities, are based on the concept of a minimum value (Ref.
5). It is then desirable to arrange the process for a very narrow gaussian
distribution (which may require a high speed of apparatus response) and

AUTOMATIC INSPECTION AND CONTROL

4-05

possibly skew the distribution curve (Fig. 3) or recirculate rejects for
readjustment.
Flukes Ignored. When an average error signal is fed back, it may be
advisable to exclude the extreme values by rejection before permitting
the computing apparatus to calculate the average; similarly there will
be an optimum averaging number or time constant for any particular
numerical distribution.
4. SENSING ELEMENTS FOR INSPECTION

The operation of inspection may depend on quantitative factors, and
also on the qualitative factors already mentioned. For the former the
whole range of classical measuring techniques is available for adaptation
(Fig. 4), but the latter may require careful study of alternatives and
some ingenuity in application.
For the quantitative measurements it is not sufficient to take a laboratory-bench test instrument and put it into continuous service. Many
such instruments depend on frequent setting-up and zero-setting adjustments, and it may be necessary to modify the basic method of operation
in order to obtain a stable mechanism that will not require adjustment
over long periods.
The principal requirements of the sensing instrument can be listed
as follows:
1. Stability and absence of the need for recalibration and zero adjustments.
2. Robustness, of a much higher order than for laboratory instruments,
preferably with fully sealed housing.
3. Reliability by designing conservatively for long life. Ultimately
magnetic amplifiers and transistor circuits will be preferred to tube
circuits.
4. Modulated a-c systems or differential systems always to be preferred
above d-c amplifiers.
5. Ease of servicing, using miniature plug-in "packages" easily exchangeable by maintenance staff, but factory-serviced.
6. Compatibility with other devices, for ease of interconnection and
building up of systems.
5. INSPECTION AND CONTROL SYSTEM DESIGN

In most applications the magnitudes of the parameters to be inspected
are fixed, and it is sufficient to deal only with the first derivative or percentage error. For example, if it is required to gage an object nominal
length L, limits ±5%, significant gaging error Y:!%, the gaging system
need resolve only Y:! % in ± 570 or one part in 20 provided the total

4-06

MANUFACTURING PROCESS CONTROL
Simple control
of input flow ~

~ Stirrer

~

Varying
mixture

Reservoir

:=::====== Blended mixture

_~ _ _ _ _ _ _ _ _ _ _ _ Limi~

Density
of
mixture
Limits
FIG. 2. Smoothing to eliminate excessive variations. Smoothing by reservoir or other

means eliminates excessive variations due to repetitive changes, where phase lags
are not objectionable.

Uncontrolled weight
distribution curve

o

Electronically controlled
weight distribution with
reject systems for extra
light and heavy specimens
Saved
ingredients

o

FIG. 3. Normal gaussian curve showing symmetrical limits, and also the asymmetri-

cal limits that occur with "legal minimum" legislation; here a skew gaussian distribution is preferred. Effective spread of weight distribution histogram of uncontrolled dough divider (top curve). Reduced spread of weight distribution of dough
pieces (bottom steep curve) after combined effect of electronic computer weight
control and pass-and-reject gate action eliminating the heavy and light weight dough
pieces. LlV = legal minimum weight. Note shift in mean weight ilS and effective
saving in material used.

Indicating recording and display

It
»
c
-t
o

Actuator devices

~

Arithmetic and quantitative
decision devices

»

-t

~E

~-t;

~;;-

n
zen
-c
m

()

-t

(5
Z

»
z
o

~

"O.~

:;-5
~E

l;;c

~~
...,0...,

~~

Ubi iiHh
Quantitative sensing

~

z:.

~

.i:

'6

~

flllll

~~

Ii!JdJU

~~

·fj
eng

()

o
Z

-t
;;0

o
r-

~

Qualitative sensing
~

FIG. 4. Classification chart of inspection sensing techniques and decision-making and actuating mechanisms.

~

4-08

MANUFACTURING PROCESS CONTROL

magnitude of the main dimension A is constant. This is a very moderate
specification. If a simple computation such as density D is to be made
from the parameters length L, area A, width W, and weight M, we have
D = M / (L X A X W), but if one is only interested in the fractional
error in density SD, one needs measure only the three fractional errors
SA, SL, and SlY, and approximately SD = SjJJ - SA - SL - SlY for small magnitudes of error.
Thus for relatively narrow limits of error, the numerical computation
system can be a very simple one, using summation operations only, without the need for an operation of multiplication or division.
It is desirable that the system be constructed physically as a group of
predesigned "black boxes," chosen for their compatibility, so that one
may be connected to another without the need for any transformation or
conversion. Unfortunately such coordination does not exist between all
classes of commercially available automation components.
In the density gaging system of Fig. 5 it is a considerable simplification
to employ the same pattern of differential transformer positional-transducer for all four functions of A, L, W, and M, and to carry out the latter
weighing process by detecting the deflection of a standard cantilever.
The gaging and computation system of Fig. 5 operates in the following
manner:
1. The molded objects are moved from station to station on the conveyor.
2. At successive stations, variations in height, diameter, and weight
are sensed by variable inductance heads. Height transducer gives function SL; diameter transducer gives "area" function SA.
3. The information is indicated in d-c meters and used to modulate an
a-c carrier in each channel, and recorded as a voltage analog on a slowly
rotating magnetic drum.
4. Information is read out time-displaced, so that data on a particular
object are available simultaneously. It is demodulated, and the d-c
signals are used to actuate limit circuits and for a simple analog computation of density.
5. Limit circuits control rejection of individual objects, and a quality
control chart is plotted.
6. An average signal is fed back as error correction to the molding
process.
Similarly, in an air gaging system, pneumatic controller components
would be used throughout, up to the point where an electrical command
output becomes necessary.
Conditional gaging systems are similar to the numerical computing

AUTOMATIC INSPECTION AND CONTROL

4-09

Primary
limit
control

A

n

Demodulators
and Amplifiers

Bulk
crase

FIG. 5. Schematic arrangement of a simple gaging and computation system for inspection of density of molded objects over a small range of variation.

PI
P2
MIl
MI

Photocell (presence indicator)
Photocell (counters)
Magna-gage head
Magna-gage indicator

S Switch unit
AD Amplifier and oscillator

AD Amplifier and detector
L Primary limit setting control

ones outlined, except that the acceptance limits for one or more parameters
are conditioned by the magnitudes of the other parameters.
6. MANIPULATION OF TIME SCALE

With multistation transfer machines it is usually convenient to perform only one operation at each station: for example, it would be difficult
to both weigh and gage simultaneously. Some mechanism for automatic
recording or register is then necessary.

4·10

MANUFACTURING PROCESS CONTROL

A simple form is a system of pegs or markers associated with each
position on the conveyor system to enable an accept/reject or other instruction to proceed synchronously with the test object to a later station
where it will be acted upon.
More elaborate arrangements of this sort can be made with conventional digital storage techniques, up to any speed or accuracy likely to be
required in practical cases.
As already discussed, a resolution of one part in 20 is adequate in most
inspection applications. It is possible to register the magnitude as a
voltage analog and then to read out simultaneously data measured at
intervals of time at several successive stations.
The same approach is useful in giving a temporary identity to articles
while on a conveyor, so they may be registered and dealt with individually
at a later stage in the process, either on an accept/reject basis, or by a
correction operation, bringing the object to a standard weight, etc. For
such analog memory systems a slow-running magnetic tape or drum is
adequate.
7. DISPLAYS AND RECORDING SYSTEMS

When it is necessary to involve a human being in an otherwise automatic inspection and control system, the principle to be followed is that
of "management by exception." By this procedure the steady operation
is regarded as the normal or quiescent state, and the human supervisor's
attention is called only to extreme conditions or such trends that may
approach the extreme limits.
A complete "mimic" display of the system is usually provided by the
apparatus designer for convenience of the operator in setting the process
in motion. This "mimic" is usually diagrammatic with visual indicators
or recorders for each key parameter and integrating or counting equipment displaying accept/reject data. In addition summary displays are
provided for those administratively interested, usually in the form of
moving displays, electric counters, or printout by electric typewriters.
Such displays can be provided at reasonable cost, with standard equipment, provided that a degree of compatibility exists through the whole
system.
Presentation of data in this way can usually be shown to recover its
equipment cost by a saving in capital on inventory, as all stages of production can thus be closely geared to demand. Process control by feedback from inspection data reduces the cost of rejects and confers on the
product the character of greater uniformity which is highly regarded by
the user.

AUTOMATIC INSPECTION AND CONTROL

4-11

8. ELECTRICAL COMPONENT TESTING

Incentives. To ascertain the future life behavior of a particular electrical component, the life testing to destruction of other similar components gives only indirect evidence. 'Vhere electric circuits become
more and more complex, it has, therefore, been necessary to attempt nondestructive testing of even the simplest components prior to their insertion in more complex systems if the final life reliability of the whole
complex system is to be of a very high order.
Apart from the requirements of the scientific testing of electrical devices as single items or as a network, there have been three main incentives to evolving systems of automation in electrical component testing.

1. The continuous supervision of a long component, such as an insulated
wire component, prior to its incorporation in a more complex device so
as to eliminate an incipient fault before it can cause expensive trouble. An
example is a submarine cable.
2. The testing of circuit networks prior to inserting more costly components, such as electronic tubes, transistors, etc.
3. The desirability of large scale testing of components for the purposes of "type approval."
EXAMPLE. An automatic component testing equipment was designed
for the automatic testing of batches of up to 1000 resistors (Ref. 9). The
resistors can be tested under full load over a wide range of environmental
conditions from -80° to + 1000e with controlled humidity variable from
very dry to full precipitation. The resistors are automatically measured,
and the results are recorded on a continuous chart, containing 1000 discrete
areas; the testing sequence is controlled by a five-dot code punched paper
tape. The system is flexible and up to four months continuous testing can
be programmed by this tape.
To implement a decision to carry out a program of mass testing of components the following steps have to be taken:

1. The program sequence of climatic and electrical parameters has to
be decided upon and then punched onto the five-hole code tape. (About
one hour.)
2. The jig block has to be loaded with the 1000 components, all of which
are mounted on separate insulated pillars. (Achieved in approximately
one day.)
3. The program tape unit is then loaded, also the various chart recorders, including the continuous 1000-chart recorder (the ease of rewind
flow of paper is checked). (About one hour.)

4-12

MANUFACTURING PROCESS CONTROL

4. The jig block is then mounted within the climatic cabinet. (About
15 minutes.)
5. After general supervision of all the equipment the program tape unit
is started. (The equipment will refuse to start unless all the appropriate
doors on dangerous power units, etc., etc., are closed and safe.) After this,
the equipment will start its own automatic test run program. (May last
up to 4 months or be as short as a few weeks.) All measurement readings
(50,000:""100,000) are sorted by the apparatus into the 1000 discrete areas
of the chart, giving the life history of each component separately.
6. At the end of the test program which has been prepunched on the
tape (whether it is a few weeks or months from start) the equipment
gives an automatic indication that it has accomplished its task. The
whole equipment switches itself off.
7.· At this point the doors can be opened in complete safety as all the
high voltage equipment, etc., is also dead.
8. The resultant charts can now be examined (after their removal from
the chart spools) for the best test behavior of the component, and any conclusion can be derived from these test results.
9; Another test can be in progress while doing (8), at leisure.
Improvements in this system can be made by punching the results on
paper tape rather than using the 1000-chart recorder system. The output
tape could then be fed into an electronic computer programmed to analyze
the results.
Conclusions. Automatic component testing is an essential step forwarp in automation of a highly complex but none the less wearisome and
boring task If one wished to carry out such exhaustive test proceedings
on 1000 components in conventional climatic equipment, one would probably have to. envisage using twenty or more people. Surplus laboratory
personnel just do not exist and are usually engaged on the normal research
program. By the aid of automatic equipment two or three people can
carry out the task In fact, the two or three people who would normally
be engaged on a small scale testing program can now carry out the statistically valid large scale testing program. Such automatic testing system
equipment might well become common in the future for modular single
slab functional circuits.

REFERENCES
1. R. M. Belbin, New fields for quality control, Brit. Management Rev., 79-89,
April 1957.
2. N. H. Mackworth, Vigilance, Nature, 178, 1375-1377 (1956).
3. W. Heron, The pathology of boredom, Sci. American, 196, 52-56 (1957).

AUTOMATIC INSPECTION AND CONTROL

4-13

4. J. Loxham, Automatic controls for machine tools, Inst. Production Engrs., Convention P1'Oceedings, Harrogate, England, July 1957.
5. J. A. Sargrove and P. Huggins, Automatic inspection-the anatomy of conscious
machines, Institute of Production Engineers, Conference Proceedings, Margate, England, June 1955.
6. E. L. Watkins, Inspecting missile airfoils automatically, Control Eng., 3,
100-106 (1956).
7. R. Hochschild, Eddy current testing: A new tool makes inspection automatic,
Control Eng., I, 35-41 (1954).
8. J. N. Wilson, Nondestructive testing of nuclear reactor components, ISA J.,
4, 322-325 (1957).
9. J. A. Sargrove, Automation in component testing, paper presented at the
International Symposium on Electronic Components, Royal Radar Establishment,
Malvern, England, September 1957.

B

MANUFACTURING PROCESS CONTROL

Chapter

5

Materials Handling
A. J. Schenk

5-01

1. Conveyor Systems
2. Problems of Conveyor Controls

5-02

3. Multiple Drive Conveyor Requirements

5-05

4. Basic Electrical Controls

5-09

5. Conveyor Control Circuits

5-14

6. Synchronized Conveyor Systems

5-17

7. Control Systems for Synchronization

5-20
5-23

8. Selective Dispatching Systems
References

5-27

1. CONVEYOR SYSTEMS

The meaning of the term "materials handling" has expanded tremen~
dously in tho last few years. It includes such diverse equipment as lift
trucks, skid platforms, hand-pushed monorail, gravity roller conveyors,
and many types of powered product movers. This chapter will discuss
only a few types adaptable to automatic control for integration into more
or less complex systems and commonly called conveyors.
Applications. Conveyors are used for movement and/or storage of
parts or products between manufacturing operations, through processing,
assembly, testing, and packaging and to warehouse or shipping point.
Conveyors can control production rate by simply varying speed of system to compensate for manpower available, etc. They provide the tie
between automatic machines to make an automated system. Conveyor
applications can be broken down into four rough classifications:
5-01

5-02

MANUFACTURING PROCESS CONTROL

Materials such as coal, sand, ores, chemicals, and
grains. Using troughed belts, buckets, pneumatic, and similar types of
conveyors.
2. Package handling. Cartons, boxes, tote pans, and similar packages
for products. Using gravity roller and wheel conveyors, flat belt, live
roller, pusher bar, slat, chutes, and similar types of conveyors.
3. Trolley and chain conveyors based largely on rivetless type chains.
Includes trolley, floor pusher, power and free, and similar types.
4. Special designs for handling products between machining operations
including reciprocating transfers, turnovers, rollovers, and lifts operated
by air or hydraulic cylinders.
1. Bulk handling.

Design of Automatic Controls for Conveyors. In general, there is
no such thing as a "standard" conveyor. There are standard components,
but every conveyor is tailor-made to perform a certain function in a
specific place. System design requires:

1. A thorough knowledge and analysis of devices controlled. This includes their limitations as well as potentialities. Equipment that is suitable for precision machine tools may be totally inadequate for less precise
conveyors without expensive added operating means.
2. Close cooperation is required between mechanical parts designer and
control designer to assure that control elements can be incorporated in
correct positions in basic design. The control requirements frequently
dictate elements in the mechanical design. Too frequently, the control
design is left until too late, the designed mechanism is inflexible, and expensive rework is required to make the machine operate.
3. Design of controls is a logical step from a complete description of
mechanical sequence of functions required. Simple sequence functions
using limit switches, wipers, pushbuttons, relays, solenoid valves, and
motor starters are used to control most conveyors.
4. 'Vhen more units are coordinated together, centralized panels with
provisions for starting, stopping, speed changing, and condition signaling
for each unit may be required. The special requirements for multiple
drivers, synchronization for automatic transfer between several conveyors, and selective dispatching require more challenging consideration.
2. PROBLEMS OF CONVEYOR CONTROLS

General. Application of electrical controls for operations of conveyors
poses problems which are not present in the control of precision machines.
Even large transfer machines, while consisting of a large number of parts,
will occupy relatively small, compact areas. Conveyors often operate
over very large areas. Individual conveyors are seldom less than 100 ft

MATERIALS HANDLING

5-03

and are frequently 2000 to 10,000 ft or more long. Conveyor systems
may extend into several buildings and on more than one floor. Large
portions of systems may be overhead in otherwise unused space and are
relatively inaccessible.
Conveyors are seldom assembled and tested except in their permanent
location. Once a conveyor is installed, the plant must get into production quickly so there is a minimum opportunity to make changes or adjustments. This requires careful engineering to ensure immediate operation. Frequently adjustments must be made at expensive overtime costs.
Mechanical precision is not a general characteristic of conveyors. Basic
designs have been fixed by usage and proved adequate before the advent
of special controls now added. Many conveyors are designed around
drop-forged rivetless chains. These chains have least weight and cost for
their strength. Most are heat treated while the larger sizes may be made
of alloy steel for greater strength.
Few chains are made to precise pitch. Dimensions of drop forged chain
change slightly as forgings and trim dies wear. Normal runout is about
1 %, in. per 10 ft of #458 chain, the most commonly used size. Rough
spots wear down quite rapidly during first weeks of operation. Then wear
and elongation changes remain about constant at a slower rate. Chains
can elongate as much as 5% before they need replacing.
Attachments for loads can normally be spaced only at multiples of
twice the chain pitch. Special provisions may be made for multiples of
pitch spacing at higher cost. If load spacing is important, it may be
necessary to select a different type of chain.
All parts of these conveyors have loose fits and are normally not guided
closely. Load carriers are seldom exactly alike and can hang at various
angles and be out of line horizontally or vertically or both. This creates
problems when attempting to operate limit switches and signal devices
from conveyor parts.
Overload protection for conveyor drives must be provided when they
are driven by electric motors. Those driven by pneumatic or hydraulic
power can usually stall safely without damage.
The most effective method utilizes a floating drive. The drive machinery is mounted on a platform that rests on wheels in a fixed frame.
Chain pull is counteracted by springs so that floating frame position is a
measure of force exerted. If chain pull exceeds designed value, a limit
switch is operated to stop the conveyor. Drive frame can still travel
farther to absorb energy of "drive parts without damage. This method
is independent of speed.
Fixed drives can use an adjustable slip clutch with underspeed switch
to indicate stall, overload cutout with parts to separate and operate a

5-04

MANUFACTURING PROCESS CONTROL

limit switch, or overcurrent relays. Signals from motor current are unreliable if a mechanical variable-speed device is used between motor and
speed reducer.
Slack chain control must be provided since any chain will elongate
from wear. If a rivetless chain is permitted to run too loose, pins may
fall out or center links slip and lock crossways and cause jams on turns
and drives.
A takeup is usually a 180 0 turn mounted movably so that effective
track length can be changed. Movement is controlled by screws, screws
with springs for manual adjustment periodically, or automatically by
spring, counterweight, or adjustable pressure air cylinders.
Travel of takeups is limited by the necessity of carrying chain and
loads across a slip joint between the fixed and movable tracks, and providing sufficient strength in a limited space. Minimum travel must be
sufficient to take out at least two pitches of chain and still permit chain
coupling.
When equal load spacing must be maintained, provisions are made to
move the whole takeup frame bodily each time the limit of travel is
reached. It is usually necessary to cut the track and insert new sections to
fill the gap. Eventually one complete space will be removed and the
process started over again. A conveyor must be out of production while
changes are made.
Location of takeups is important, particularly for multiple drive conveyors. They are usually located at points of lowest tension or elevation.
For example, a point past a drive exit between a dip and a rise would be
ideal.
Automatic takeups must have sufficient power to keep a chain tight
under any variable conditions of loading. This means that there may be
several hundred to more than 1000 lb initial tension in a chain. Since
each horizontal turn or vertical bend adds 2 to 10% to chain tension on
entering side, excessively high chain loads can develop.
Conveyors passing through ovens should have takeups located nearby
so that when the heat is turned off and the chain contracts on cooling,
it can be released to the oven with little force. Oven turns have been
pulled down or damaged by lack of attention to this point.
Conditions of loading of a conveyor can affect selection of control
elements. Most assembly conveyors are uniformly loaded. Those passing through units for chemical treatment, painting, etc., are frequently
cleared each day and reloaded the next day. Storage types at times are
hea vily loaded in sections only.
The problem is greatest when a conveyor passes through ovens and/or
has many vertical bends and high lift loads. Chain pull lift load at the

MATERIALS HANDLING

5-05

top of a vertical bend due to loads on the incline is equal to the live load
per foot of conveyor times vertical height of lift. The difference between
the lift load from empty carriers and that from loaded carriers is frequently much more than friction load for the entire conveyor.
Under some conditions there may be runaway forces tending to overspeed drives. If a conveyor must be stopped, drive brakes are required.
Improper lubrication can double or triple normal drive pull requirements. This is important when variable-speed, constant-torque motors
are specified.
Most conveyors can be readily rearranged, shortened, lengthened, or
combined. Model and method changes usually require conveyor rearrangements. Loads may increase in size, weight, and spacing. Controls
and components should be selected for best adaptation to change as well
as for standardization.
Adjustable speed requirements affect control means. Single drive
conveyors usually use a variable-speed pulley or a variable-speed transmission either adjusted manually by handwheel on the drive or remotely
by speed-changing motors.
Conveyors with multiple drives or those which must run at precise
speeds or in synchronization with other units require more elaborate
controls.
3. MULTIPLE DRIVE CONVEYOR REQUIREMENTS

Long or heavily loaded conveyors require more than one drive to keep
chain tensions within allowable limits. For long life and reliability it
has been found to be best to keep working tensions below 4 to 6% of
ultimate strength. EXAMPLE. For a #458 chain with ultimate strength
of 48,000 lb the maximum load is 2500 lb. Higher loading may be used
with slow speed, few turns, and little change in elevation.
Multiple drives permit use of lighter, standard construction and practically unlimited length. Surge, which would cause trouble through paint
spraying, for example, is reduced by low chain pull and by strategic
location of drives.
The common problem in all multiple drive applications has been control of slack chain without building up excess tensions and overloads.
Conveyors passing through ovens must have means to take up elongation
of chain from heating and to relax when chain shrinks on cooling. Also
chains continually wear. For example, a typical 7800-ft conveyor will
lengthen by 1 in. every 8 hours.
The classic method requires that drives have high-slip characteristics,
that is, will slow down under increased load. Any difference in speed
will develop an increased load on the faster running drive and decreased

5-06

MANUFACTURING PROCESS CONTROL

load on the slower. This causes the faster drive to slow down and/or
the slower drive to speed up.
Constant Speed. If chain can be kept taut at all times, even standard
a-c motors will divide loads. Constant-speed conveyors can utilize
high-slip (8 to 13%) a-c motors. Tests show the load on each motor
will be equal even though chain tensions at the drive may be widely
variable or different. High-slip motors work best with moderate drive
pulls.
Variahle speed, particularly with remote control of speed changes,
becomes a more complicated problem. Drives must divide loads but
not necessarily equally. Drives can seldom be located at ideal points
with equal loading because of clearances, ovens, process equipment, and
other interferences.
Control Methods. Change of drive speeds in response to chain pull
variations may be made (1) by developing excess forces at drive or (2)
by using a feedback signal from a control takeup in conveyor path. The
first method has been used most frequently but requires manual adjustment of elements for correct results. The second can automatically
compensate for variations in load, speeds, and components automatically.
The method selected depends on types of variable speed devices used on
the drives.
Driving means used have been as follows:
1. Constant-speed, normal torque, a-c motors with variable speed
transmissions.
2. Variable-frequency, high-slip a-c motors.
3. Direct-current motors with high-slip characteristics, either by compound winding or armature dropping resistors and shunt field control.
4. Eddy current clutch motors with' electronic control with torque
limiting and adjustable slip characteristic features.
Balancing by Force
Constant speed a-c motors with variable-speed transmissions are
used with floating drive frames. Where speeds are changed only infrequently, a mechanical rigging between the transmission adjusting screw
and fixed frame causes speed to vary with load owing to speed differences.
Hand wheels can disconnect the balance rigging so that a base speed can
be set on each drive simultaneously. Drives are adjusted for best operation. Mechanical balancing makes necessary speed adjustments.
Floating drive frame position can also be used to operate a potentiometer slider to provide a signal for servo motor electronic control of
variable-speed transmission to change speed in response to varying chain
loads and also by remote control. One drive is made a master whose

MATERIALS HANDLING

5-07

speed is changed by manual switch. Tachometer generators on variablespeed shafts of drives provide velocity signals. Follower drives match
speed and preset drive load relationships to master drive.
High-slip (8 to 13ro) a-c squirrel cage motors supplied by a
variable frequency 3-phase alternator may be used. The alternator is
driven by mechanical speed changer from a constant-speed motor. Voltage varies approximately with frequency. Standard 220-volt, 60-cycle
motors can be operated over a range of 20 to 100 cps. All motors are
connected in parallel with alternator through thermal overload relays.
Conveyor starts and stops with alternator.
Drives must be located for nearly equal loading. Care is required in
matching motor size to load. Best results are obtained when motors are
nearly fully loaded.
Direct-current motor drives require a motor generator set and operator's panel for each conveyor to supply variable armature voltage.
Motors are compound wound for 10 to 20ro slip or are shunt wound
with armature voltage dropping resistors to vary speed with load.
Excitation for generator and motor field is supplied by belt-driven
generator, electronic tube, or dry type rectifier. The generator proyides
for safe stopping on power failure when dynamic braking is used.
Motor armatures are connected in parallel with each other and in
series with generator armature and d-c contactor contact. A thermal
overload relay and ammeter is provided for each motor.
Motor shunt fields are connected in parallel to the exciter. Each is
provided with a series vernier rheostat for adjusting drive balance. Increasing field resistance causes motor to tend to .run faster, forcing it to
take more load to hold its speed down to that of the other drives. Ammeters sh9W drive loads and show operator wh~m correct adjustment is
made. Experience will determine if conveyor "runs best with equal or
unequal drive loads.
"
Conveyor speed is controlled by a rheostat in series with the generator
field. This controls armature voltage, and speed is approximately proportional. vVhen more exact speeds are required, generator field may
be controlled electronically.
Motor and generator sizes must be carefully considered. Motors
operate in the constant-torque range below base speed theoretically, but
when shunt field rheostats are used, base speed increases and torque
decreases. This can be compensated for by increasing ratio of V-belt
drive between motor and speed reducer. In calculating drive speed ratio
use motor base speed plus 10 to 15% when conveyor travels at maximum
design speed. This will assure ample torque and permit slow down to
minimum speeds.

5-08

MANUFACTURING PROCESS CONTROL

Note that motor manufacturers may indicate an 8 to 1 speed range
but that continuous operation at minimum speed and full load is not
recommended. At extremely slow speeds, regulation is very poor and
heating becomes a problem. Best results are obtained when normal
probable speed is near base speed.
Since cost of motors and generators rises rapidly with size, there is
sometimes pressure to keep them as small as possible. This leads to
overloading and poor operating conditions develop. Many companies
now specify that motor generator and control be large enough to supply
at least one additional drive. Otherwise if conveyor requires an extension, new equipment would be required.
Eddy current clutch motors with electronic excitation can be used.
Electronic control matches output speed as indicated by builtin tachometer generator with reference voltage from manually set potentiometer.
Torque-limiting and sensitivity circuits permit matching drive loads as
indicated by motor current ammeters. Each control is kept electrically
separate. Reference potentiometers for the drives are ganged. Flanking potentiometers provide individual adjustment.
One control is adjusted for close speed regulation. Other drives are
set with lower sensitivity. Two sets of control wiring are required. One
is used for motor starters with interlocks with electronic control panels.
The other, interlocked with control panel time delay relays, controls
the on-off energization of clutches.
Balancing by Feedback
Control takeups following all but one of several drives on a conveyor
provide means to operate a feedback signal to synchronize the drives.
Any difference in speed between two drives will cause the takeup between to move. This movement, coupled to a potentiometer or rheostat
slider, provides signal to correct the speed of the drive feeding chain into
the takeup to stop movement.
A rheostat in series with the motor shunt field can be used with d-c
motors. A potentiometer, in parallel with an adjustable tap resistor in
control panel, provides a signal between slider and tap for electronic
servomotor speed control with mechanical speed changer. Movement of
control takeup need not be more than 3 or 4 in.
Limit switches operated by extreme travel of takeup are recommended
in drive control circuits and are provided with signals on a central panel.
This ensures stopping the conveyor and trouble point indication before
damage if a conveyor jams or a control component fails.
A long travel takeup should be used after the one uncontrolled drive.
This is called a slack chain takeup and accepts all the elongation of

MATERIALS HANDLING

5-09

chain due to wear or heat expansion. It must have sufficient travel to
compensate for movement of control takeups to synchronize drives, temperature change length, and wear elongation for a reasonable time.
Location of control takeups are important to ensure that movement
will be due to speed difference only. Takeups may be operated by
counterweights or air cylinders with adjustable pressure regulator.
Takeup tension need only be sufficient to keep chain stripped from drive.
As long as control takeup is neither fully open or closed, tension is just
right. The control takeups may be built into either 90 0 or 180 0 turns.
This method is fully automatic and controls drive speeds regardless
of variations in speed or load. Minimum chain pull is developed since
each drive pulls its section of conveyor only. Drive loads can be unequal and different sized drives may be synchronized. Since no manual
adjustment of individual drives is required, production supervisors can
be permitted to make speed changes.
Follower drives must be capable of running both faster and slower
than the master at extremes of production speed. Rheostats for d-c
drives have value to raise base speed of motors by 200/0. The master
drive has manual field rheostat to raise its base speed by 100/0. Control
rheostats, by field control, can make follower drives run up to 100/0
faster or more slowly.
The layout of some types of conveyors do not permit use of control
takeups. These conveyors then must use one of the force methods with
manual adjustment.
4. BASIC ELECTRICAL CONTROLS

Controls for conveyors and automation should be designed with emphasis on the requirements of the men who must keep the systems operating. The best approach is to have a system that will automatically stop
safely in case of failure, and provide signals to pinpoint the area of the
trouble. Usually more time is required to locate the cause of the failure
than to correct it.
Modern factory equipment is becoming more complex and diversified.
Conveyors add to the complexity. It is difficult to recruit and train
enough qualified maintenance people. If stoppages are frequent, maintenance men learn exactly what to do. The more reliable a piece of equipment is, the more important it is to spot troubles quickly. If maintenance
personnel changes frequently, or if the regular maintenance man is away,
the foreman or some other mechanic must take over. Then it is an advantage to have controls that are easy to understand, to maintain, and
to service.
The cost of down time in modern plants is prohibitive. The savings

5-10

MANUFACTURING PROCESS CONTROL

of even a few minutes in restoring production operations will pay for a
great deal of wiring and extra signals. It is sometimes difficult to sell
this idea to purchasing departments or those with little experience in
operating production machinery. Conveying systems cannot be installed
in duplicate as is possible with machine tools. A stoppage at one point
stops the whole system and all related operations.
For example, an automobile final assembly line may be set for 60 jobs
an hour. One minute lost means bne car that may not be built that day.
Union rules generally do not permit speedup to make up for lost time
or production.
Joint Industry Conference (J.I.C.) Standards

These standards provide an accepted guide for Materials Handling
Control. The prime purposes of the standards are to:

1. Reduce maintenance and increase reliability.
2. Increase safety for operating and maintenance workers.
3. Reduce down time by making control functions easier to trace, understand, and repair.
Most companies try to standardize on only a few makes of motors and
control components. This reduces their spare parts inventory. It is important to determine, in writing, just what will be acceptable in a particular plant.
Enclosures must be semi-dust-tight with gasketed openings. There
can be no knockouts to open accidently or openings through which
liquids or dust can enter. Since most control panels are custom designed,
this requirement adds little to the cost. Disconnect switches must open
both power and control circuits.
Enclosure size and layout of components should permit installation
later on of at least 15 or 20% more relays and terminals. This gives the
engineer an opportunity to take care of inevitable errors or the requiremen~ of future changes in the field. Extra contacts on relays are good
insurance. Relays with contacts interchangeable for either normally
open or normally closed reduce costs.
Control voltage is usually specified as 110 volts a-c. There are many
more components readily available and stocked for 110 volts a-c than
any· other voltage. This voltage is high enough to ensure good contact
and relay operation even with long control leads. Standard incandescent
lamps can be used for local signals at emergency stop pushbuttons.
Panel Wiring. All external wires must come to numbered terminals
in control panels. All internal wires must be marked with numbered
labels on each end. All wires must be stranded and use acceptable

MATERIALS HANDLING

5-11

crimped-on terminals. Color coding of wires for different functions is
required. Fiber wiring channels with removable covers are preferable
to laced cables for ease of installation, change, and tracing. Relays,
push buttons, and other similar components in a control panel should be
marked with labels corresponding to diagrams.
Relays should preferably be identical. Four pole relays will take
care of nearly all normal conditions. If more poles are required, it is
better to parallel added relays. Generally, industrial type relays have
given little trouble, and provisions for plug-in types are not necessary.
The principal difficulty with relays has been dirt in normally closed
contacts.
Signals. Limit switches operated by machine parts or products are
generally used for signals to control functions.
The control engineer must work with the mechanical designer to be
sure that limit switches can be located at the proper points. Frequently
some mechanical part is already in the way when the field electrician
starts to adjust limit switches. Then a compromise must be worked out
either to change the original part or control diagram or both.
It is recommended that limit switches be mounted on clamp-on brackets
or in other ways to allow for plenty of adjustment. Switches should be
designed so that accidental reversal cannot cause damage to the operating arms or plungers. Timing of operations is usually based on· the
position of the limit switches.
Standard machine-tool type limit· switches either require too much
movement to operate the contacts or have too little overtravel, or the
operating arms are too short to work directly off conveyor parts. This
requires additional operating arms and cams in special mountings. Some
limit switches are designed especially for conveyor work. These have
(a) heavy operating shafts turning in ball beari~gs, (b) extended arms
up to 15 in. long, (c) shorter travel to operate, and (d) up to 90° total
travel. This permits the arms to be made cam shaped so that switch
operation will be the same regardless of the direction of travel of parts
past the arm.
It is desirable to restrict the number of types of limit switches used on
a system. Also, it is preferable not to use more than one normally open
and one normally closed contact on a switch. If more contacts are required, use relays operated by limit switches. Each switch can be wired
exactly the same with a 4-conductor cord and lock type cap so that prewired switches can be stocked. A permanently wired receptacle located
near the switch position is wired for the correct connection used.
Limit switches are more likely to fail mechanically than electrically.
In case of failure, it is only necessary to remove and replace the faulty

5-12

MANUFACTURING PROCESS CONTROL

switch, plug it in, and adjust the operating arm to get the machine hack
into operation.
"Wiper" circuits have been developed to reduce problems of limit
switches. Standard llO-volt relays are used in series with the primary
of a specially designed transformer. The secondary of the transformer
can be wound for 5 to 24 volts. With proper values in the transformer,
its impedance, with the secondary open, will prevent the relay from
picking up. When the secondary is shorted, its impedance is lowered,
and the relay is energized. See Fig. 1.
k-------

lID-volt, 60-cycle

-----~

CRl

~
I

I

I
I

I
I

wa}

Wb)
on carrier

CRl

Sol. valve

~I- - - - - - - - - - - - - . ~

~'-~Lj ~I' tfr~~~i

Tab on conv.
(grnd.)

FIG. 1. Typical "wiper" circuit selector for conveyor carriers. Short circuiting secondary of transformer causes relays to energize. See Table 1 for symbols.

The secondary is connected to insulated wipers which are contacted
by the conveyor parts. Two or more wipers can be connected by selectively controlled patterns of contacts for different combinations of
signals. Or one side of the secondary can be grounded and one wiper
can contact any metal part of the machine.
Wipers are plated steel springs supported at an angle of about 45°
to the direction of travel by pivoted arms which lift clear if parts reverse.
No movement is required for operation. This permits a variation of

MATERIALS HANDLING
TABLE

1.

SYMBOLS USED IN

FIGs. 1

o-()--o

Relay, starter operating coils

0-1/--0

Normally open relay contact

'ik-o

o

5-13
AND

2

Normally closed relay or
thermal overload contact

o--fy-o

Solenoid coil

}_{J

Disconnect switch
Normally open limit switch
Normally closed limit switch
Normally open, momentary contact pushbutton
Normally closed, momentary contact pushbutton

-Q..Lo-

.... _+-=.::L..
--<>

Maintained contact pushbutton

0--

Fuse
Control or voltage transformer
Signal light, letter indicates color:
ar:nber, green, red, etc.

o--ill---o
"
/

Local light, adjacent to pushbutton
or other equipment
Solid line to show panel wiring
Broken line, connections external to panel
Contacts and coils of same n:;lme
operate together

plus or minus ~ in. of contact alignment for positive contact. Voltage
at the wipers is less than 24 volts, and it is safe to use exposed contacts.
'Vipers can be connected with simple open wiring. This reduces cost of
installa tion.
This type of circuit is particularly adapted to automatic loading and
unloading of overhead trolley conveyors and power-and-free conveyors.
'Vipers have long life and are cheap and easy to replace. The greater
latitude for variations in operating positions reduces problems of field
adjustment. Combinations for shorting the transformer are infinite.

5-14

MANUFACTURING PROCESS CONTROL

Relay contacts and manual selector switches can be added in the secondary circuits.
Other means of providing signals include photoelectric relays, with or
without modulated light, proximity limit switches using radio-frequency
circuits and operated by absorption of energy by a passing metallic part,
and magnetic pickup devices. These are usually more expensive and
subject to failure of tubes and lamps. The elimination of physical contact warrants their use with proper safeguards in same applications.
Safety circuits should be designed to prev~nt damage to personnel or
equipment. Hazards should be analyzed for the worst conditions. Emphasis should be on keeping machine running, 'and not stopping until the
last possible moment. It may not be necessary to stop so often. This
requires the machine to stop quickly on signal and indicates drive motor
brakes. If a machine stops before parts jam, it is usually easy to clear.
If parts are damaged, repair will require a costly down time.
5. CONVEYOR CONTROL CIRCUITS

Separate circuits should be used for distinguishing between overload
or jam conditions, and production stops. The first type usually requires
the assistance of a maintenance electrician or a mechanic. The trouble
must be located and cleared, and then a r,eset pushbutton is operated
to restore service. See Fig. 2.
Production stops are made with maintain-contact type pushbuttons
so that the system will start immediately after the button is returned to
the run position. Local indicating lights, with about 25-watt off-white
lamps, can be located above and adjacent to pushbutton stations. They
should be located so that they may be seen from a distance.
Circuit Checking. It is desirable to be able to monitor circuits from
a central point. One method is to use the back contacts on emergency
run-stop pushbuttons and limit switches to operate signal lights. This
does not guarantee, however, that the actual operating contacts are functioning. Also, a large number of signal lights w~th nameplates is required.
At least one wire from a junction of each pair of contacts in a circuit
can be brought back to the central panel. A tap switch with the center
terminal connected to a small signal lamp can be used to sample each
contact. A name card identifies each point. To check the circuit, the
tap switch is rotated until the light shows. Then the next contact in
the series is the one which is open. Operating circuits are checked
quickly.
Jams on conveyor systems must usually be cleared by reversing the
drives. Jams may be caused by parts falling off, damaged carriers, or

MATERIALS HANDLING

5-15

malfunctioning of a component. Drives can be reversed by manually
operated reversing switches with extra contacts to block out holding
circuits. A motor should run in reverse only as long as a jog pushbutton
is held in. Reversible motor starters may also be used, with proper
precautions.
Decentralized Versus Centralized Systems

Location of controls will have a bearing on their design. As a general
rule, control panels should be located so that a man working on the
controls can see the operation controlled.
vViring installation costs are usually reduced with a number of small
control panels at correct locations. Each unit has its own fused disconnect switch for isolation. Control components on a conveyor can be
marked to correspond with the diagram in the panel. Frequently, mechanical breakdowns can be located only by means of the electric circuits.
Visual check of conditions at the point of stoppage will frequently show
the difficulty so it can be corrected.
With a decentralized system, the power supply for various motors
may be taken from the nearest distribution duct. All control circuits
should be taken" from the same lID-volt transformer source and distributed to the various unit panels. This permits fewer wires to transmit
signals. Branch circuits should be adequately protected with fuses or
circuit breakers to permit isolation of faults.
A central panel is frequently provided with means for starting and
stopping various conveyors in the system and showing area operating
condition. A map of the system may be included. It is not necessary
to show all the individual points of stoppage but only which local panel
has trouble. This permits the maintenance electrician to go directly to
the area involved.
A centralized system would have all controls grouped in one area
remote from conveyors controlled. Some customers seem to prefer this
method. This is particularly true when using d-c equipment with motor
generator sets. This involves longer wiring for large systems and problems of communication with the areas in difficulty.
A telephone system can be readily installed with a jack in each panel.
The maintenance electricians carry portable telephones with a jack to
plug in at any point. The telephone wires can be run in the same conduits with the control wires. Thif:l permits electricians at various locations to communicate or to call for help from the maintenance foreman.
A signaling device preferably should be included with the telephone
circuits.

r

_

I~~-

i---r-i-h
I
I
I

0.

/ Combination, fused,
motor starters with
~ IIO-volt tran·sf.
near drives

/

I

Ma

Brake
motor

I
I

I
I
I
I
I
I
I
I

L.

1

I
I
I
I

Brake
motor

I
I

o.
:-- C If-J==~l~OV'-;IV ;If LJ

J

 - = - - G C CRRa
R t rI
Drive
L.S.a
CRRa

Drive
L.S.b

CRRb

(a)

FIG. 2. Typical circuit for two-drive conveyor with automatic transfer controls, showing means to separate normal
operating stops from trouble stops and interlock of power for drive motors with control. See Table I for symbols.

~

Z

c:
"T1

»
n

--I

c:
2S!

Z

G)

-c

:::0

o
n
m

Ul
Ul

n

o
Z

--I
:::0

o
r-

MATERIALS HANDLING

5-17

1------- IIO-volt from system transformer ------I!

(b)

Motor starters

------

r---'

I

I I

-~

,---,

I

---+----i

II ~~
WD A II
II ~L:
WD
II
P.B.!
P.B.2
P.B.n
-~- +I~+ -~- -rrrT -~....."". L __ ...J
~ L __ J
""I-.....

"~

-----0

0'---- -

-Q--

Tap switch
and light
Operating
relay
Local lites
near P.B.
(typical)

FIG. 2-(Continued)

6. SYNCHRONIZED CONVEYOR SYSTEMS

A number of individual conveyors may be synchronized to permit
manual or automatic transfer of product or product supporting carriers
between them. Conveyors may be of different types operating at the same
rate but at different speeds and load centers. A number of synchronized,
separate conveyors are used, rather than one long conveyor, for one or
more of the following reasons.

1. Separate periodic operation of one or more conveyor units. Chemical surface preparation processes require that parts must not be left in
them when system stops more than a short period. When some types of
paint are used, sprayed parts must pass into or through an oven before
stopping for the night.

5-18

MANUFACTURING PROCESS CONTROL

This requires means fo,r separate operation of the conveyor units before
or after main system stops and storage for the parts removed.
2. The conveyor secti'on subjected to chemical actions, paint, etc.,
should be as sh.ort as possible.
3. Different load spacing may be required. A paint spray operation
requires that loads be separated but the following oven conveyors require
closer spacing for economy;
4. Different types of conveyors. Parts might be suspended from an
overhead conveyor and .d~posited on castered trucks drawn by a floor
conveyor or vice versa. Conveyor position is synchronized longitudinally,
and transfer is effected by changes in elevation of one o.r both conveyors.
5. Feeder conveyors bringing special parts to an assembly line ,may be
synchronized with main conveyor to assure matching colors, for example,
at a correct time. Transfer of parts would normally be manual.
Requirements for Synchronized Conveyor System
1. Equal load spacing must be maintained on each conveyor. Special
provisions must be made so that no slack chain may be removed unless
a complete space is taken out.
2. Drives must be provided with means for remote control speed
changing and with brakes for quick, uniform stopping.
3. Controls must provide for interlocking all units to run and change
speed together. They must set the speed of individual conveyors to
maintain position relationships, permit manual emergency operating and
starting, and provide signals to show malfunction or local stoppage.
Components of the control will vary with the types of conveyor drives
used.
4. When transferring between two conveyors end to end, provisions
must be made for positively pushing the carrier across the gap ,between
them. The delivering conveyor pushes the carrier beyond the point where
receiving conveyor can pick up the load, and then disengages. The carriers stand momentarily until picked up by the receiving conveyor.
Clearances between the carriers determine the allowable tolerance for
conveyor synchronization to prevent either jamming of the carriers or
missing the take-away pusher.

Use of Synchros

Position signals are obtained by synchros driven by individual conveyors. They should preferably be located adjacent to transf.er or junction points to minimize effects of chain length change.
The master unit can be one of the conveyors or a separately driven,
interlocked unit. A synchro transmitter is used on the master with

MATERIALS HANDLING

5-19

synchro control transformers on the followers. Some conveyors may be
controlled as followers and act as submasters for other units.
Synchros may be driven by small caterpillar chain units engaging
main conveyor chain. This permits location at the most advantageous
points. Gearing is provided to make the synchro turn exactly one or
more revolutions per conveyor space. See Fig. 3. The number of revolutions of synchros per space is determined by length of space and relation-

FIG. 3. ,Caterpillar drive for synchros with change gears to permit respacing of conveyor loads. A similar unit may be used to drive multiple cam switches and may
also be used for synchronized conveyors. (Courtesy Jervis B. Webb Company.)

.,

ship to the desired accuracy and practical sensitivity of the control means.
In some systems, particularly with very slow speed (3 to 24 inches per
minute), better results may be obtained by higher synchro speeds or more
revolutions per space. Much depends on the dynamics of the system used.
Most synchronized systems have been used with loads in all spaces.
This means that control cannot be permitted to find its own locked-in
synchronizing point by moving ahead or back one space. Some means is
required to indicate out of synchronization and also exact synchronizing.
A sensitive relay with adjusting rheostat ~nd rectifier placed across
the output of the control transformer is energized when the error is more
than a preset amount. It has little effect on the electronic circuit at
normal operating error. However, there is zero voltage at both 0 0 and
180 0 • If used with several revolutions of synchro per space, the number
of like indications increases.

5-20

MANUFACTURING PROCESS CONTROL

A second set of synchros driven at one-half revolution per space and
connected to a similar signal relay provides an exact signal. Contacts
on" two relays in series provide a signal only when both are at zero voltage. Relays can be provided with extra backlash requiring higher voltage
to pick up and will drop out closer to true zero position. We term these
"junction relays." They provide contact for the interlock circuit to stop
the system if for any reason it goes out of synchronization, and also to
signal for manual jogging of units back into step. Also they can be
used to stop conveyors automatically in synchronization after separate
operation of one or more units.
Correct transfer between conveyors can be assured only when units
are synchronized between certain limits. This means that the system
should run automatically only when synchronized. Out-of-step condition can be caused by mechanical jams, failure, misadjustment of control
components, etc. This condition should stop the system and indicate
the point of trouble so that the electrician can find it quickly. A signal
should indicate whether the offending unit is ahead or behind. A manual
control with a pushbutton can be used to move the conveyor into position
and restart the system. The electrician can then watch the operation to
determine the cause of the trouble without interfering with production.
Continual starting and stopping of new systems has been a considerable
source of difficulty. When a new system is installed, or model changes
are made, there is usually a period during which the system will not run
continuously. Frequently a system may be stopped several times per
space. It is difficult to make all conveyors stop in the same length of
time. If, after starting, a conveyor is permitted to run long enough for
the controls to correct the position, there is no trouble. Continual
jogging will eventually cause enough error to trip the junction relays
and require manual repositioning of units.
It is possible to add a discriminator circuit and necessary relays to
permit first the starting of units that are behind, and the starting of the
others at the correct time. This adds to cost.
7. CONTROL SYSTEMS FOR SYNCHRONIZATION

The two systems most used have been (1) a modified Ward-Leonard
d-c system with motor generators and (2) drives with electronically controlled mechanical variable-speed transmissions and a-c motors.
Direct-Current Motor Systems
Control Methods. A separate motor generator set is usually used with
each conveyor to be synchronized. Speed is controlled by varying the

MATERIALS HANDLING

5-21

generator field completely or in part electronically. A master timing
control with feedback from a synchro on the conveyor sets the pace.
Three common methods use (1) an electronic rectifier to supply all the
generator field, (2) double windings with a manual rheostat in one (the
other winding is controlled by a buck or boost amplifier), and (3) an
electronic circuit to operate a motor-driven rheostat in series with a
manually set rheostat. The last two methods permit limiting the amount
of speed change that can be made to bring the conveyors into synchronization. Conveyor speed should not change more than about 10% above
or below the preset speed.
vVhen the individual conveyors in a group can run together always, it
is practical to use one motor generator set for them all. Shunt-wound
motors are used, and individual speeds are varied by shunt field control.
A rheostat is used in the master conveyor motor field to raise its base
speed so that the drive motors of the follower conveyors can run slower
than the master. The shunt fields of the follower drive motors use electronically controlled separate field power supply. The master conveyor
has its speed controlled by reference to the master timer. The junctions
between the master and follower conveyors are equipped with synchros
to give position signals for control of the follower drives. Changing the
generator field voltage raises or lowers the speed of the system as a whole.
Manual operation in emergencies should be provided. The standard
excitation of the motor generator set can be connected through selector
switches and manual rheostats to replace the electronic controls. This
permits the maintenance electricians to switch quickly to manual control
to keep the conveyor operating while the trouble is located and repaired.
It is common practice to provide a duplicate motor generator set with
throw over switches for quick change in emergencies.

Production Speed Control

A master timer with adjustable speed can be used to set the conveyor
speed. This is a small, synchronous speed motor with change gears or
accurate variable-speed transmission to drive a synchro transmitter at
one revolution per job space. A synchro control transformer driven by
the conveyor is geared to make one revolution per job space. Tachometer generators, driven by the master timer and a conveyor drive, provide for velocity feedback. Synchros provide accumulated error signals
for an electronic control for a motor-generator field. Changing the speed
of the master timer sets the production rate. See Fig. 4.
Controls for the master timer and the conveyor are interlocked so that
they run and stop together. Provisions should be made for mauual

5-22

MANUFACTURING PROCESS CONTROL

Typical control for d-c motor generator set with adjustable speed master
timer in lower section. Magnetic amplifier controls generator field to synchronize
conveyor to master. (Courtesy Jervis B. Webb Company.)

FIG. 4.

adjustment of conveyor speeds in case of failure of components bf the
master timer.
The systems are usually used with high unit value production such
as automobile assembly., Requirements usually are that the production
rate can be set to a variation of one-tenth to one-half job per hour)n a
range from 20 to 80 jobs: per hour. When change gears are used, a very
large number are required. The Graham transmission provides sufficient power for driving" and is infinitely variable. Once adjusted, it
maintains precise speed range ratio for a long time.

MATERIALS HANDLING

5-23

Alternating-Current Motor Systems
Systems using mechanical variable-speed transmissions are well
suited to decentralized controls. N ear each drive is a standard, combination, reversible motor starter. Servomotors drive the adjusting screw
of the transmissions to vary the speed. The master conveyor speed is
set by manual operation of a reversing switch on central control.
The follower drives are controlled through amplifiers with feedback
from tachometers on the drives and synchros on the conveyor. A master
timer is usually not required. Servomotors may also be operated by
fast-slow switches.
Amplifiers for controling follower servomotors are located adjacent to
the motor starters. This permits observation of the speed control from
the panel. A selector switch marked "Auto-Off-Hand," with forward
and reverse jog buttons, is mounted in the control panel.
Zero center meters on the control panel can be used to indicate whether
a follower conveyor is running faster or more slowly, and ahead or behind, the master.
Limits of synchronization are set by the use of a sensitive relay called
a "junction" relay across the output of the control transformer. During
normal operations, the output of the control transformer is near zero and
the relay does not pick up. If conveyors get too far out of step, the
junction relay is energized to stop the conveyor system and~how a
signal light. An electrician inspects the conveyor or control ~ signals
meter, turns the selector switch to "Hand," and jogs the conveyo'r in the
correct direction until the signal goes out and the conveyor is synchronized. The selector switch can then be returned to "Automatic,"· and the
system again operates as a ·unit.
8. SELECTIVE DISPATCHING 'SYSTEMS

A selective dispatching system provides means for automatically transporting products or load ca;'triers from one or more originating points and
discharging to a number 'of destinations, along one or more main line
conveyors.
Selection means may be external to conveyors but synchronized with
them, or may be carried by product carriers. Signals from selection means
may initiate operation of deflectors, switches, or unloading devices directly
or only may warn operators that approaching units are to be removed
manually.
Conveyors Types and Applications
Belt and live roller conveyors with power-operated deflectors or

switches.

Conveyors usually run at fixed speeds, from 40 to 150 fpm.

5-24

MANUFACTURING PROCESS CONTROL

Selection means usually consist of timing "memories" with separate channel for each destination point and driven in synchronization with conveyors. All conveyors and timing means in a system must start and
stop together. Packages may be located at random and not in any fixed
relationship to the conveyor.
A typical system would handle cartons from one or more central points
to various points in a warehouse, or to a number of shipping areas for
truck or railroad car loading. Products are usually accumulated in trains
which travel as units. All parts of the train go to the same destination.
Trains tend to increase the capacity of such a system as a space of 10
or more feet is required between trains to clear switches or deflectors.
Selection of the destination is performed manually by an operator at
a central point. As the head of a train passes a given point, the operator
presses a destination button which starts a timing element. Length of
timing element travel is directly proportional to the distance between
the starting point and the destination. A signal is given to a deflector
or switch control just before the train of packages arrives at its destination.
Considerable development work has been done in marking packages
with coded reflectors to operate photoelectric relays at deflector points.
This is most satisfactory when a particular kind of package always goes
to the same destination.
Timing memories have been built with separate motor-driven timers
for each station or special multichannel mechanical timing units driven
from a common motor, or punched and magnetic tape, or wheels and
movable pins set by solenoids and operating limit switches. A recent
development by several companies is a magnetic drum providing readout signals even at zero speeds.
Packages in this type of system normally do not recirculate. If discharge station becomes full, the complete system must stop until cleared.
Timing elements are reset to starting position at end of cycle for reuse
by another train. Memory systems have been developed which allow
the packages to recirculate.
Deflectors or switches normally remain in the position last used until
it is necessary to change position either to clear or discharge the next
passing train. This permits setting up a predetermined path for as long
a train as desired. Accumulated errors are no problem as each dispatch
starts a new cycle. In a similar manner, individual packages may be
dispatched from a central station to a number of destinations. Usually
this is used for relatively small capacity operations since there must be
spaces between packages.
Trolley conveyors with automatic loading and unloading stations have

MATERIALS HANDLING

5-25

been used to distribute parts in baskets and pans, and cartons. Normally
there is a separate loading station for each part which always goes to
the same destination.
Carriers on trolley conveyors carry coded contacts indicating which
stations they must discharge into. A repeating series of carriers passes
each station. When an empty carrier of correct destination approaches a
loading station with a load waiting, loading devices transfer the load to
the carrier. The loading device is blocked out if the carrier is not empty.
A selector switch can be provided to change the destination from any
loading station by selecting properly coded empty carriers.
Unloading stations remove any package from any carrier with a corresponding code. If the unloading station is filled, a package remains
on the carrier and recirculates until the next time around or until the
station is ready to receive. If desired, an unloading station can be shut
off and the loads may stay on the conveyor and form a recirculating
"bank."
Loading and unloading stations usually have space for holding several
units, means for separating units and for moving units into or out of
the path of carriers. Most are air operated, electrically controlled. Design of the carriers and stations depends on the shape and size of parts
or units to be handled.
Controls are usually decentralized with a control panel for each station
or group of closely spaced stations. Means are required at loading stations to indicate that a unit is ready to be loaded, to show the approaching carrier classification, whether loaded or unloaded, to retract loader
when carrier is in position to receive load and safety circuits to stop the
conveyor in case of malfunction of parts. Unload stations require means
to indicate that the receiving station is not filled and to indicate a load
on the approaching carrier and its classification, and safety circuits to
stop the conveyor if the condition is not correct.
Other coding methods. Another application could have carriers manually loaded and automatically unloaded at a number of points, with
manual selectors set by the operator who loads the carrier. Or selection
can be made by pushbuttons to a timing memory device synchronized but
separate from the conveyor, as carriers pass a central point. Or selector
devices on a carrier may be set automatically from punched cards placed
on the carrier with the package, removed automatically at a central
point, decoded, and signals used to set the selection code.
Selective dispatching has been used mostly with power-and-free conveyors or overhead trolley conveyors. Contact making devices can be
disposed in various physical patterns to provide combinations. Each
signal station has a unique pattern of limit switches or wipers which make

5-26

MANUFACTURING PROCESS CONTROL

contact simultaneously. Only the correct combination will complete the
circuit to initiate a cycle .
. 'The selecting means is determined by the number of selections required;
if· carrierE:? are required to pass over more than one conveyor, signal systems .?ore mounted on the carriers. See Fig. 5.

FIG. 5. Typical power and free carrier with selector switch and contacts for fourteen
combinations. Photo shows unloading track switch leading to free track to the
right. Limit switches and "wipers" provide signals to control track switch. (Courtesy
Jervis B. Webb Company.)

By the use of wiper circuits, a change in signals can be accomplished
by using tap switches with several decks to connect contacts in various
combinations. A selector switch nameplate can be lettered or numbered
to correspond to operation names. The operator does not have to remember combinations. Selections can be made by moving contact device~ into various paths parallel to the travel or by changing connections
between contacts. A cam contact can be made to stand in one of two
positions and be set mechanically by means of a solenoid-operated plunger
as a carrier passes a selector setting station.

MATERIALS HANDLING

5-27

Overhead trolley conveyors and power-and-free can be coded by tabs
in various combinations attached to trolley brackets. Each conveyor
load-carrying point has the possible tab positions of "high," "low," "left,"
"right," "forward," "rear."
A recent development permits the use of various radio frequencies for
signals. Each signal station has an oscillator tuned to a frequency below
500 kilocycles. Carrier signal device consists of a coil tuned by capacitors
through selector switch to match a station frequency. When the coil
passes a station with corresponding frequency, energy is absorbed to provide a signal to operate a relay. This can provide a visual or audible
signal or start an automatic cycle.
Automation conveyors between machine operations usually have
separate controls. Interlocks with machine controls should be kept
completely electrically separate. Limit switches to be operated by the
parts handled or machine elements provide the signals; if relays are used,
there is always a possibility that the control of one part may be shut off
and the signal lost.
Indexing conveyors require rapid travel and accurate positioning.
Heavy loads create problems of acceleration and deceleration to prevent
shifting of positions.
Electric clutch brakes permit control of torque by simple electrical
adjustments. They require no mechanical adjustments, and torque remains constant during life of friction surfaces.
Accurate positioning requires uniformity of time of stopping. A signal
for stopping must be the same every time. A multiple cam switch driven
by the conveyor without backlash will have a uniform signal. If limit
switches are operated by parts of the conveyor that are not exactly uniform, the timing will be different.
Positioning of loads which tend to run ahead by gravity can be controlled by an electronically controlled eddy-current clutch brake unit.
This permits the use of preset speed steps for slow down before stopping.
A solenoid brake makes final stop and holds in position.

REFERENCES
1. J.l.C. Electrical Standards, Conover-Mast Publications, Inc., New York.
2. N.E.M.A. Standards Publication for Precision Snap-Acting Switches, IC 3-1959,
National Electrical Manufacturers' Association, New York.
3. Materials Handling Handbook, American Society of Mechanical Engineers, New
York,1959.

5-28

MANUFACTURING PROCESS CONTROL

PERIODICALS
1. M aterial Handling Engineering, published by the Industrial Publishing Corp.,
812 Huron Road, Cleveland 15, Ohio.
2. Modern M aterial Handling, published at 795 Boylston Street, Boston, Massachusetts.
3. Automation, published by Penton Publishing, Cleveland 13, Ohio.
4. Control Engineering, published by McGraw-Hill, 330 West 42nd Street, New
York 36, New York.

B

MANUFACTURING PROCESS CONTROL

Chapter

6

Numerical Control of Machines
J. Rosenberg

1. Types of Control Systems
2. Information Requirements

6-01

3. Numerical Codes and Their Selection

6-13

4. Storage Media Applicable to Numerical Control

6-18

6-12

5. Incremental and Absolute Control logic

6-19

6. Transducers

6-21

7. Servo System Considerations

6-23

8. Programming (Preparation of Control Tapes or Cards)

6-28
6-31

References

1. TYPES OF CONTROL SYSTEMS

Conventional machine tools in present day use fall naturally into two
maj or categories.
a. Positioning. This type performs operations only at discrete points
in its traverse. For such machines position control systems, which determine the location only of end points, have been developed. Examples
are drilling machines, boring machines, punching machines, welding machines, and riveting machines. Table 1 gives the characteristics of typical
position control systems.
h. Contouring. These machine tools remove metal continuously and
are usually required to generate a solid surface in space. Examples are
milling machines, profilers, lathes, grinding machines, and broaching machines. The slides of such tools must be under continuous control, in
order that proper synchronization for the generation of the complete con6·01

0-.

b
t-.)

TABLE 1. CHARACTERISTICS OF TYPICAL POSITION CONTROL SYSTEMS
System
A

B

C
D

E

F

G
H

I
J

Storage
Medium
4-in.-wide
punched tape

Code
Decimal

I-in.
or
I-in.
I-in.

BCD,
decimal
Decimal
BCD

P.T., IBM,
R-R cards
P.T.
P.T.

3ftin. punched
tape

Decimal

Feed Rate
(in.jmin)
100

60
80
100
Multispeed
3-loop
control
100

Accuracy
(in.)
±0.0005

±0.0005
±0.0002
±0.0002 in.jft
±O.OOOI

I-in. punched
tape'

BCD

±0.OO02

I-in. punched
tape
i-in. steel tape

BCD
Analog

90

±0.001

4i-in. punched
tape
IBM cards

Binary

50

±0.0005

Decimal

144

±0.0001

+0.0001

Type of
Transducer
Decimal shaft
position encoder
driven by
ball screw
Syncros driven by
rack or ball screw
Stepping motor
Linear or rotary
syncro
Differential transformer plus
potentiometer
BCD shaft position
encoder plus
resolver
Optical grating,
incremental
Indentation on
steel tape, limit
switch
Binarv shaft
position encoder
Gage rods plus
limit switch

Comments
on Controls

~

»
z
c
»
n

."

Open loop

-t

c

;::c

Final approach
from one
direction

Z
Q

."

;::c

0
n
m

CJ)
CJ)

n
0

Z

-t

Mechanical
followup
system

Mechanical
followup
system

;::c

0r-

NUMERICAL CONTROL OF MACHINES

6-03

tour may be assured. The characteristics of path control systems that
have been developed to satisfy the requirements of this class are shown in
Table 2.
Control Characteristics. Position controls are characterized by a
small volume of input data, simple control logic, simple nonlinear, intermittent servo actuators, relatively low costs, and modest demands on the
operator. Path control, by its nature, requires large volumes of command data, high-speed control logic, linear servo characteristics, fairly
high equipment costs, and a considerable amount of intelligence and training on the part of the user. Machine tools under continuous control remove much more material per unit time than the tools which function
only at discrete points, usually involve servo actuators of. higher power
capacity, and possess greater versatility. Most machines with path control can be so programmed as to perform operations only at specific locations. Thus position control can be considered inherent in path control
systems, although the reverse is not true.
The most sophisticated and reliable control systems of both types have
been conceived with closed loop or true servo control characteristics.
However, open loop actua.tors have been incorporated by designers of each
type of control. Open loop controls offer the advantages of simpler logic,
fewer components, and appreciably lower costs. There also exist samples
of hybrid systems, wherein two or more control loops exist, one of the
non servo type, the second with true feedback characteristics. Later in
this chapter typical examples of controls of several types will be briefly
described.
The Operator. All numerical control systems, whether for position or
path control, may be best understood if considered as man-machine combinations. Instead of requiring less judgment than manual machines,
they demand more judgment on the part of the human who programs (prepares instructions) for the control system, since commands are obeyed
without further human intervention. This concept is a natural result of
the elimination of judgment on the part of the machine tool operator, by
virtue of the presence of a complete series of machining commands on the
permanent storage medium which serves as the input to the machine tool.
The operator of conventional machining systems is expected to exercise
judgment and make many·· decisions, and it is differences in judgment
which distinguish the good from the average machinist. In the numerical
control cycle, the human who prepares the program, a man likely to be a
specially trained tool engineer, must be thoroughly familiar with tooling,
fixturing, and all the parameters which are now decided by two, three, or
more individuals responsible for the total machining process. In the new
scheme of things, the programmer passes final judgment on all these

0-

TABLE 2.

System a
A

B

C

D

E

a

Type of Path
Interpolated
Straight line
segments of
tool center

CHARACTERISTICS OF TYPICAL PATH CONTROL SYSTEMS

Interpolator
Input Data

System
Resolution (in.)

~X,~Y,~Z,

0.0002

Interpolator
Separate
from Control
No

segment
time

Straight line
segments of
tool center

~X,~Y,~Z,

Straight line
and parabolic segments of
tool center

Two points
(line) three
points
(parabola)

Straight line
and circular
segments of
tool center

~X, ~Y, ~Z

Straight line
segments of
tool center

~X, ~Y, ~Z,

6,J::...

0.0002

No

clock pulse
rate
0.001

0.001

No

Yes

(line), PI,
P 2, and
center
(circle)
0.000125

segment
time

Letters identify same systems as those in Table 3.

Yes

Type of
Comparator
Reversible
binary
counter

Type of
Transducer
Linear optical
grating

Type of
Actuator
Hydraulic
valve and
linear or
rotary
actuator

Reversible
binary
counter

Rotary
electromagnetic grating

Hydraulic
valve and
motor

Analog
voltage
amplitude

Toroidal transformer, rotary switch,
induction
potentiometer

Hydraulic
valve and
motor

Rotary
electromagnetic grating

50-cps static
magamp
anda-c
servo
motor

Reversible
decimal
counter

Analog
voltage
phase

Rotary synchro

~

Z
c:

"T1

»
n
--I

c:

::0

Z
G)

"'tJ

::0

0

nm

Ul
Ul

Rotary or
magnetic
amplifier
and d-c
motor

n

0

Z

--I
::0

0r-

NUMERICAL CONTROL OF MACHINES

6-05

variables; the machine operator can intervene only by interrupting the
cycle.
In order that the differences between position and path control may be
more readily understood, a generalized block diagram of each type of
system is shown in Figs. 1 and 2.
Position Control System. Figure 1 illustrates a typical control system
of the closed loop or servo type. The steps in the operation are as follows.
1. Programming Sheet. As in present day shop practice, the entire
operation begins with the part drawing. This is the medium by which the
designer of the part defines as concisely and unambiguously as possible
the finished workpiece. From the drawing the tool engineer or programmer prepares an organized chart containing all the locations for each slide
at which machine operations are desired. He also enters other instructions for the machine tool, such as the initiation of a drilling or punching
cycle, the indexing of a multi spindle drill turret, the turning on or off of
coolant, and other details which may be considered auxiliary machine
functions. The programming sheet should contain this information in the
sequence with which it must be conveyed to the numerically controlled
machine.
2. Storage on Punched Tape. The next step in the manufacturing
cycle is the conversion of programming data to a storage medium. This
is done by inserting the digital or numerical instructions into a keyboard
which actuates a tape punching mechanism. The keyboard may be that
of a typewriter, or an adding machine, or may be designed for the specific
purpose of numerical programming. As a block of data representing a
slide coordinate in inserted into this keyboard, it is permanently recorded,
line by line, on a section of perforated tape. Important tape parameters,
such as code, format or sequence, and mechanical size will be discussed
later in this chapter. Step by step, all the information from the programming sheet is converted into correlated blocks of perforated information on a roll of punched tape.
3. Verification. As soon as the programming phase has been completed,
the operation should be verified. This may be accomplished either by
comparing a simultaneously printed record with the original program
sheet, by playing back the punched tape into a printer, or by visual
inspection of the perforated tape, line by line.
4. Memory Readout. The completed and verified tape instructions are
then inserted into the punched tape reader, ready to assume command of
the machining operation. Since one line across the punched tape is likely
to contain a maximum of eight bits of digital information, a block is
composed of several lines of tape data. Lines of tape data must be
scanned sequentially and put into temporary (buffer) storage in such a

0.

6

0.

Input
keyboard·
and
tape
punch

Punched
tape
absolute
position
storage

~

Z

C

-n

»

()
~

C
::0

Z

Q
Machine tool instructions
Machine cycle completed

~Position

command

o"

::0

()

m

en
en
Difference

Rotary
transducer

signal

'Position
'reached

()

o
z

~

::0

orAbsolute position feedback

FIG. 1. Typical closed loop position control block diagram.

NUMERICAL CONTROL OF MACHINES

6-07

manner that the entire block will be available simultaneously to the control system. The function of the box labeled "Data Distributor" is to
transmit the line data from the reader to the appropriate regions of the
temporary storage register. A block end signal on the punched tape instructs the reader to cease operation, and initiates the control cycle.
5. Machine C antral. The complete position command is preseJ?ted
continuously by the temporary storage register to the position comparator. The other input to the comparator, which may be of the analog or
digital type, is obtained from the rotary transducer, permanently attached to the lead screw which displaces the slide. The difference between commanded and actual position is continuously presented to the box
titled "Servo Amplifier," whose output causes the servo actuator to rotate
the lead screw until the difference has been reduced to zero. At this point
the slide will be at the intended location, and the comparator will signal
that the command has been satisfied. The temporary storage register,
which in addition to position commands also contains machine tool instructions, will cause the tool to perform its machining cycle.
6. Cycle C antral. As soon as the cycle has been completed, a signal
from the machine tool instructs the tape reader to proceed with the reading of the next block of tape data. The entire operation has been simplified so that only the principles are illustrated. In most actual cases, two,
three, or more blocks of position commands representing the location of
two, three, or more movable slides, must be processed and satisfied prior
to each machining operation. As may be seen from the above outline, the
operation of a position control system is an intermittent affair. At any
given time either the tape reader will be in operation,the slide will be
moved, or the machining operation will be in process. The three phases
in general will not occur simultaneously.
Path Control System. A generalized block diagram of a path control
system for a milling machine may be seen in Fig. 2. Table 3 shows the
data flow and codes in typical systems. The steps in the operation are:
1. Pragram Manuscript. Again the operation begins with a part drawing. Because in this case a considerable amount of processing must be
performed on the drawing data, an organized form usually termed a
manuscript is prepared. This manuscript generally lists the important
dimensions of the finished part, along with other instructions pertinent to
the preparation of the final storage medium for the machine tool control.
Examples of nondimensional data include tolerance, cutting feed rates,
spindle speeds, type and diameter of cutting tool, rate of material removal,
type of coolant, and instructions to the machine operator for the change
of cutting tools or holding fixtures.
2. Computing and Starage of C amputed Data. At this point the

0.:

6co
Card
punch

Part
drawing

Card
reader

General
purpose
computer

Card-totape
converter

Punched
tape

Manuscript

Tape
reader

Director
(interpolator)

Magnetic
tape

~

Z

C

"T1

Desk
calculator

Planning
sheet

»
n

Input keyboard
and tape punch

--I

C

2!:!
Z
Q

"'tJ

~

o
n
m

Ul
Ul

Transducer
(incremental)

Servo
actuator

Servo
amplifier

Position
comparator

Magnetic
tape
reader

n

o
Z

--I
~

o

r-

Machine
tool

FIG. 2. Typical closed loop path control block diagram.

TABLE 3. DATA FLOW AND CODES IN TYPICAL PATH CONTROL SYSTEMS

System a
A

B

C

D

E

Storage
Medium into
Interpolator
7-channel,
O.5-in. magnetic tape
or 8-channel, I-in.
punched
tape
7-channel
punched
tape
Punehed cards
(Rem-Rand)
8-channel,
I-in.
punched
tape

7-channel,
7 •

s-Ill.

punched
tape
a

Code
Binary with
parity
check; binary with
parity
check
across tape
Binary along
tape; parity check
across tape
Decimal
Modified
BCD
(6, 4, 2, 1)

BCD with
parity
check
across tape

Type of
Buffer Store
in Interpolator
Flip-flops

Code
Binary

Interpolation
Code
Binary

Interpolation
Storage
Medium
None

Control
Code
Binary

Transducer
Code
Binary
(incremental)

Z

c:
!:
m
:.0

n
Magnetic
core
shift
registers
Stepping
switches

Binary

Relays

Modified
BCD
(6, 4, 2, 1)

Magnetic
core shift
registers

Letters identify same system as those in Table 2.

Binary

None

Binary

Binary
(incremental)

>
rn

0

Z

-4
:.0

Decimal

Modified
BCD
(5, 2, 1, 1)

Analog

Decimal

Binary

None
8-channel,
O.5-in.
magnetic
tape, binary (incremental)
code
14-channel,
I-in. magnetic tape,
phase
modulated

Analog
voltage
amplitude
Decimal

Analog
voltage
amplitude
Binary
(incremental)

0

r-

0"'T1

!:

>
n

:::I:

Z
m

en

Analog

Analog

0-

b-0

6-10

MANUFACTURING PROCESS CONTROL

process may take either of two paths: (a) manual computing and storage
on punched tape, or (b) automatic computing and storage on punched
tape.
Manual Method. If the part to be machined:'is a simple one, the main
task to be accomplished is that of determining the path of the tool center
offset by the tool radius from the finished part. This may be performed
manually by the use of a desk calculator. Locations of the breakpoints
in the tool center path are then entered, in the proper sequence, along
with feed rate instructions and machine tool auxiliary commands, on another form frequently called a planning sheet. The organized data from
the planning sheet are then entered line by line on the input keyboard of
a tape punch. This keyboard also produces a printed copy of the entered
data, for verification against the planning sheet.
Automatic Method. If, on the other hand, the desired part is complex,
automatic data processing by means of a general purpose (GP) computer
is in order. Data from the manuscript are entered into the keyboard of a
card punch, which produces a sequence of punched cards for input to the
computer. Besides calculating the tool offset· path, the computer may
also approximate the desired contours of the finished part with the minimum number of chords or circular arcs which will satisfy the tolerance
and surface finish requirements stated in the drawing. Other typical
tasks for the GP (general purpose) computer may be the calculation of
tool offset for a ball nosed cutter, or other shaped cutting tool. Routines
for the automatic cleanup of pockets may be included, and in some cases
automatic compensation for characteristics of the machine tool or servo
system may be required. Tool deflection may be compensated for, and a
series of step velocity commands inserted, to prevent overshoot, excessive
dimensional errors, or actual information loss during the machining operation. When the computer is employed, its output data are usually converted by automatic means to punched tape which serves as input to the
interpolator. The translation of comp·uter information directly into
punched tape is accomplished by the use of a converter, translating either
from magnetic tape or punched cards into punched tape.
Cont~ined in the punched tape are coordinate data specifying the terminal poirtts of each feed for a single segment of the path of the center of
the cutting tool, along with feed rate or slide ,velocity instructions, programmed·stops (points at which the machine is brought to a halt for
operator intervention), and auxiliary machine tool functions. If the part
is so simple that it can be machined by a sequence of four straight line
segments, the punched tape is likely to contain only four blocks of data.
If, on the other hand, a sequence of sophisticated, empirical curves must
be produced with a fine surface finish, hundreds or thousands of individual

NUMERICAL CONTROL OF MACHINES

6-11

path segments may have been calculated by the OP computer, and hundreds or thousands of data blocks have been recorded on the punched
tape.
3. Director (interpolation). Since the punched tape contains block
data defining each segment in the cutting tool path, wh~le the machine
tool servomechanisms require simultaneous, continuous, co'ordinated commands to produce accurate paths in space, still another. form of data
processing must take place. The conversion of discrete dimensional information into continuous coordinated command data for the machine
servos is defined as interpolation, and is performed by a special purpose
computer usually termed a director. To prevent intolerable errors which
analog interpolation would likely introduce during large traverses, interpolation is commonly performed in a digital manner with 'digital output.
4. Storage on Magnetic Tape. Data emerging from the director will
therefore usually be in the form of simultaneous trains ,of incremental
pulse commands, a separate train for each slide to be displaced during
the interval. The large volume of information represented by these pulse
trains may be conveniently recorded on separate channels of magnetic
tape. The precomputed magnetic tape serves as a final storage medium,
one which instructs the machine tool each time the part must be machined. Some control systems avoid the use of magnetic tape, feeding
the pulse train's directly into the position comparator by incorporating the
interpolator into the control unit.
. ;
5. Machine Control. The servo portion of the control system appears
almost identical to that given in Fig. 1 for position control. Incremental
motion commands are fed, either from the director or from magnetic tape,
into a position comparator, which also receives displacement signals from
transducers monitoring slide motion. The difference between command
and feedback is' continually fed from the comparator to the servo amplifier which generates the power to drive the servo actuator. The actuator
displaces a ball lead screw or rack to produce slide motion.
Differences between Positioning and Path Control. Although the
logic appears the same, details of design and .operation in path control are
vastly different from those in position control. In the case of path control, information flows continuously from the magnetic tape into the position comparator, as the machining process takes place. Data input' and
slide motion occur simultaneously on two or three channels. Thus the
storage medium is read, the slides are actuated, and cutting takes place
simultaneously, instead of sequentially as mentioned under position control. Other differences are high storage bandwidths, high data processing
rates in the positIon comparator and transducer, and linear servo amplifiers and servo actuators. The servo systems must be matched from one

6-12

MANUFACTURING PROCESS CONTROL

slide to another, in order that accurate paths can be achieved. Faster
response, higher bandwidth servos are generally involved. Transducers
producing incremental output information are usually employed to mate
with the incremental character of the input instructions to the comparator.
2. INFORMATION REQUIREMENTS

Selection of the types of storage media for each type of control system
has been influenced largely by the economics and convenience of use for
each application.
Position Control. Such systems operate in an intermittent fashion,
the three phases being storage readout, slide positioning, and then machine operation. Assuming that the maximum displacement of any slide
is 99.999 in., and that two-axis or X-Y motion is involved, a total of ten
decimal digits of dimensional information must be read between successive machining cycles. If a few extra pieces of information, such as
identification of slide or selection of one of several machine functions, are
included, and if a decimal digit consists of some combination of four
binary digits, for each machine operation approximately 50 binary bits
must be unloaded from the storage medium.
For inexpensive punched tape readers, the scanning of 50 bits will require approximately one second. The machining operation will usually
require one second or more (drilling or punching) , and the actuation of the
slide over a small traverse will also take at least one second. Thus three
seconds is a minimum interval for the completion of a single machining
cycle; during the one-second interval when the storage is interrogated the
data output rate is 50 bits per second. This relatively low rate is well
matched to the characteristics of punched tape and punched tape readers.
The low cost and high reliability of tape and tape reading equipment has
lent added emphasis to the selection of these components in most current
position control systems.
The low sampling rate required of the transducers monitoring slide
motions, together with the advantages of absolute position readout, has
led to the use of shaft positiqn encoders as the feedback elements. Shaft
encoders utilizing brushes and printed circuit commutator segments have
been found to be of adequate reliability and life expectancy in this connection.
Path Control. Information requirements for path control are vastly
greater than for position control. Accurate generation of paths in space
require that each of the synchronized servos receive continuous, accurate
input data. Although a line in space contains an infinite number of
points, for practical purposes a finite number of incremental pulse commands has been found adequate, especially in view of the smoothing ac-

NUMERICAL CONTROL OF MACHINES

6-13

tion of servo systems. For a skew line in space, representing the diagonal
of a cube one inch on edge, to be traversed at 60 in. per minute along each
axis in a typical contouring system, data input to each servo in present
systems will vary from 1000 to 5000 bits per second. The incremental
value ranges from 0.001 to 0.0002 in. If the total requirements for the
three slides are included, the director or tape must generate between 3000
and 15,000 bits per second. The storage bandwidth may therefore be 300
times greater than that in position control. At the present time, magnetic
tape offers the only practical solution to such requirements.
Such unusual data input needs for control systems have influenced the
incorporation of directors into most path control systems. For smooth
and accurate motion, the servos require periodic information simultaneously on each channel. GP (general purpose) digital computers are
organized to perform operations on only one word of information ata
time, and provide output in a similarly discontinuous manner. Thus the
computer is poorly mated to the data requirements of the servos. Furthermore, the furnishing of 15,000 new pieces of data per second would
strain the capacities of even the fastest presently available computing
instruments, to say nothing of the high costs of such machines (upwards
of one million dollars). It is for these reasons that the digital interpolators or directors have been developed. Accepting relatively little data
at their input, they provide at fairly low cost simultaneous high-rate periodic output trains, properly synchronized among the channels.
As a consequence of the high pulse rates required for input to the position comparators, the incremental feedback transducers evolved for contouring systems also process data at high rates. Commutator type position encoders have been found noisy and of limited life. Noncontact
transducers, of the rotary or linear magnetic or optical grating type, are
universally employed in such applications, even though they provide much
smaller output signals. The high mechanical and electrical noise environment has led to sophisticated shielding and amplifying measures in order
to preserve information reliability in this very critical, low-energy level
portion of the control system.
3. NUMERICAL CODES AND THEIR SELECTION

A comparison of the block diagrams of Fig. 1 and Fig. 2 shows that
numerical codes are likely to differ. In both cases, economic and technical
factors govern the decisions. Information bandwidth requirements, storage media, available transducers and their codes affect code selection. In
any single position or path control system, it is common for one code to
be used in the first storage medium, another in the GP computer (if one is
-employed), another in the second storage medium, another code em-

6-14

MANUFACTURING PROCESS CONTROL

ployed in the control itself, and still another present in the feedback
transducer. Not only codes but also format (location of data in the
memory medium) play an important part in system design.
Point Positioning Code Selection

Because of the low information bandwidths required, most point positioners utilize a punched tape input medium. Punched cards or magnetic
tape are less frequently found, since handling equipment is more expensive. The punched tape is usually of the teletype variety, with a width
of Ys or 1 in., depending on the number of hole positions or channels across
the tape. In order to make an entire position location available simultaneously across one line of tape, a few systems employ a very wide, nonstandard multichannel plastic tape. In return for the advantage of
simultaneous information availability, the designer must accept the disadvantages of difficult line registration, special and rather expensive tape
punching and reading equipment, and slow reading capabilities. For
description of equipment, see Vol. 2, Chap. 5, Equipment Description,
and Chap. 20, Input-Output Equipment for Digital Computers.
Punched Card Codes. The Hollerith code is shown.in Fig. 3. Although 'this code utilizes card space fairly inefficiently, it has the advantage of being standard on all IBM card reading and punching equipment,
computers, and many special data converters. The code used with
Remington Rand equipment is shown in Fig. 4.
Punched Tape. vVhere position control systems have been designed
to utilize existing keyboard and tape punching apparatus, Flexowriters
and the Flexowriter code and format are usually found (see Fig. 5a).
Since the Flexowriter has an alphanumeric keyboard, one line across the
tape must accommodate any alphabetic or numeric symbol. Flexowriter
punched tape has an eight-channel capacity, with one channel used for
parity checking, or error sensing. Since one line transmits a single
decimal digit of the intended table position, a typical Flexowriter tape
control will employ six lines to command an address in one axis, and
twelve lines for a two-axis location. As this tape is read, line by line,
and entered into buffer storage (usually relays) in the control unit, the
Flexowriter numerical code (binary coded decimal) is often converted
into one more convenient for comparator or storage purposes. At least
one position control utilizes decimal relay storage, converting from the
Flexowriter code as it is being read. In this case, the decimal relay
storage acts as a switch or commutator to set up from the digital input
an .unambiguous carrier phase instruction, since the transducers and
comparator are analog in nature.
For maximum tape density, a straight binary code would be optimum.

6-15

NUMERICAL CONTROL OF MACHINES
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(b) Industrial 8-hole

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----:--9

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(c) Teletype

FIG. 5. Punched tape codes and format.

brushes determined by the direction of motion. Analog transducers may
be potentiometers, resolvers, or synchros. The last may operate into
carrier phase or amplitude detectors. In the digital sense, they possess
no code characteristics. Table 4 shows several binary codes.
Codes in Contouring

Since contouring systems require the services of a general purpose
computer for the programming of complicated parts, the computer input
code is used in the preparation of instructions from manuscript. Most

NUMERICAL CONTROL OF MACHINES

TABLE 4.

a

6-17

BINARY CODES

Decimal

Gray

Binary

Special
Transducer a

0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20

000000
100000
110000
010000
011000
111000
101000
001000
001100
101100
111100
011100
010100
110100
100100
000100
000110
100110
110110
010110
011110

000000
100000
010000
110000
001000
101000
011000
111000
000100
100100
010100
110100
001100
101100
011100
111100
000010
100010
010010
110010
001010

100010
110010
010010
011010
001010
001110
011110
010110
110110
100110
100111
110111
010111
011111
001111
001011
011011
010011
110011
100011
100001

Modified binary coded decimal.

current users of contouring controls rely on some type of IBM equipment and therefore employ the Hollerith-coded IBM punched cards.
Remington Rand punched cards are used in the Univac series of computers, while some smaller computing systems utilize Flexowriter or
other punched tape codes (see Table 3).
It is possible to become specific only when dealing with codes for
storage input to the interpolator in the control system. One typical
system employs a standard Flexowriter tape as input. A modified
binary coded decimal (5, 2, 1, 1) is used for interpolation. Another system uses punched tape with straight binary code, the binary number
representing the displacement for an axis during a given interval being
arrayed lengthwise along the tape. This system also performs interpolation and control in binary code.
Still another control system accepts Remington Rand punched cards
in code, at its input, and interpolates by a combination of digital and
analog techniques. In hybrid systems, a formal discussion of coding
becomes somewhat irrelevant. One system employs an adding machine
keyboard for data input and tape punching service, utilizing 8-hole, I-in.
tape with two modified binary coded decimal (BCD) (6, 4, 2, 1) num-

6-18

MANUFACTURING PROCESS CONTROL

bers across a line of tape. This particular BCD was selected to minimize
cost of equipment in the buffer relay register. Interpolation in this system takes place in decimal (one of ten positions) code, and is achieved
with high-speea decimal magnetron beam switch tubes. The output is
recorded in incremental (binary) form on magnetic tape, since absolute
position tape storage would require excessive storage bandwidth. As
information is fed into the comparator of the control system, it becomes
decimal again.
Practically all transducers utilized in path control systems are of the
incremental type. These transducers are either rotary electromagnetic
(noncontact) gratings or linear optical gratings of high resolution.
Standards. Technical committees of two large "organizations, the
Aircraft Industries Association (representing a large group of equipment
users) and the Electronic Industries Association (representing controls
manufacturers) are in the process of evolving standards for codes, format,
and physical media used in control systems. While the original effort
was devoted to punched tape for position controls, these standardization
activities have been broadened to cover punched and magnetic tape
standards for position and contouring control systems.
Summary. The single most important factor in selection of codes is
equipment cost. Next in importance comes convenience to the operator,
such as the availability of standard Flexowriter or IBM apparatus for
functions other than numerical control. The next most important factor
is the information rate required. There are other considerations, but
of relatively minor importance. Reliability is usually considered, but
is assumed to coincide with minimum control logic and minimum equipment cost.
4. STORAGE MEDIA APPLICABLE TO NUMERICAL CONTROL

Three different storage media are commonly "employed in numerical
control systems .. These media, punched tape, punched cards, and magnetic tape, are also those universally employed in computing and data
processing systems. Volumetric efficiency, cost, and information output
rate dictate the selection of storage for various control systems and at
different points within a given control system. Punched cards and
punched tape are used almost exclusively for storing absolute positions
or their equivalent: One or the other is therefore found in almost all
position control systems and at those points in contouring systems where
position storage is mandatory. vVhere continuous path storage is inherent in the philosophy of a contouring system, magnetic tape is found
almost exclusively. Its high packing factor, modest cost, and very high
bandwidth potential (it can be used for the recording of wide band video

NUMERICAL CONTROL OF MACHINES

signals, if desired) make it the best choice. For details of storage media
see Vol. 2, Chap. 5, Equipment Description, and Chap. 20; Input-Output
Equipment for Digital Computers.
Punched Cards and Tape. Punching and reading equipment for
cards and tape have been highly developed by applications which considerably antedate numerical control. The advent of this new technology
has therefore caused very little change in handling equipment. Perhaps
the only significant effect has been the development of punched tape
readers which can simultaneously present 40 or 50 bits of output data.
Special, very wide tape punches and readers (up to 12 in. in width) have
been evolved by some controls manufacturers. Also, field readers for
standard I-in. tape, which sense simultaneously 10 or 20 codes (lines)
of tape, are now beginning to appear on the market. If developed sufficiently to become competitive in cost with standard single-code readers,
such apparatus could have an appreciable influence on control system
design, since it permits the elimination of rather expensive data distribution and buffer storage equipment.
, Magnetic Tape. Magnetic tape has been in widespread use for telemetry and digital computing equipment. Recording and playback apparatus, optimum operating parameters, and tape durability and pulse
reliability generally leave much to be desired. The problems have been
(a) recording and reading heads which will assure intimate contact between tape and the head pole pieces, (b) homogeneity of oxide deposition
on the tape to prevent dropouts and nodules, and (c) preparing the oxide
surface of tapes so that oxide migration to the playback heads wi,~l be
greatly reduced or eliminated. Magnetic tape is used for complete path
storage in both digital and analog phase applications. It is probably! the
weakest link in the entire data processing chain, yet it offers the systems
designer such a great economic advantage by permitting separation of
interpolator from machine control unit that its use for commercial controls seems almost inevitable. Table 5 lists the problems in using magnetic tape.
5. INCREMENTAL AND ABSOLUTE CONTROL LOGIC

Since data transmission rates required for positioning controls are
relatively low, absolute position storage has been generally adopted because of the very high reliability it affords. A minority of position controls employs incremental logic, wherein only the displacement from the
previous location is given. In contouring applications, however, incremental data transmission is almost mandatory, because of the tremendous
appetite of such controls for input data. Most path systems operate on

6-20

MANUFACTURING PROCESS CONTROL
TABLE

Problem
Reliability
Tape-head
intimacy
Dropouts
Crosstalk, signal
amplitude

Bandwidth

Stability
Dimensional
Magnetic

5.

MAGNETIC TAPE PROBLEMS

Solution
Metal-faced heads, polished surfaces
Polished tape surface
Sandwich tape construction
Quality control of tape base and oxide mix
Pretesting of tape
Tight dimensional control of tape width, width stability,
careful design of tape guides and tension control devices
Better interchannel magnetic shielding
Precision tape reels
Improved reel storage and transportation containers
Improved head manufacturing techniques and materials,
permitting narrower head gaps, better channel-tochannel alignment
Higher tape speeds
Higher modulus tape bases, prestressed (tensilized)
Development of high remanence, stable magnetic coatings

incremental digital data; a minority employs analog data storage and
interpola tion.
Comparators. As for comparator logic, position controls working
with absolute data possess either true parallel digital subtractors, or less
complex comparators which provide an error signal of proper sign but
not necessarily proportional to displacement error. Comparators designed for analog followup systems are usually simpler. However, they
place requirements for high component accuracy, linearity, and stability
on the digital-to-analog converters which are employed between the
buffer storage and the comparator logic.
Path control digital comparators are usually reversible counters, which
contain the instantaneous difference between command and feedback
information. Complex logic, including storage capacity, is necessary
ahead of the counter to guarantee that all command and feedback pulses
reach the counter sequentially, since it can process only one pulse at a
time without error. Comparators in analog systems are either phase or
amplitude sensitive, and of high linearity and stability.
Interpolators. In the interpolator portion of path control systems, a
variation of the digital binary rate multiplier is commonly found. (See
Vol. 2, Chap. 30.) This offers a very economical means of producing
multiaxis coordination for linear paths. Somewhere between the original
manuscript and the interpolator a decimal-to-binary conversion must
take place automatically.

NUMERICAL CONTROL OF MACHINES

6-21

One digital interpolator performs linear and circular interpolation.
vVhere curved surfaces are frequent, this capability can greatly reduce
the amount of preliminary data processing and the data volume held in
position storage. A form of frequency division, which permits a continuously changing relationship between pulse frequencies on different
channels, produces a high-speed, all-decimal digital differential analyzer.
As an understanding of the capabilities of numerical contouring control
increases throughout the metal cutting industry, and more sophisticated
part designs are introduced to such systems, it is likely that second degree
interpolation will become more important in the future. While parabolic
interpolation offers the greatest flexibility to the mathematician, for metal
removal circular interpolation appears more practical. The interpolated
path is that of the center of the cutting tool; the contour produced is
offset by a constant, the tool radius, from the tool center path. Whereas
the path offset to a circle is another circle, one offset by a constant from
a parabola is not another parabola, but an equation of eighth degree.
6. TRANSDUCERS

Position Measurement. The parameter whose dimension is of greatest interest is the machined surface of the desired part. In position
controls, the ideal can be closely approximated, since the position of
the part on the moving table and the center of a drilled hole would coincide within the eccentricity tolerance of the hole drilling mechanism.
Positioning systems commonly employ precision lead screws to drive
digital shaft position encoders with a resolution of 0.001 in. or better.
If positioning speeds are high or resolution is well beyond 0.001 in., it is
desirable to lift the brushes on the lowest order digits until the slide nears
the home position, to extend the life of the encoder. For analog servos
rotary potentiometers, resolvers, or synchros are either connected to a
precision lead screw or geared to a rack and pinion mechanism. There
are examples of absolute rotary position encoders based on optics and
photosensitive pickup elements. A rather sophisticated extension of the
conventional synchro transformer is a linear synchronous transformer
based on a linear inductive grating. Utilizing etched circuits on glass
plates and high audio frequency carriers, this device is capable of extremely high linearity and resolution and, when geared to lower speed
synchros, can give an unambiguous position indication.
Independent measuring elements are generally absent in open loop
systems, whether of the position or contouring type. The prime mover
may also play a part in measurement. Examples of open loop devices
are stepping motors, synchronous variable-speed motors, mechanical
gage rods, and in the simpler systems limit switches.

6-22

MANUFACTURING PROCESS CONTROL

Path Control Measurement. Path control transducers for closed
loop systems are fewer in type, probably because the higher system development costs have produced fewer demonstrable contouring systems
to date. Because the point of tangency between the rotating cutting tool
and the finished surface of the workpiece changes with direction of cut
on a milling machine, direct measurement of the workpiece dimensions
has thus far not been reduced to practice. The next most desirable measurement is that of actual slide position.
Linear Optical Gratings. The most sophisticated linear position transducer now in use is an optical grating with a resolution of 0.0002 in.
Originally developed for light diffraction measurements in physical laboratories, such gratings offer position mensuration independent of mechanical elements such as lead screws, racks, and gears. Attaining
sufficient linearity and high resolution requires tight control of ruling
and grating reproduction, and good dimensional stability over the normal
range of operating temperatures and humidity. At least two advanced
contouring systems employ linear optical gratings.
Rotary Converters. For many applications, lead screws employing
hardened, precision ground threads with split nut ball bearing races for
backlash elimination can be manufactured with sufficient linear accuracy.
Where traverse is so long as to make the moment of inertia of a rigid
screw too great for the servo system, precision racks with dual preloaded
pinions have been developed. In either case, a rotary incremental transducer of the electromagnetic grating type has been found to be a convenient solution. The lead screw or rack plus rotary grating can offer
an overall accuracy as high as ± 0.0005 in. in a stroke of 72 in. This
exceeds the accuracy of slide straightness and squareness, concentricity
of cutting tools and their spindles, and the deflection characteristics of
cutting tools at .reasonable side cutting loads. Based on the amplitude
modulation of an approximately I-megacycle carrier, this rotary transducer offers the advantages of appreciably lower cost, simplicity of
installation, shielding from contaminants, and greater electrical noise
isolation from the machine tool environment.
Possessing similar advantages are analog output rotary transducers,
such as synchro transformers, resolvers, and potentiometers. While they
furnish higher output signal power, and therefore greater noise immunity,
they often havea more limited information rate capability than do rotary
digital transducers. At least two examples of the digital type can be
found in contouring systems, and two of the analog type.
Machine Tolerances. At the present time, the accuracy of measurement equipment. exceeds that of the machining equipment. This is probably due to the fact that machine tools now employing numerical controls

NUMERICAL CONTROL OF MACHINES

6-23

are of conventional, pre-1956 design. It is likely that machine tools,
designed specifically for servo controls, will possess tolerances compatible with the better present day transducer equipment. Regular contouring accuracies of ± 0.002 in. can now be achieved by several machine
control systems. Users are now expressing interest in systems with an
overall accuracy in the order of ± 0.0002 in. Although this figure is
probably within the reach of present day control technology, a good deal
of machine tool evolution and metallurgical research will likely be necessary to make this dream a reality.
7. SERVO SYSTEM CONSIDERATIONS

This section will examine parameters germane to closed loop systems,
since the word "servo" by definition excludes open loop control. In
earlier sections, storage media, interpolators, comparators, and transducers were discussed. Elements of the forward portion of the servo
systems include servo amplifiers, servo actuators, and slide driving
mechanisms.
Servo Amplifiers. The role of a servo amplifier is to receive the error
outp~t signal from the comparator, at a fairly low power level, and to
perform amplification so that sufficient wattage is available to power
the servo actuator.
'
Relay Amplifiers. The simplest form of power amplifier is a relay.
With an input signal of a few milliwatts, its contacts can deliver hundreds
of watts. The output is of course discontinuous, having no intermediate
output levels, only zero or full power output. Relay amplifiers are used
occasionally in the forward loop of some point positioning systems. Since
only the ultimate location is of importance, the On-Off (bang-bang)
nature of their motion may be acceptable.
In some instances, combinations of relays to provide several velocity
steps have been designed as improvements over the basic two-condition
servo. Since a relay amplifier will cause a slide to be actuated over a
traverse directly proportional to the on-time, such servos are considered to be pulse-width-modulated. A d-c motor normally serves as
the prime mover driven by the relay amplifier. An important consideration in the selection of an amplifier-actuator combination is its response
time, or the length of time required to accelerate the slide from zero to
full velocity. Since a relay can be operated within a few milliseconds of
time, the response time of this combination is determined by the acceleration time of the motor itself. A conventional d-c shunt motor, with
poor torque-to-inertia characteristics, requires hundreds of milliseconds
to, reach full speed from standstill.

6-24

MANUFACTURING PROCESS CONTROL

Proportional Amplifiers. The next step in amplifier sophistication
beyond the relay is the proportional amplifier. Examples of proportional,
though not necessarily linearly proportional, amplifiers utilized in positioning controls are thyratrons, rotary magnetic amplifiers (such as
amplidynes), which are in reality special motor-generator combinations,
hydraulic valves, and magnetic clutches. Thyratrons can respond within
one cycle of the carrier or power supply frequency, and are therefore
relatively fast. They are used to drive either d-c variable-speed shunt
motors or a-c servo motors. Again, the acceleration time of the motor
controls the response of the total system. The total for the thyratronmotor combination may vary from 50 msec for a true low-inertia d-c
or a-c motor driven by a 60-cycle thyratron amplifier up to 0.5 sec in
the case of a high-inertia d-c motor. The thyratron offers the advantages
of moderate price, high speed, and -a very high-power amplification factor.
Its disadvantages are fairly short life expectancy and characteristics
which are affected by the ambient temperature.
Rotary Amplifiers. Rotary magnetic amplifiers, developed during
World War II for the actuation of large loads such as gun mounts, searchlights, and radar platforms, have a long record of successful performance.
One notable characteristic, a very high power gain, has led to the use of
this device in the current drive to the electromagnetic coils of cyclotrons,
wherein the current must be controlled to within 0.01% or better for
successful particle acceleration. Rotary amplifiers are generally used
to drive variable-speed d-c motors. Besides high gain, they offer fairly
long life and insensitivity to mechanical shock. Their disadvantages are
rather high price, slow response, and frequent maintenance which is typical
of rotating electrical machinery involving brushes and commutators or
slip rings. Rotary amplifiers are considerably slower than thyratrons.
A rotary amplifier-d-c motor combination may require 0.3 to 0.5 sec to
accelerate from standstill to full speed.
Hydraulic Amplifiers. Another device with a considerable history
is the hydraulic actuator, driven by a precision hydraulic valve. Since
valves can provide a very high mechanical power gain, they are usually
excited by vacuum tube amplifiers operating at a level of 2 or 3 watts.
Valves functioning at a fairly high pressure, such as 2000 or 3000 psi,
can easily drive actuators to an output of 5 hp or more. In positioning
systems the compliance of a large column of hydraulic fluid produces no
great disadvantage; therefore an inexpensive hydraulic cylinder is often
found as the actuating element. Hydraulic valves possess the desirable
attributes of high power gain, high output power capacity, and very high
bandwidth (short response time). The valve-cylinder combination can
be designed to provide full speed output from standstill within 10 or 15

NUMERICAL CONTROL OF MACHINES

6-25

msec. Undesirable features are fairly high price (intermediate between
thyratrons and rotary magnetic amplifiers), instability of characteristics
due to accumulation of gas in the hydraulic reservoir or foreign particles
in the valve elements, and a short life expectancy due to wear by contaminants on the moving spool, which must generally be ground to a
tolerance of one or two ten-thousandths of an inch. The small size and
low weight, which make hydraulic valves and actuators so indispensable
to aircraft servo systems, are of very little importance in machine tool
applications.
Differential Hysteresis Magnetic Clutch Actuator. This relatively
new actuator in the position control field is a proportional device of rather
large power gain, requiring only several watts of input excitation. Other
advantages are moderate cost (about the same as thyratron amplifiers),
long life expectancy, and high response speed. Driven by a constantspeed motor, a magnetic clutch can accelerate its load to full velocity in
50 or 75 msec. Its acceleration time is therefore better than any proportional actuator except hydraulic prime movers. The disadvantages
are relatively little history and limited maximum output (about 0.5 hp
at present). Another point in its favor is the fact that nonprecision reduction gears can be used, since the working clutch can operate against a
slight drag produced by the inactive clutch, thus eliminating backlash.
Amplifier-actuator combinations which have found application in contouring controls are those which are fairly rapid in response, and have a
linear relationship between error input and power output. Rotary amplifiers and d-c variable-speed motors have been in use for a number of
years. Hydraulic systems, with valves feeding rotary hydraulic actuators,
have also been used extensively. A more recent innovation is the combination of static magnetic amplifiers and two-phase a-c servo motors.
Not to be confused with the fairly slow saturable reactor, magnetic amplifiers were developed for military use during the early 1950's; later
models employ new materials and manufacturing techniques to give outputs of 1 hp or greater.
Amplifier-Actuator Selection. All three combinations, rotary amplifiers and d-c motors, hydraulic systems, and magnetic amplifiers and a-c
motors, are rather high in price, so the selection is based on other characteristics.
1. Bandwidth is a parameter of great importance. Hydraulic systems,
which employ rotary motors instead of linear actuators to avoid objectionable compliance, can provide a bandwidth, including the mechanical
load, of 30 or 40 cps. Very rapid slide acceleration can thus be effected.
Magnetic amplifier-servo motor packages can develop a bandwidth, including load, of 5 to 8 cps when excited by a 60-cps power source. If the

6-26

MANUFACTURING PROCESS CONTROL

inconvenience of a 400-cps generator can be accepted, the bandwidth
may be doubled. The rotary amplifier-d-c motor combination can provide a useful response of 3 to 5 cps.
2. Stability and service form another basis for comparison. The greatest freedom from maintenance is offered by the static magnetic amplifier,
since it contains no moving parts. The long-term electrical stability is
also excellent, with intervals of a year or two between readjustments
already a reality. The life and stability records of rotary amplifiers and
d-c motors are fairly good. There may be bearing problems in the rotary
amplifier, but they are not greater than that of any rotating machine.
Since they are d-c machines, the brushes and commutators produce electrical noise and are subject to wear. The same is true of the d-c motor.
Service intervals are likely to be less than one year.
3. Reliability. Hydraulic systems, with appreciably faster response
and greater peak power outputs, require that their oil reservoirs be kept
meticulously clean and free from gas. In an industrial environment, oil
replacement (or cleansing) and removal of entrapped gas by purging may
be required at intervals of 30 to 60 days. In addition, the stability of the
very precise valve may be adversely affected by the accumulation of
foreign ~aterial on the critical spool assembly or wear by hard foreign
particles.:- While considerable progress has been made in improving the
reliability of high-performance servo valves, the current record indicates
the valve is the least stable amplifier element of the three herein discussed.
Purely Mechanical Elements in the Servo Loop. Since all three
commonly used actuators have a rotary output, a, reduction gear box is
the first element in the mechanical chain. Next c,omes the rotary-to-linear
, converter, ,which is generally a lead screw for short and medium strokes,
and a rack and pinion for large traverses. The, slide and its bearings
comprise the driven element, while the reaction of the cutting tool on the
workpiece is still another source of loading on the actuator.
In relative order of importance to the servo engineer are the backlash,
friction, and moment of inertia of the total load as seen by' tlie rotary
servo actuator.
Backlash. Backlash can be virtually eliminated by the use of ballbearing lead screws with two preloaded nuts and rack drives containing
two separate preloaded pinions. Such drives can be manufactured to a
very high degree of precision, and with a long life expectancy, but at
considerable cost. A precision screw or rack costing $5000 per axis is
not unusual.
It is more difficult to fabricate gear boxes of high efficiency and low
backlash. With precision spur gears located on accurately bored bearing

NUMERICAL CONTROL OF MACHINES

6-27

centers, a backlash figure referred to the input shaft as low as l4 or Ys
degree can be achieved. Since an appreciable reduction ratio is· often
necessary, a gear box with at least three meshes to minimize moment of
inertia will be found. Although split, preloaded antibacklash gears are
common in instrument drives, their use in power drives for machine tools
is yet uncommon. In order to be effective, very high preload torques
would be necessary, with attendant gear wear.
Friction. The art of precision gear cutting and train as~embly is
being intensively explored at the present time, and improvements in
precision can be expected. Another approach, less acceptable to the
servo engineer, is the practice of installing oversized gears, so that at
least initially the train is free of backlash. The very high static and
running friction introduced by this expedient may create a servo stability
problem, however. The highest quality spur gears are first hardened,
then ground or hobbed.
Inertia. Since gear reduction ratios are generally greater than 10: 1,
most of the inertia in the mechanical system is contributed by the rotor
of the drive motor and the moment of the first one or two gears. These
elements generally contribute at least 500/0 of the total system moment
of inertia. vVhere a long stroke or a high thrust is necessary, a largediameter lead screw can introduce a noticeable moment of inertia. It is
mainly for this reason that strokes in excess of 6 ft usually utilize a
rack and pinion drive. The moment of the lead screw may· contribute
300/0 of the total system inertia.
Lastly, the mass of the slide and the workpiece should be considered.
Although the inertia may not be appreciable, the mass may react- upon
the lead screw in such a way as to cause significant end motion due to
compressibility of the retainer bearings, and almost certainly the static
and running friction of the slide bearings will be affected by the weight
of the slide and its load.
Stiction. Next to backlash, stiction (static friction) can generate the
greatest obstacles to servo stabilization. Especially ·where stictioh exceeds running friction by 200/0 or more, it will be difficult to produce slIde
motion which is smooth over the entire range of feed rates, from maximum feed (rapid traverse) down to a creep feed or under 1 in. per
minute. Usually loop gain, and therefore acceleration, is compromised
in an effort to overcome pulsating slide velocity at the very low and
very high feed rates. In an effort to improve the situation, the more
progressive machine tool manufacturers are designing anti friction bearings for their slides. This usually involves roller or ball bearings riding
linearly on hardened ways. Since the slides must be restrained against
unwanted motion in many directions, antifriction mechanisms can be-

6-28

MANUFACTURING PROCESS CONTROL

come very involved, very expensive, and difficult to adjust and maintain.
It is not unusual to find a slide which has been initially adjusted to provide extremely smooth velocity becoming jittery because of a small
change in friction resulting from wear or vibration. Plastic sliding
bearings were formerly employed but were found unsatisfactory.
Looseness of slide bearings can build up owing to the compounding of
two or three slides upon one another, and produce very undesirable vibrations. Although it does not represent servo instability, the vibration
produces very poor machined surface finishes and can also result in the
premature breakage of very expensive, hard, brittle cutting tools. In
machine tool parlance this shortcoming is called "fishtailing."
Cutting Thrust. Another important detail is the reaction of the
cutting tool on the servo system. Very few machine tool manufacturers
have ever made cutting measurements to provide the servo engineer with
load information. Generally the thrust provided by the actuator at the
slide is far in excess of that introduced by the cutting tool. In most
cases the friction of the slide, screw or rack, and gear box completely
masks the cutting thrust. However, there are situations, such as slab
cutting with a large face mill, where the load introduced is 10 or 200/0
of the total actuator horsepower. Thus, final stabilization should be
done under actual operating conditions. In milling machines,· climb
milling (work moving in the same direction as the cutting edge of the
tool) should be investigated, since the spindle motor feeds power into the
slide (instead of opposing it). The servo system must here act as a brake.
8. PROGRAMMING (PREPARATION OF CONTROL TAPES OR CARDS)

Position Control. Computation is seldom necessary in reducing part
drawing data to the form necessary for entry to the input keyboard. Since
machining takes place only at discrete points, after the table has reached
the intended position and come to rest, calculation of tool offset is not
involved; the table location and center of the cutting tool (punch, drill,
boring tool, spot welder, rivet) coincide.
A program sheet, listing input data in the same code and sequence as
required for the control Junction, must be prepared from the part drawing. Most control systems function on an absolute basis, with all positions referred to a fixed origin on the compound table. Drafting practices are inconsistent with this philosophy; not only are part details
dimensioned from a variety of references (hole centers, external surfaces,
corners) but also permissible tolerances are inconsistent and often
cumulative. Data reduction is chiefly concerned with redimensioning of
the part to the proper reference, .arid itemization of the locations and
machine operation commands in the most efficient sequence.

NUMERICAL CONTROL OF MACHINES

6-29

Drawings are almost without exception dimensioned in decimal code;
decimal input is also common to most controls. In those cases where
binary input is required, the conversion is usually performed prior to
preparation of the program sheet. Manual code conversion, with the aid
of tables, may be practical; automatic conversion by electromechanical
or computer means can be arranged. In either case, it amounts to addition of powers of two until the total equals that of the decimal number.
Path Control. Several operations must be performed on drawing
data to provide input information for interpolators in path control
systems.
a. Redimensioning. All significant locations on the part, such as hole
and radius centers, breakpoints (where different lines or curves intersect),
points through which fa ired curves must pass, and other critical data,
must be dimensioned with respect to a single origin. This reference
should be off the part, so that all dimensions are positive.
b. Tool Planning. A tool engineer should choose the machine tool,
specify the holding fixtures and cutting tools, decide in what sequence the
material will be removed, how deep a cut will be made at each pass, and
from his experience call out the optimum tool tooth loading by specifying
the spindle speed (rpm) and feed rate of the part relative to the cutting
tool. The last decisions will determine the accuracy of the final part,
since they control the tool loading and therefore the elastic deflection
under load, and also the surface finish of the product.
c. Part Programming. The tool engineer's decisions must be converted
to a detailed list of operations. A point on the part holding fixture is
selected as a secondary reference, from which the cutting tool starts and
ends its motions. The gross points in the outline produced by the rotating tool as it roughs out and finishes cutting of the final part must be
called out. Usually the redimensioned part drawing is amended to show
the paths followed by the tool during cutting and noncutting segments
of motion. Tool changes, interruptions for inspection, and other machine operator's instructions must be itemized.
d. Data Processing. All the breakpoints in the path described by the
center of the cutting tool must be accurately calculated. Since most
interpolators perform only linear interpolation, the start and end of each
straight line segment in the entire tool path must be determined, and the
displacement of each axis during each segment (AX, AY, AZ) derived by
subtraction. Tool offset corrections must be included.
Where curved contours are required, the tool path is broken down to
the minimum number of linear segments which will meet the accuracy
and surface finish specified. In processing data for interpolators which
can describe circular or other second degree equations, the curved con-

6-30

MANUFACTURING PROCESS CONTROL

tour is also reduced to the least number of segments. Here the quantity
of segments is appreciably fewer (by a factor of 10 or more).
In addition to the above operations, data reduction must also include
derivation of specific commands to the interpolator relating to slide feed
rates. In most cases the feed rate specified by the tool engineer must be
converted to either a clock pulse rate or total time interval for segment
interpolation. The vector velocity of the part is broken down into its
components along each axis, and each component related to output command rate. Some interpolators receive feed rate vector commands directly, and perform this computation automatically.
Still other functions which may be performed under this category are
controlled slide acceleration and deceleration (to accommodate for servo
limitations), overshoot prevention (on inside corners), offset compensation for shaped cutting tools (tools other than flat end mills), and automatic pocket cleanout.
If the services of a GP (general purpose) computer and computer programmer are available, all data processing can be channeled through this
facility, and accomplished with ease. Large-scale users of NC (numerically controlled) equipment follow this practice. However, it is feasible
to perform data reduction manually, on desk calculators, for simple and
even complex part designs. Where the director is capable of first and
second degree interpolation, tool offset and curve fitting computation
can be accomplished manually with little difficulty by a trained operator.
The first large-scale installation of NC systems took place during 1958
in aircraft manufacturing plants. Several plants organized a cooperative
mathematical programming effort to prepare a library of subroutines for
the IBM 704 GP computer, specifically for NC data processing. This
program is titled APT-2 (Automatic Programmed Tools).
e. Interpolator Input Pr~paration. The final step is preparation of
the storage medium which commands the interpolator. Where a GP
computer has been employed for data processing, an automatic converter to prepare the punched tape or cards. from computer information
is the most logical solution.
If a converter is unavailable, or manual data processing has occurred,
then the part. programmer prepares a Planning Sheet (it may be titled
Process Sheet or Manufacturing Outline) listing all data in the precise
sequence for entry into the input keyboard. A typical part will require
at least 100 lines of entry on a Planning Sheet and may exceed 500 lines.
Next, a trained operator will enter these data into the keyboard, and
produce the card or tape storage medium. Verification of this step,
either by comparison of two independently punched tapes (or cards) or
by printout of the data from an automatic reader, constitutes the final
step in the programming chain.
I

NUMERICAL CONTROL OF MACHINES

6-31

REFERENCES
1. J. D. Cooney and B. K. Ledgerwood, 31 Numerically-controlled point-to-point
positioning systems, Control Eng~, 5, Pt. I, January 1958, pp. 68-98; Pt. II, February
1958, pp. 99-122; Pt. III, March 1958, pp. 99-144.
2. P. J. Farmer, Automatic control, Aircraft Production, 21, 64-74 (1958).
3. P. J. Farmer, Automatic digital control, Aircraft Production, 21, 4-15 (1958).
4. P. J. Farmer, Data-controlling milling, Aircraft Production, 21, 102-113 (1958).
5. Y. C. Ho and E. C. Johnson, Design of a numerical milling machine system,
Proc. Eastern Jt. Compo Conf., pp. 11-24, 1957.
6. Massachusetts Institute of Technology, Servomechanisms Laboratory, Design,
Development, and Evaluation of a Numerically Controlled Milling Machine, Final
Report, March 15, 1956.
7. G. T. Moore, The Numericord machine-tool director, Proc. Eastern Jt. Camp.
Con/., pp. 6-10, 1957.
8.J. M. Morgan, J. W. Wilson, and G. R. Carroll, Cincinnati Numerical Control,
Presented at Cincinnati Technical Activities Seminar, September 30 through October
10, 1957.
9. J. Rosenberg, Logical organization of the Digimatic computer, Proc. Eastern Jt.
Compo Conf., pp. 25-29, 1957.
10. A. K. Susskind, Digital information processing for machine-tool control,
I. R. E. Convention Record, 5, Pt. 4,145-149 (1957).
,11. A. K. Susskind, Notes on Analog-Digital Conversion Techniques, Technology
Press and Wiley, New York, 1957.
12. Automatically programmed tools (APT) developed under USAF Air Material
Command Contract Number AF-33(038)-24007. Vol. 2, APT Programmers Manual;
Vol. 4, Description of APT Computer Programs; Vol. 5, Operators and TroubleShoo·ters Manual; Vol. 6, Modification and Change Procedures. Servomechanisms
Laboratory, Massachusetts Institute of Technology, Cambridge, Mass.

CHEMICAL PROCESS
CONTROL INSTRUMENTATION

C.

CHEMICAL PROCESS CONTROL INSTRUMENTATION
7. Instrumentation Systems, by P. S. Buckley and J. M. Mozley

C

CHEMICAL PROCESS CONTROL INSTRUMENTATION

Chapter

7

Instrumentation Systems
P. S. Buckley and J. M. Mozley

1. Trends and Limitations in Systems Engineering
2. Control Functions
3. Pneumatic Control Systems
4. Electric and Electronic Control Systems
5. Hydraulic Control Systems
6. Pneumatic Components
7. Electric and Electronic Components
8. Self·Actuated Controllers

7-01
7-03
7-10
7-17
7-18
7-18
7-60
7-75

9. Control Panels

7-79

References

7-81

1. TRENDS AND LIMITATIONS IN SYSTEMS ENGINEERING

In the process industries, as exemplified by the chemical and petroleum
industries, the use of instrumentation and automatic controls has tended
to follow certain typical patterns (Ref. 4). The best practice today consists of transmitting process data from the plant to a central control room
where there are data recorders, indicators, controllers, and command devices for setting the level of those process variables which are to be controlled. From the control room command signals are sent back out to the
plant to final control elements, usually control valves. Usually, the process
variables are controlled separately and individually; in a plant with a
high degree of automatic control this sometimes leads to interactions between control systems.
This chapter has been organized and presented for use in a systems en7·01

7·02

CHEMICAL PROCESS CONTROL INSTRUMENTATION

gineering approach to the design of process control systems. The design
methods and principles are covered in Chap. 1, Systems Design, and in Vol.
1, Part E, Feedback Control. To use these procedures, the engineer must
have certain data on the static and dynamic behavior of processes as well
as data on the static and dynamic characteristics of instruments and control components. Equations for and data on process dynamics are now
becoming available (see Ref. 16). In using the material in this section one
must keep in mind certain facts about present day process control equipment and its applications.
1. The quantitative techniques of designing control systems developed
since about 1940 for military purposes are just now beginning to penetrate into the process industries where control system design has usually
been qualitative.
2. Quantitative methods of designing control system components for
specific dynamic behavior have not been widely used in the design of
typical process instruments.
3. The commonest process control instruments are pneumatic. As a
result of (2), they are often less than optimum with respect to such
factors as impedance matching, power supply, saturation, and dynamic
nonlinearity.
4. Measurement problems are much more severe in chemical process
operations than in standard electrical and mechanical operations. Highly
corrosive fluids, fluids containing solids and gummy materials, high temperatures, and high pressures often require that measurement devices be
protected from the environment whose properties they are trying to
measure. Both static and dynamic accuracy may suffer, and the questions of reliability and maintenance may be serious.
5. Partly as a result of (4), process control systems are almost always
designed with provision for manual control in case of emergencies.
6. A process control system is usually a single variable control system
(such as temperature or pressure control), and it is rare for systems to
have numerically identical parameters. This means that it is hard to
justify for each problem the extensive research and engineering that goes
into mass-produced, identical control systems.
7. The objectives of process control system design are quite different
from those of servomechanism design. In typical servo designs, performance is maximized, size and weight are limited, and cost is usually not a
major consideration. In typical process controlsystems, cost is minimized
for a certain lower limit on performance, and size and weight are usually
not important. The process control system is usually a regulator, while
the servomechanism is a followup system. It should be noted that the
same control system may be required to function both as a regulator and

INSTRUMENTATION SYSTEMS

7-03

as a servomechanism. The distinction is that a regulator keeps the value
of the controlled variable constant in the face of disturbances, while a
servomechanism makes the output of the controlled system follow the
input.
In view of the above, although special purpose control systems are
sometimes designed, application of the systems engineering philosophy is
usually directed toward effective utilization of commercially available
process instruments. By providing better power supplies, by improving
the impedance match between components (see Sect. 2), and by careful
attention to installation practices, it is sometimes possible to achieve
phenomenal improvement in system dynamics. Often, too, a simpler, less
expensive, and more readily maintainable system results.
In the sections which follow, the term "system" is usually used in the
restricted sense of applying only to instrument components; the process
is not included except in the early part of Sect. 2. A comprehensive discussion of available components was not possible, and the ones chosen
for discussion are typical only. Neither approbation nor condemnation
of any manufacturer's equipment is intended or implied.
Other important aspects of process control and process control hardware are discussed elsewhere in this handbook. To handle most effectively
the mass of data from a big refinery or chemical plant, data loggers,
which include scanning, monitoring, and interlock functions, are being
used to an increasing extent. These are discussed in Chap. 14, Data Processing. To tie together local or individual control loops into an overall
process control system, process control computers have been developed
(see Chap. 13, Computer Control). These computers are making it possible to optimize automatically process economics.
2. CONTROL FUNCTIONS
Introduction

A simplified schematic diagram of a typical process control loop is
given in Fig. 1. For purposes of clarity, none of the normally provided
subsidiary features, such as manual-automatic transfer stations, fail-safe
devices, safety interlocks and alarms, and indicating and recording equipment, have been included. The operation of the control loop may be
qualitatively described as follows. When disturbances act upon the
process, they cause a change in the measured variable, which has been
selected to be most representative of the desired process condition. The
measured variable actuates the transmitter which relays a signal representative of the magnitude of the measured variable to the controller. As
indicated in Fig. 2, the controller compares the transmitted value of the

7-04

CHEMICAL PROCESS CONTROL INSTRUMENTATION
Set point

Actuating
signal

Measured
variable

Final
control
element

Manipulated
variable

Disturbances
FIG. 1. Simplified process control loop.

measured variable () to the desired value of the measured variable ()s
which is stored in the controller as a set-point adjustment, and produces
an error signal ()E, equivalent to the difference between the transmitted
and desired values of the measured variable. The error signal is operated
on by the controller mechanism to produce the controller output P, an
actuating signal of sufficient power to operate the final control element.
The final control element adjusts the flow of energy or material (manipulated variable) entering or leaving the process in the proper direction so
as to force the error to zero. The functional relationships developed between P and ()E by the controller mechanism are known as the control
functions· or control modes. The control functions may be continuous or
discontinuous.

()-~)>()---~

FIG. 2. Generalized controller block diagram.

7-05

INSTRUMENTATION SYSTEMS

Continuous Control Functions

Although the number of possible continuous control functions which
might be used is very large, only three are used to any great extent in
process control. These are (a) proportional action, (b) ~utomatic reset
or proportional plus integral (floating) action, and (c) rate or derivative
action.
Proportional Control. In the proportional control mode,. the cont.roller output P is proportional to the control error OJi):

where K = proportional gain.
In process control the more common expression for the proportional
factor is proportional band or throttling range, defined by' the following:
100
Per cent proportional band = - .
K
The frequency response amplitude characteristic of a proportional controller is not perfectly flat as indicated by the defining equation above,
but has some dynamic features dependent upon the particular controller
design and the controller load.
Reset Action. A controller having only integral or floating action is
not too common. Usually proportional and floating action are combined.
Ideal proportional plus automatic reset action may be defin~d in the time
domain as

P = KOE:+ KR fOE dt.
Laplace transforming leads to the equation
P(s)

=

(K + ~R) OE(S)

= (}E(S) KR
S

=

or
where

(}E(S)

pes)

KR

(}E(S)

S

-- = -

(~S +
KR

1)

K
(~S
s(K/KR) KR

(TRS

+ 1)

K

=-

TRS

+ 1),
(TRS

+ 1)

TR = K/ KR = Automatic reset time constant.

The frequency response plot of this idealized control function is given
in Fig. 3. The effect of automatic reset is to give greater controller gain

7-06

CHEMICAL PROCESS CONTROL INSTRUMENTATION
VI

Q)

.c

'u
QJ
"0

~

~

~
QJ

"0

.a
'c

K

til)

III

:E

log w
VI

~

0

tiD
QJ

/ / .....

"0

-

~~-45

~

QJ

~
a..

-90

_.....

/

/

/

--

,//

FIG. 3. Frequency response, ideal proportional reset action.

at the low frequencies, starting at the corner frequency, l/TR, and increasing at a rate of 6 db/octave as frequency decreases. An increased phase
lag is also associated with this action. It is common in process control to
refer to the amount of automatic reset action by the magnitude of l/TR
expressed as repeats/unit time (equivalent to radians/unit time).
The idealized automatic reset action described above is never actually
obtained in a practical controller because of the expense involved in its
mechanization. The reset action most often realized is similar in performance to a lag network having the transfer function
peS)

--=

BE(S)

aK

+1
.
aTRs + 1
TRS

The frequency response plot of this control function is given in Fig. 4.
The reset gain a ranges from zero to 500 depending upon the controller
design and sometimes upon the value of the proportional gain K. This
interaction between the reset gain and proportional gain is not generally
desirable but cannot be avoided in certain controller designs.
Rate Action. The rate or derivative control mode is never used alone
in a process controller. It most commonly appears in conjunction with
proportional or with proportional-reset action. Ideal proportional rate
action may be characterized in the time domain by

P = KBE

.

dBE

+ K D -dt·

INSTRUMENTATION SYSTEMS

7-07

en

Qj

..c
"0
CI.l
"0

CI.l
"0

I

"ctlO

I

q:,~

~

.a

I

1

1-:;:;

ro

:E

r---~--~--------~-----------------

log w

en

o

CI.l
CI.l

l

q:,f.J.

-45

~

CI.l

en

~

-90

a...

FIG. 4. Frequency response, realistic proportional reset action.

By Laplace transformation,
P(s) =
(}E(S)

K(KnK s + 1)

K(Tn S

=

+

1)

Tn = KD/ K = Derivative time constant.

where

The frequency response plot of this idealized proportional rate control
function is given in Fig. 5. The effect of derivative action is to give phase
en

Qj

..c
"0
CI.l
"0

~

~
r-----~----------~
~

I
I

CI.l
"0

.a

"c

K

I

tlO

ro

1

lTD

:E

log w
en

~

+90

tlO

CI.l

""C

-

q:,~ +45

~

CI.l

en

ro
.c

a...

----._-//

_/

o -----------

FIG. 5. Frequency response, ideal proportional rate action.

7-08

CHEMICAL PROCESS CONTROL INSTRUMENTATION

lead. Also associated with this desired phase lead is an inescapable increase in controller gain at the higher frequencies. In process control, the
amount ~f derivative action is expressed as rate time in units of time,
equivalent to the magnitude of Tn.
In a practical controller, it is physically impossible to achieve ideal
derivative action. In fact, such action would· ren~er the controller useless, since it w,ould amplify process "noise" (which usually predominates
'at' the higher frequencies) and would saturate the controller output.
Therefore, the practical implementation of rate action is very similar to
a lead network having the transfer function

+

pes)
(}E(S) = K

[TDS
1 ]
(l/{3)TDS
1

+

The frequency response plot of this more practical control function is
given in Fig. 6. The value of the rate time is Tn. The rate gain f3 ranges
III

W
.c

'u

<1l
""0

<:er..
~ r-------------~-------4_-----+--<1l
""0

.a

K

'c:tlO
ro

:E

log w

III

~ +90
~

""0

~ +45

/

~

,/

<1l

III

ro

..c

c..

o --

_/

/

/

/-,,

,"-

"-

'

.......

---

FIG. 6. Frequency response, realistic proportional rate action.

from 0 to 50 depending upon the controller design and sometimes upon
the value of the proportional gain.
Controller Mechanisms. :Mechanization of control functions can be
accomplished in a variety of different ways, electronically, pneumatically,
hydraulically, mechanically, or by any combination thereof. The task
of quantitatively analyzing all these specific devices, indeed even of
qualitatively describing most of them, is next to impossible. Therefore,
the reader is referred to the voluminous controller manufacturers' literature for these specific details.

INSTRUMENTATION :SYSTEMS

7-09

However, two important types of controllers will be discussed by
means of selecting examples-the electronic controller (see Sect. 7, Elec- .
tric and Electronic Components) and the pneuinatic controller (see Sect.
6, Pneumatic Components). The latter is important since pneumatic controllers are by far the most commonly used type in the chemical and petroleum industries. The former is important because it represents a new
trend and is being applied more and more frequently in industrial process
control systems.
Discontinuous Control Functions

A great many types of controllers operate in a discontinuous fashion.
In one class of discontinuous controllers, the corrective action is a discontinuous function of the measured variable. In this class are the off-on or
two-position controllers, which are used widely in industrial process control and which will be described briefly here. In another class of discontinuous controllers, the corrective action and/or the error sampling are
discontinuous functions of tlflle. Members of this class are discussed in
Chap. 12, Sampled-Data Control, and Vol. 1, Chap. 26, Sampled-Data
Systems and Periodic Controllers, and will not be treated here.
The off-on controller is used primarily because of its simplicity of design and construction and its correspondingly low cost. Its successful
use is restricted to processes which are characterized by one predominantly large first-order time constant and small dead time.
The off-on controller action is given in Fig. 7. \Vhen the controlled
variable is outside the differential gap in one direction, the corrective
action is maximum or on; when the controlled variable is outside the
Corrective
action
On

~

~

Differential
gap

Measured
variable

Off

FIG. 7. Off-on controller action.

7-10

CHEMICAL PROCESS CONTROL INSTRUMENTATION

differential gap in the other direction, the corrective action.is minimum or
off. The purpose of the differential gap is to increase the switching period
so as to reduce wear.
Analysis of the off-on controller alone is fruitless and must be done in
conjunction with the process which it is to control. Use of analog computers is highly recommended for this type of problem. However, some
powerful analytical methods are available where access to an analog computer is inconvenient. Oldenbourg and Sartorius (Ref. 9) have analyzed
the off-on controller with processes having dead time and a single firstorder lag, and have developed charts for predicting the period and maximum amplitude of the controlled variable. Kochenburger has developed
a describing function technique suitable for analysis and synthesis of
off-on control systems (Ref. 8). The powerful phase plane technique,
useful in analyzing systems of lower than third order, has been applied
to off-on control systems by Eckman (Ref. 5).
3. PNEUMATIC CONTROL SYSTEMS

Historically, pneumatic and hydraulic devices antedated the development of electronics. For reasons of cheapness and safety (no spark
hazard, no combustible hydraulic fluid), pneumatic equipment took and
maintained an early lead in the petroleum industry, which until World
War II was more advanced than any other process industry in its use of
automatic control.
Board-Mounted Controller

The commonest arrangement of pneumatic devices in a pneumatic
control system has both the process variable transmitter and the final
control element in the plant with other equipment located on or behind
an instrument panel (control board) in the central control room. As
shown by Fig. 8, this system may be cut into three noninteracting segments for testing or for system design.
Transmitter Input to Controller Input. It is assumed that the tram;mitter input impedance is high in comparison with the signal source impedance. This is sometimes not true, however, as for example when a
pressure or differential pressure transmitter is connected by long, smalldiameter impulse lines to the signal source. Displacement type level
transmitters also have a low input impedance. This necessitates consideration of the interaction between the process and the transmitter. The
frequency response of a typical transmitter plus 250 ft of ~ -in. o.d.
(O.180-in. i.d.) tubing is shown on Fig. 9 (Ref. 4). This is valid for
pressure or differential transmitters; for temperature and liquid level the
frequency response of the input circuit must be added in. (Note tHat P
has the units of Ib/ft2.)

7-11

INSTRUMENTATION SYSTEMS

Manualautomatic
station
Process
variable
transmitter
()i

= process variable

(S)

Recorder

____ S~!.r:.a~c~n.!!:~ ~~~ ______ L __________ !~I~ ________ _

FlO. 8. Typical pneumatic control system.

Cycles per second
0.1

0.01

--

0
2::3

5i

0.5

-6

0.25

-12

--r-...

.0

ro

~

i~
Ql

"0

~

0.1
0.05

'c

~
:::E

0.025

.0

'*

-18

~

-24

'u

0.01

~

r--....

'",
"-

~-30

'"

-36

Ql

"0

:Ec: -42
t:lD

ro
:::E

-48
8;

Sine wave
-54 I-generator

250 II ~ 0.J80-in.
i.d. tubing

p.

Transmitter

-60 I -66 I -

-72

Controller

p.e)

....!...!!::!..=
KG(')
6 (jw)
)w
j

Input signal 8j

I

I

I

I

['\1\

\

o
-30
-60

-90 :G
QJ

-120

I'\.'\

-150

I\.

"

I

6D

~

-s


OD
c:

-180 ~

VI
~

-300

FIG. 14. Frequency response of typical pneumatic transmitter plus short. line:
with short line load only; (2) with short line plus long branched line.

(1)

(high internal impedance) this is equivalent to a short circuit, anddistortion and poor performance result.
Length of Transmission Line and
Branched Loads. For reasons which

are discussed earlier it is not easy to
draw simple generalizations about the
effects of either transmission line length
or branched loads. As line length increases, the input impedance approaches
the characteristic impedance of the line.
For line lengths of 250 ft and greater
there is little change in the loading of
the device driving the line. As l!ne
length approaches zero, the input impedance approaches the line termination impedance. Generally, speed of
transmission is proportional to line
length. See Figs. 20 and 28 in Sect. 6.

To M.-A.
station

1: 1 relay

Controller

Cutoff
relay
To valve
input

FIG. 15. Isolation of controller output line to main control board.

7-16

CHEMICAL PROCESS CONTROL INSTRUMENTATION
Cycles per second
1 :" ..

01

0

.&
:l

<5
VI

..c
rc

0.5

-6

0.25

-12

:Q:
o~

~

~

Ql
"C

.z
'c

0.1
0.05

~ 0.025
::!:
O.O~

IGII
,,-- ~

r---.:::::

-

-18

'

-

l - i----

VI

Qj

..c -24
'0
Ql

r--

-------

-

;--

~ -36
~

.z

-

Ps

S.W.G.

cP2 ......

.~ -48
rc

-60

~
-

"8 ".",;"

PI?

Valve
positioner

:G

-120

~

- -150

250 It x
0.!80-in .
i.d. tubing

f-

-90

~

Cutoff
relay

10 It x 0.!80-in.

-42 -

-30

'\

:-.........

-..: -30

~

o

,...,.

"C

Ql
"C

::!:

-54

f-

-60

f-

-66

f-

p.(jw)
K = 1 psi/psi
Reset rate = minimum
IP.lss = ± 4% of controller input signal range

I I

"" I

I

ci
'ii'o
c:

I

I

I

I

rc

-

-210

-

-240

a:

- -270

• This branch removed for case 1

I

-6

VI

- - = KG(jw)

,
Indicator

bO

- -180 :

Pp(jw)

-72

FIG. 16.

-- ----~
/T,I'-.

...........

'.

I

I

-300

Frequency response of typical pneumatic controller plus short line: (1)
without branched load; (2) with branched load.

Branched loads, as shown by Figs. 14 and 16, can have quite a detrimental
effect on performance.
Impedance of Transmission ~ine Termination. The termination is
almost always a volume~pure capacitance., For very small volumes the
transmission line acts as though it is terminated in an open circuit, while
for large volumes, such as the dome of a spring-and-diaphragm valve, the
line may act as though it is short-circuited.
Signal Level. The Instrument Society of America and the Scientific
Apparatus Manufacturers Association have standardized on pneumatic
transmission systems with a range of 3-15 psig. Additional ranges of 327 psig and 6-54 psig have recently been made standard. The higher
the signal level, the faster is transmission.
Signal Amplitude. Most pneumatic devices are decidedly nonlinear in
a dynamic sense. For very small input signals, say less than 0.1 psi peak
to peak, the effects of internal stiction and hysteresis are noticeable. For
signals of 0.5-1.0 psi peak to peak most devices are fairly linear provided
they are terminated with a high impedance. Signals much above 1.0 psi
peak to peak usually cause saturation and clipping; also a shift in the

INSTRUMENTATION SYSTEMS

7-17

output d-c level occurs because of unbalanced action of the loading and
exhaust pilot valves.
Air Supply Impedance. If the pneumatic power supply has high
internal impedance-and this is often the case-device and system performance are affected adversely. The usual trouble is that the supply
line is too long or tob small, but sometimes the supply regulator cannot
supply enough air. Generally speaking, the supply regulator should have
an impedance of no greater than 0.1 psi/scfm over the desired airflow
range. Instrument header pressure is commonly 46-60 psig, which means
supply lines to and from the regulator should not be less than % in. o.d.
(0.305 in. i.d.), and the line from the regulator to its load should not be
more than 10 ft long. If more than one device is to be supplied from a
single regulator it may be necessary to "decouple" each device by insertion of a volume (1 cu ft or greater) in the supply line just ahead of the
device. For devices such as boosters or positioners which require lots of
air but do not require regulated air pressure, it is best to omit the supply
regulator and connect the device directly to the air header by a line at
least % in. o.d. (0.305 in. i.d.).
Nature of Restrictions in Transmission Systems. An increasing
number of pneumatic systems use plug-in connectors with internal check
valves to prevent air leakage during disconnects. These connectors and
the pneumatic switches in the manual-automatic station sometimes have
such small openings relative to the tubing cross-sectional area that effectiveness of transient signal transmission is seriously reduced.
4. ELECTRIC AND ELECTRONIC CONTROL SYSTEMS

Unlike pneumatic control systems, electric and electronic control systems do not fall into well-defined patterns. Both a-c and d-c transmission systems are used, and manufacturers employ a wider variety of 'components and techniques to accomplish given measurement and control
functions than do manufacturers of pneumatic gear. The use of impedance-matching techniques is standard and system performance is not as
critically dependent on component location and arrangement as for pneumatic systems. Usually the electric system is not, however, entirely electric. The valve-actuating mechanism is most often pneumatic, although
self-contained electrohydraulic positioners are beginning to be used.
An interesting feature of present electric control systems is that they
are analogs of conventional pneumatic systems. The inherent flexibility
of electronics as exploited for computational and control functions in aircraft and military applications has as yet not been employed· in process
control systems.
A typical electronic process control system is show~ on Fig. 17. At

7-18

CHEMICAL PROCESS CONTROL INSTRUMENTATION
Transmitter

Recorder or
indicator

Process
variable
Manual-automatic
station

FIG. 17. Typical electronic process control system.

present there is no uniformity among manufacturers as to the mode of
signal transmission. Swartwout uses a hybrid transmission system: (a)
ac from the transmitter to the controller, (b) dc from the controller to the
electropneumatic converter, and (c) pneumatic transmission from the
converter to the valve. Robertshaw-Fulton uses all d-c transmission, and
the controller output normally goes to an electropneumatic or electrohydraulic positioner rather than to an electropneumatic converter.
5. HYDRAULIC CONTROL SYSTEMS

Hydraulic controls have been most commonly used for heavy duty
service in steel mills, coke ovens, etc. They are characterized by extremely durable construction for long, maintenance-free service under
difficult operating conditions. Usually they are located in the field
rather than in a central control room. Typical applications inclu~e turbine and engine control, flow and pressure control, gas holder level control, and gas mixing control. Hydraulic control systems are not usually
divided into separate components such as transmitters and controllers, but
commonly have many of these functions combined in one apparatus.
A hydraulic flow control system made by General Precision Equipment
is shown on Fig. 18. The differential-pressure detector, set point, summing circuit, and hydraulic amplifier constitute a regulator package.
When used in conjunction with a piston actuator as shown, the total
comprises a system with integral (floating) control action.
6. PNEUMATIC COMPONENTS

Pneumatic Transmission Systems
Pneumatic Circuit Elements. Pneumatic circuits may be analyzed
and designed in a manner analogous to electric circuits except that careful

INSTRUMENTATION SYSTEMS

7-19

Flow~

Power cylinder

Differential
pressure
detector

Oil supply

FIG. 18. Typical GPE hydraulic flow control system.

attention must be given to nonlinear and distributed effects (Refs. 10 and
11). In the ensuing discussion nonlinearities are linearized by standard
methods.
Pneumatic Capacitance.
a. Pneumatic capacitance is defined by the expression
pes)

1

Q(s)

Cs

--=-

where s = Laplace transform variable,
Q = air flow, ft 3 /sec,
P = air pressure, Ib/ft2 abs,
C = capacitance, ft5 lIb.
For a simple volume filled with air,
where V = volume, ft 3 ,

0.720 V
Cadiabatic = - - Pay
V

Cisothermal

7-20

CHEMICAL PROCESS CONTROL INSTRUMENTATION

b. If the volume is not simple but has some additional form of compliance
associated with it, the expression above must be modified. Consider, for
example, the capacitance of a bellows or topworks of a spring-and-diaphragm valve:

where A == average cross-sectional area of bellows or diaphragm, ft 2,
K == spring constant, lb/ft,
C = capacitance due to average volume.
c. The capacitance per foot of }i-in. o.d. (0.180-in. i.d.) tubing is

C' =

0.000177
Pay

(ftSlib) 1ft

(isothermal value).

The capacitance per foot of %-in. o.d. (0.305-in. Ld.) tubing is
C' =

0.000506
Pay

(ft5 lib) 1ft.

If the tubing does not have rigid walls, as for example if rubber or plastic
tubing is used, it may be necessary to add in the effect of the compliance of
the tubing. Then

C' = V'

where V'
P av
D
b
E

=

=
=
=
=

(_1
+~) (ftS/lb)/ft
Pay
bE

volume per ft of tubing, ft 3 /ft,
average pressure, ibift 2 abs,
mean diallleter of tubing, ft,
tubing wall thickness, ft,
bulk modulus of tubing wall material, Ib/ft2;

Pneumatic Inertance. Inertance is the hydraulic or acoustic analog of
inductance. It may be defined as follows for tubing:

pes)

= sLQ(s)

where
lp
L = - - , lb sec2/ftS ,
32.2A
where l = tubing length, ft,
p = density of air, Ib/ft3,
A = tubing cross-sectional area, ft2 .
.For U-in. o.d. (0.180-in. i.d.) tubing
L'

::I

6.18 X 10-3Pav (lb sec 2 /ft S)/ft.

INSTRUMENTATION SYSTEMS

7-21

For %-in. o.d. (0.305-in. i.d.) tubing
L'

= 2.15 X 10-3 P av (lb sec2 /ft 5)/ft.

Pneumatic Resistance. Pneumatic resistance for tubing or valves may be
defined as

R =

api
aQ

lb sec/ft5.
Q=Qav

Laminar Flow. For >i-in. o.d. (0. 180-in. i.d.) tubing,

R

R' = - = 301 (lb sec/ft5) /ft.
l

For %-in. o.d. (0.305-in. i.d.) tubing,
R'

R

= - = 36.6 (lb sec/ft5) /ft.
l

Plus-Minus Flow. Most pneumatIc equipment operates in such a
fashion that the average or steady-state flow through the pneumatic
transmission line is zero. This is necessarily so since the load is usually
a bellows, spring-and-diaphragm topworks, or some other purely reactive
load. If we assume that a large sine wave of pressure is applied at the
input of the transmission line, then within a half-cycle flow will be laminar, transitional, turbulent, transitional, and laminar. The pattern of
this flow, which we have chosen to call "plus-minus" flow, negates use of
the techniques commonly employed for linearizing resistance when the
amplitude of flow variations is small compared to the average flow. If,
of course, the amplitude of the driving pressure sine wave is never large
enough to force the flow out of the laminar range, then the value for
laminar flow resistance may be used.
To handle this problem it is necessary to take into account the magnitude of the driving signal and the length of tUbing. Figure 19 presents a
correlation which has been found to give fairly good results. Strictly
speaking, however; it is necessary by trial-and-error calculation to find
out at each frequency of driving signal just how much of the signal appears across the resistance in the line. ; This value of pressure drop per
foot is then used on Fig. 19. At very low frequencies the flow will be
laminar throughout the line. At high frequencies there will be turbulence
at the inlet to the line which, however, will die down within a short distance so that overall flow may be treated as laminar.
Pneumatic Transmission Lines. Simplified Theory for Short Lines.
a. Low-Impedance Termination. It often happens that a pneumatic
line is terminated by a large capacitance such as that due to the top-

7-22

CHEMICAL PROCESS CONTROL INSTRUMENTATION
10
II

I

I

I
ro
·iii

7
~/

~

.~/

c.

.~

~

i7j

!J.PR

::J

VI
VI

-l-P

~

....~

.~

Q)

bO

e

~.

~

"§
"b~ I
o· /
.~:L

Q)

>
ro

X
~

.~

"§'/

~

"ti

0·'[

"'\"'/

ro

Q)

c.

.~.

..\~I

V

I

.s

.!..
Q)

·1

.~

~.

~

C.

j

0.1
"E
Q)
u

;:::
·iii

a..

17

0.01
10

100

1000

10,000

(Ib sec/ft 5 )/ft

Reff ,

I

FIG. 19. Effective resistance of air lines at 25°C at any pressure level.

works of a valve. In this event the capacitance of the line may be
neglected as being small by comparison. The equivalent circuit is then
Qi

R

L

~-l\
L
1 R = total line resistance

r!

ro

CL

TJPr.
_

L = total line inertance
CL = capacitance of load

The output-input pressure ratio is
~L(S)

1

--=

~i(S)

2

LC Ls

+ RCLS + 1

The driving point impedance is

Zi = R

+ Ls + -

1

CLs

LCLS2

+ RCLS + 1

= ------CLs

This analysis gives rough checks with experimental data for lines from
5 to 10 ft in length which are terminated by the topworks of a spring-and-

7-23

INSTRUMENTATION SYSTEMS

diaphragm valve. For longer lines it gives a fair check for amplitude but
not phase.
b. High-Impedance Termination. It is often true that a pneumatic line
is terminated by a high impedance, such as the input chamber of a controller or the input bellows of a valve positioner.
The equivalent circuit is
R

L

T.+
c

_

........_ _ _ _ _ _ _ _.....I

L

c

where C = capacitance of line. The output-input pressure ratio is
1

L

(~ + C

L)

2
8

+ R (~ + C

L) 8

+1

and the driving-point impedance is

z·=

L(~+ C1
}2 + R(~+ CL)8 + 1

, (~ + CL) + ~
8

8 [

L

(~ + CL) + R (~ + CL) + 1]
8

2

.

8

This has been found to give excellent results, both for magnitude and
phase, for lines up to 30 ft in length with small volume terminations.
Distributed Treatment of Pneumatic Transmission Line. Because of
distributed capacitance, a long pneumatic line and its load cannot be
treated as a lumped circuit. Instead, it must be handled as a distributed
system, and one may employ an analysis very similar to that of electric
transmission lines. Since a full treatment of this subject is well covered
in electrical engineering literature, remarks here will be restricted to a
brief discussion of transmission line parameters and important transmission line relationships in terms of frequency response.
Let us consider first the transmission line parameters:
a. Series Impedance, Zs

Zs = R'

+ jwL'

= complex series impedance per unit length
of line (L' and R' are on a per foot basis).

b. Shunt Admittance, Y s

Y s = G + jwC' = complex shunt admittance per unit length of line
(C' and G, the conductance, are on a per foot basis).

7-24

CHEMICAL PROCESS CONTROL INSTRUMENTATION

c. Propagation Factor, "I
"I

=

VZs y s

=

V (R' + JwL') (G + JwC')

For fluids in conduits with
impervious walls G = O.

d. Characteristic Impedance, Zk
Zk -

J

Zs -'Ys -

JR' ++
G

JwL'
JwC'

At low frequencies, the ratio of qk for 7,i-in. o.d. (0.180-in. Ld.) tubing to
Zk for %-in. o.d. (0.30S-in. i.d.) tubing is 4.9; at high frequencies it is 2.9.
From these parameters, certain important transmission line relationships
may be derived:
a. Driving Point Impedance, Zi
ZL + Zk tanh "Il
Zi= Zk-----------Zk + ZL tanh "Il

where ZL = transmission line termination or load impedance,
l = line length, ft.
b. Output-Input Pressure Ratio, PL/P i
I

ZL + Zk l
---e'Y
2ZL

+ ZL -

Zk

e-'Y

l

2ZL

I

cosh "Il

Zk
+ -sinh "Il
ZL

c. Output Pressure-Input Flow Ratio, PL/Qi

Zk

+ ZL tanh "Il cosh "Il

Pneumatic Transmission Line Data. The frequency response of
several lengths of ]4 in. o.d. (0.180 in. i.d.) is shown on Fig. 20. A comparison between the frequency response of
-in. o.d. and %-in. o.d.
tubing for 200 ft. of tubing is also shown.
Optimum Transmission of Pneumatic Signals. Consider pneumatic
transmission systems such as shown in Figs. 21 and 22. Optimum trans-

*

7-25

INSTRUMENTATION SYSTEMS
Cycles per second
1 T_ _,,0~1

____. -____. - - ,__~1r-__- ,____~__~~~10

IGII f--f___ ~I-°It-rt--=~~~~-t~~-T==~--+-~

--Rr-;~

Q)

"5
~
..c
C\l

0.5

-6

0.25

-12

~

.,g

0.1

~

~

0.05

~

0.025

~

r-.....

~r- ~t----r--E.21-f-

1'---

IG 4

t--r-

11

~~t~~~-r~~
__
~~---T--~~=
___
-=~~~~~I~G3~1~~0

-18

-30

1"\

~ "-,,~

~ -24~-+-+---~--~~~-4~~--~--4-~~~~-60

.a .'c

~ -30 1-+--+-+_---+-_---+-~_*"'~+_""~_+_-_+_-1Jl~l\~

:E

Q

0.01

"'f'f'.. "t\

90

-

~. - 36 I-+--+-+----l---l__-+-----I'o'\.-+-I\~'\'<---+--'l.,,~-l----l--+-~ -120

~ -42 f-

r::::-Yi

~ -48f- ~
:E

f-I

High

~;~~~~:~i~~

PLU~I~.
.
PiUW)=KG()w);K=IPSI/psl

-54f_ 60 f-

=::

PLi.::l

I

Case I : 30 It x O.lBO-in. i.d. tubing
Case 2 : 100 It x O.lBO-in. i.d. tubing
Case 3 : 200 It x O.lBO-in. i.d. tubing
g
calse 4 : 200 It xI 0.305-in. i.d·ltubin

I

\

""\

\

-150

~1J2

"~

\1J4

1\

I

~

~
\

-180

Z.

'1

Qi

~

240

-+---+--+--1-:::

FIG. 20. Frequency response of pneumatic transmission lines.

Ii

PL

=========~===================================~~=~
FIG. 21. Passive transmission system.

Relay

p';==[:~>~Pa__________Q_~
___________________
PL__~
Zi!"'""'~_________ t. - - - , - - - - - - - - - - o..~1
~Short connection
FIG. 22. Transmission system with active elements.

CIi

~

~

t\. -2100..

.-.+-_ _---+I__\__
\_\-+--------------,

~

-

Hl

Hv

Main vessel
Inflow,

Qi

Displacer

'--'

Displacer
lK- housing

---0-

Outflow,
'---_ _ _--'-_- Qo

FIG. 33. Typical installation of displacement type level transmitter.

7-31'

INSTRUMENTATION SYSTEMS

The principle of operation is as follows. A cylindrical displacer with
a specific gr,avity somewhat heavier than that of water is partly immersed in the liquid whose level is to be measured. The displacer is
suspended from a torque arm which is connected to a torque tube; Support for the displacer then comes partly from the buoyancy of the liquid
and partly from the spring action of the torque tube. A rod inside the
torque tube is fastened to its free end. An eccentric cam or lever on the
other end of the rod acts as a flapper to a fixed nozzle. Angular motion
on the free end of the torque tube is thereby converted to a proportional
displacement between nozzle and flapper. This results in an output air
pressure approximately proportional to liquid level. An adjustment of
the nozzle position serves to shift the output air pressure range, and
thereby functions as a set-point adjustment for automatic control.
Figure 33 shows a typical installation involving an external housing.
It is important to note that there are two modes of resonance which the
system designer must consider carefully. The first is that which exists
between the two liquid levels, level in the main vessel, Hz, and level in
the housing, H v (Ref. 13). For most installations,
Hv(8)

1

- - - - = ------------------

HZ(8)

LTAa

2

RTAa

--8 +--8+ 1
PZ

PZ

where LT = total inertance, lb sec 3 /ft 5 , between the two liquid levels,
3
Pl = liquid density, Ib/ft ,
RT = total hydraulic resistance, lb sec/ft5 , between the two liquid
levels,
Aa = annular area, ft 2 , between displacer and housing.
In practice, such installations are sometimes afflicted with severe resonance.
The leg between the main vessel and the displacer housing must be kept as
short as possible and it is occasionally necessary to insert resistance, usually
.m t h e form 0 f
. ratIO,
. RT
.
a val
ve, to·
raIse t h e d ampmg
-- Jl£;a
- L ,to a sat IS2
TPZ
factory value.
The other mode of resonance is that due to the mass of the displacer and
the torque tube spring constant:

Kz

1

-----X-------------------------Kz + KTT
M
b
----82+
Kz

+ KTT

Kz

+ KTT

8+ 1

7-38

CHEMICAL PROCESS CONTROL INSTRUMENTATION

where HF = displacer motion, ft,
M = displacer mass, lb sec 2 /ft, = WF/g,
b = viscous friction, lb sec/ft, between liquid and displacer,
KTT = torque tube spring constant, lb/ft,
K z = liquid "spring constant," lb/ft,
= Pl (7rDF2/4) ,
DF = displacer outside diameter, ft.

When used with liquids whose specific gravity approaches that of water,
commercial transmitters have resonant frequencies in the range of 2-3
cps and are underdamped, with damping ratios less than unity. 'Vhen
the pilot output is terminated in a low-impedance load such as the topworks of a large spring-and-diaphragm valve, this resonance may be
fairly well damped out. If, however, the pilot output is terminated in a
high-impedance load such as a valve positioner, resonance may be severe.
In this event it may be necessary to remove it with a suitable filter circuit
inserted in the output air line.
Ball-Float Transmitters. Where it is desired to measure or control
level within narrow limits, say 0.5 in. or less, a ball-float transmitter is
often used. This usually has a fixed output pressure range with an adjustment to the nozzle or flapper functioning as a set point.
One design (1\1oore Products Company) is packless and uses a flexible
float arm (see Fig. 34). The analysis of this device is similar to that of
the displacement type transmitter.

Flapper-nozzle
'----___ Output
pressure

Air
supply

FIG. 34. Typical installation of ball-float level transmitter.

7-39

INSTRUMENTATION SYSTEMS

HF(S)

----=
Hv(s)

Kl
Kl

+ Kia

1

X-----------------------------MF

_ _ _ _ _ 82

Kl

+ Kia

b

+
Kz

+ Kia

s+1

where Kia = float-arm spring constant, lbjft,
K z = liquid spring constant, lbjft,
= PI [7l"DFZav - 7l" Z av 2 ],
Zav = average submergence of float, ft,
DF = diameter of float, ft.
Again, this type of device tends to be underdamped and it is sometimes
necessary to insert an appropriate filter in the output air line.
Flow Transmitters. Flow is most commonly determined by measuring the pressure drop across a fixed orifice:

Q = kAV !1P
where A is the orifice area.
An alternate procedure, however, is to hold the pressure drop fixed by
suitably varying the orifice area. The usual way of doing this is to insert
a bob into a tapered, vertical tube (see Fig. 35a) such that the bob is
supported by fluid entering at the bottom. As the flow increases, the
bob moves upward, thereby increasing the annular area between the bob
and tube. The pressure drop meanwhile remains constant. An instrument of this type is called a rotameter and has an advantage in that flow
is linearly related to bob position.
The earliest versions of the rotameter had glass tubes and were used
as indicating devices only. More recently, however, there has been a
trend to various methods of transmitting bob position and a trend to metal
tubes, particularly for high-pressure service. Although a number of
electrical methods have been developed to detect bob position, the pneumatic transmitter has been more popular. One method, used by Fischer
& Porter Company, provides an extension to the float. The top of this
extension has mounted on it a magnet whose position is tracked by an
external magnetic follower yoke (see Fig. 35b). This yoke is connected
to a precision pneumatic circuit which converts position to a proportional
air pressure.
Pneumatic Controllers

In order to show one example of how the control functions described
under Continuous Control Functions, Sect. 2 II?-ight actually'be achieved
in a practical pneumatic controller, an analysis of the Taylor Tri-Act
controller will be made. This example is based on the analysis developed by Bigliano (Ref. 1).

7-40

CHEMICAL PROCESS CONTROL INSTRUMENTATION

J

~Out

L

Tapered
glass tube

[f
T
In -----+

(a)

Internal m.

t'2

!tI

G:

~

....

2VI
o
o

n

o

z- i
::0

orz

CD

Gain
valve

i{

Co

o
.2
c:

Rl

Oro

(!)

Ul
-i
::0

C

~
m

Z

-i

»
-i

oZ
®

Output

Cutoff relay

Air supply

FIG. 36. Schematic diagram of Taylor Tri-Act controller.

Capillary restriction

(Courtesy of Taylor Instrument Companies.)

7-43

INSTRUMENTATION SYSTEMS

q2~

Rate circuit

Gain
circuit

Reset circuit

FIG. 37. Block diagram of Taylor Tri-Act controller.

According to manufacturers' data,
kd =

1

~

0

in./Ib,

Kd = 6300 psi/in.,
Al = 7r in.2,

A2 = 7r/2 in. 2 ,
flP d
flPE

= S!!.!2) (37) [
1 + 7r(37)

T

(

dS

+

Td

1

1
)

+ 7r(37)

s+1

= 05 [ TdS + 1 ] .
.
(Td/117)s + 1
Gain Circuit
flP I

=

flP d

-

R2 q2,

- flP 2

= AakgKgflPl,

flP 2

flP I = R1ql,

-

-AakgKgflPI - flP I = R 1ql,
ql

flP I

= - -

Rl

(AakgKg

+ 1),

]

7-44

CHEMICAL PROCESS CONTROL INSTRUMENTATION

llP I

llP I

I!.P, [ 1
llP I

=

llP 2 =

+ ~: (A3kgKg + 1) ]

llP d

= I!.Pd,

llP d
1

+ (R2IRI)(A3kgKg + 1)
- A3kgK gllP d

.

1

+ (R2IRI)(A3kgKg + 1)

,
,

llPd

llPg = llP I - llP 2 =
=

] •

= llP d - R2 [ RI (A3 k gK g + 1) ,

1

+ (R2IRI)(A3kgKg + 1)

(1

+ A3kgKg)

+ A3kgKg) .
RI + R2(A3kgKg + 1)
RI (1

According to manufacturers' data:
kg =

1

to in·/Ib,

Kg = 3S,000 psi/in.,

llPg

-=

llP d

3 in. 2 ,

=

As

+ 9S0)
RI + R 2(9S0 +
R I (1

9S1R I
1)

9S1R 2 + RI

Reset Circuit
llFI

= llPg(A s - A4)

llF3 = llPoA4

+

llF3 - llF2 ,

1
TrS

+ 1'

llF2 = llPoA4,
llPo = krKrKpllFl,
llFl

=

llP o
krKrKp

,

llP o

- - - = llPg(A 3 - A4)
krKrKp

llPo

-

llP g

= (A3 - A4)

[

llPoA4
+ --TrS + 1
krKrKJ)(TrS

(1

llP oA 4,

+

1)

+ A4krKrKp)TrS +

]

1

.

INSTRUMENTATION SYSTEMS

7-45

According to manufacturers' data:
A3 = 2'71/3 in. 2 ,

A4 = '71"/3 in. 2 ,
1
8 0

kr =

in./lb,

Kr = 15,000 psi/in.,

Kp = 1.0 psi/psi,
!::.P o
!::.P g

196

-=

[

+
+

TrS
1 ]
196Trs
1

Complete Controller
!::.P o = (!,Pd) (!::.p g ) (!::.Po )
!::.PE
!::.PE
!::.Pd !::.P g
I

[

= 0.5

Kc

=

+

Td S 1
] [ 951R 1 ] [196(Tr S
(Td/ 117 )s
1 951R 2
Rl
196Trs

+

+

Controller gain setting =

!::.P o

(0.5) (951R 1 )
951R 2

196(Trs + 1) (TdS

+ Rl

+ 1)]
+1 '

,

+ 1)

--- = Kc--------------------!::.PE

(196T rs

+ 1)[(Td/117)s + 1]

According to actual measurement, the maximum rate gain is 55 compared to the calculated value of 117, and the maximum reset gain is 200
compared to the calculated value of 196. This discrepancy is probably
due to some uncertainty in the values of kd,
K d , kr, and K r. Because of assumptions reReceiving
bellows
garding loading, the transfer function derived
here is not accurate at signal frequencies
higher than 1 cps.
Pneumatic Recorders

Nearly all nonelectrical data recorders
work on the same principle as shown on
Fig. 38. The free end of a bellows, bourdon
tube, or other receiving element is attached
to a pivoted arm. The other end of the arm
has a pen attached-to it. Various mechanisms are used to linearize and adjust inputoutput motion ratio. Recorders fall into two
general categories as far as type of chart is

Pivot

+

Pen

FIG. 38. Basic pneumatic recorder mechanism.

7-46

CHEMICAL PROCESS CONTROL INSTRUMENTATION

conc,erned, circular chart and strip chart. The former is usually of the
24-hour type whereas the latter may provide as much as two weeks to
thirty days chart supply.
It should be noted that while the signal to the recorder is often a transmitted pneumatic signal, it may come directly from the process. The
receiving element may, for example, be connected to process pressure by
an impulse line or to the capillary tubing from a thermal element.
Pneumatic Control Stations

The trends toward unitized process instruments and smaller control
panels has led to the development of compact control stations. These
stations incorporate the following features: (a) manual-automatic switching, (b) indication or recording of process variable, (c) indication or recording of signal pressure to control valve, (d) control point adjustment,
and (e) remote manual operation of control valve. This multiplicity of
functions requires complex hardware, and the cost of modern control
stations sometimes exceeds that of controllers.
A typical indicating control station is shown on Fig. 39. The control
knob functions as a control point adjustment while the system is on automatic, and as a remote manual loader for the valve while the system is
under manual control. The small index pointer normally functions as
indication of the control point, but when the transfer switch in the upper
left corner is in the valve position, it indicates signal pressure to the
valve. On manual control, the index reads manual signal pressure to
the valve.
To achieve "bump less transfer," that is, manual-automatic switching
without upsetting the process, it is necessary to have circuitry to provide
a means for equalizing controller output pressure and manual signal
pressure. When the manual-automatic switch is in the seal position, the
valve pressure is sealed in. The control knob is then adjusted until the
manual signal pressure is the same as the valve pressure. The system
may then be switched to either manual or automatic without upsetting
the process. It is important to note that in order to prevent the integral
action of the reset circuit of the controller from driving the controller
output to one extreme or the other while the system is on manual control,
the valve signal pressure is continually fed back to the reset circuit.
It is also important to note that the controller output does not go directly to the valve, but first passes through the manual-automatic switch.
In some manufacturers' stations the ports in this switch are so small and
offer such high resistance as to seriously attenuate controller-valve transmission system performance.

INSTRUMENTATION SYSTEMS

7-47

Reg.

--------'Cf---}

_--J

"process indication

FIG. 39. Control station.

Control Valves and Actuators

Irrespective of what type of measurement is involved or whether control is pneumatic, electric, electronic, or hydraulic, a process control system usually has a valve as its final control element. For most system
studies a control valve may be treated as a variable, nonlinear resistance.
Control Valve Flow Formulas (see Ref. 7). Control valve manufacturers rate their valves by the valve flow coefficient CV ' This is defined
as the number of gallons per minute of water which will pass through a
given flow restriction with a pressure drop of 1 psi. The following formulas
relate Cv to flowing conditions.
Liquid flow:

7-48

CHEMICAL PROCESS CONTROL INSTRUMENTATION

Gas flow:

cv =

¢Vm
-------;:=======:::=== 1'f P2
61 vi (PI - P2)P2

¢Vm' f

= 30.5pI

1

~

P2

PI

"2

PI
>2

(critical flow)

= liquid flow, gpm,
= cfh gas at 14.7 psia and 60°F,
PI = pressure, psia, at upstream side of valve,

where V
¢

P2 = pressure, psia, at downstream side of valve,
m = liquid or gas specific gravity (air and water).O).
Reliable methods do not exist for estimating Cv for highly viscous liquids
or for liquids which tend to flash on passing through the valve. For these
cases individual manufacturers sometimes do have empirical data which
apply to their own valves. It is also known that Cv decreases at high
pressure drops, but, again, quantitative data in general form are lacking.
From the above we may derive formulas which relate changes in pressure to changes in flow. These formulas represent the hydraulic or
acoustic resistance of a valve. It should be noted that the resistance
for a change in upstream pressure is not always the same as for a change
in downstream pressure.
For liquid flow:

aP I

Rvl = -

aQ

aP2

Rv2 = -

For gas flow, P2

aQ

5.78 X 10 7Qavm

2(P 1

= ------

(C v)av

2

-

Qav
7

-5.78 X 10 Qavm

--2(P 1

= - - - - -2 - (C v)av

For gas flow, P2 ~ pd2:

l
= -aPl = 466 [P
-.-

aQ

aP2

Rv2

=-

aQ

2
]

T1q av

=0

-

Qav

> pd2:

Rvl

P 2)av
P2)sv

7-49

INSTRUMENTATION SYSTEMS

upstream pressure, Ib/ft 2 abs,
downstream pressure, Ib/ft 2 abs,
= upstream temperature, oK,
= downstream temperature, oK
Q = ft 3 /sec at flowing conditions.

where PI
P2
TI
T2

=
=

Since under industrial conditions flow through a valve is almost always
turbulent, the average resistance of the valve will be

Rav

= 2 (I1P)
Q

lb sec/ft5
av

where I1P = pressure drop across the valve, Ib/ft2 ,
Q = flow, ft 3 /sec.
For liquid flow,

Rav = 12.9 X 104

(V2)
C
v

m
av

For gas flow,

Rav

=

5.50 X 103

= 1.67 X 105

(

PI 2 )
P2Cv T

m

:w

PI
2

>-

1'f

PI
<_.

av

(~) Vm
TC v

.

If P2
P2

2

Control Valve Trim Characteristics. The trim of a control valve
consists of a stem with plug, and an orifice or seat. The plug is so contoured as to obtain a. specific relationship between valve stem position
and Cv • The stem position (or lift or travel) is measured relative to its
position with the valve closed, i.e., plug fully seated. Stem travel is then
limited to some maximum value which will prevent damage to the plug
or valve body.
a. Linear Tril1L (Figs. 40 and 41). Trim is said to be linear if the
following relationship holds:

where X = stem position or travel or lift.

b. Equa~ Percentage Trim (Figs. 40 and 41). The most commonly
used trim in the process industries is the equal percentage type. For a
certain change in stem position there is the same percentage change in
Cv regardless of the valve position. Theoretically such a valve would
never shut off. Practically, the manufacturers choose a ratio of maxi-

7-50

CHEMICAL PROCESS CONTROL INSTRUMENTATION

,

,

r
~

r,

Linear

r
~

Equal
percentage

Quick
opening

FIG. 40. Control valve trim.

100

I

I

I

1. Linear

90 ' - 2.

V

./"'"

Equal percentage
3. Quick opening

80

y

Q)

£ 70

V

~ 60

'x

E50
40

u
~

30

/

II

CI.l

c...

V

V

I~

-

00

LV
10

20

V

V

V

1

20
10

~

,I

E

~c

/('
./

/

V

V

)

i.---- l----

30

40

~

50

-

60

~V
70

80

90 100

Per cent of maximum C v

FIG.41. Flow capacity curves for control valves.

mum Cv to minimum Cv , usually 40 or 50, then put a shoulder on the plug
for tight shutoff. Mathematically,
Cv

(Cv)max]X/Xmax

= (Cv)min [ - - ( Cv)min

For small variations about X = Xav:
Cv(s)

ac v

Xes)

aX

-- = where

kEP=ln

=

(Cv)avkEP

(C v)max
(C v)min

1

x--·
Xmax

INSTRUMENTATION SYSTEMS

7-51

c. Quick-Opening Valve (Figs. 40 and 41). Occasionally there is a
need for a control valve to operate either fully open or fully closed and
to do so quickly. For such service a valve usually has a short, beveled
disk plug, and is known as a quick-opening valve.
Valve Body Design. a. Double-Seated Valve. To a great extent
valve body design must be considered along with valve actuator design.
The double-seated valve with spring-and-diaphragm actuator is by far
the commonest combination used today in the process industries. As
shown by Fig. 42a, the two ports are so arranged that part of the flow

(a)

(b)

FIG. 42. Valve body design: (a) double-seated valve with v-port plug; (b)
seated valve with v-port plug.

single~

is up against the upper plug, and tends to force the stem upward, while
the remainder of the flow is down over the lower plug, and tends to force
the stem downward. It is the objective of this design, therefore, that
the coercive axial stem forces be zero. This would permit the use of a lowpowered actuator of simple design with no offset in stem position (see
discussion on actuators). In practice, perfect balance is not achieved,
and unbalance forces are sometimes quite significant (Refs. 2 and 12).
To minimize coercive axial stem forces further, manufacturers often
use skirted plugs (see Fig. 42a). The slots, usually V -shaped, in the
skirt may be so cut as to achieve either linear or equal percentage characteristics. An unfortunate characteristic of skirted plugs, however, is a
tendency to develop coercive torsional stem forces, although these may
be minimized by careful design.
b. Single-Seated Valve. Aside from the fact that double-seated valves
are difficult to build in small sizes, the advent of more powerful positioners, particularly those with valve stem position feedback, has led to

7-52

CHEMICAL PROCESS CONTROL INSTRUMENTATION

more extensive use of single-seated valves. The single-seated body,
shown in Fig. 42b, is simpler and cheaper to build than the double-seated
design. It is also potentially more efficient hydraulically (Refs. 6 and 7),
although commercial designs do not always achieve this potentiality.
c. Butterfly Valves. For controlling gas flow in large diameter pipes
where moderate or low pressure drops are involved, butterfly valves are
often used. As shown by Fig. 43, a butterfly valve consists of a disk in a

Q

n

o

0
FIG. 43. Butterfly valve.

line. The disk may be rotated through an angle of 90 degrees although a
60-degree angle usually provides nearly full range. The flow characteristics are similar to those of an equal percentage valve although the ratio
of maximum flow to minimum flow is
Air inlet"
smaller.
Many mechanisms have been devised to
rotate the disk of the butterfly valve. Hydraulic piston actuators are often used in
the steel industry whereas the spring-anddiaphragm actuator is more common in the
chemical and petroleum industries.
Control Valve Actuators. a. Spring and
Diaphragm. If one end of a spring is fixed
and a force is applied to the other end, the
Valve
stem
motion or displacement is proportional to
the force and the spring rate. In this case
Valve
the force is generated on a diaphragm by
applied air pressure (see Fig. 44). To obtain a specified valve travel to correspond
to the standard 3-15 psig range used for
pneumatic systems, the spring must be
slightly preloaded. The spring and diaphragm are sometimes arranged so that
FIG. 44. Control valve with
spring-and-diaphragrn actuator. an increase in pressure opens the valve

"~

(bOdY

INSTRUMENTATION SYSTEMS

7-53

(air-to-open), and sometimes so that an increase in pressure closes the
valve (air-to-close). In either case, if there are no coercive axial stem
forces, there exists a fixed relationship between air pressure and valve
flow coefficient, C v • If, however, as is usually the case, there is some stem
thrust due to the fluid flowing through the body, the valve actuator will
no longer have a 3-15 psig range, although the span will still be 12 psi.
For example, an air-to-open valve with a 100-in.:! diaphragm is subjected
to a 200-lb downward stem thrust, the effective actuator range will be
5-17 psig.
The transfer function for a valve with spring-and-diaphragm actuator
is approximately
Xes)
A/K

pes)

W

2

b

-s+-s+l
gK

K

where X = stem motion, ft,
P = diaphragm pressure, Ib/ft2 abs,
A = diaphragm area, ft2,
W = weight of moving parts, including stem and plug, lb,
I( = spring rate, lb/ft,
b = coefficient of viscous friction between valve stem packing,
lb sec/ft,
g = 32.2 ft/sec 2 •
The equation is useful for showing that a fast, stable valve should have a
high spring rate and low mass of moving parts. Experience has shown
that large valves (nominal size 8-in. or larger) with solid plugs sometimes
have a tendency to instability. The reason is that the damping ratio,
r = (b/2) yg/(WK) , is too small because W is too large. For valves of
nominaI6-in. size or smaller, the resonant frequency, iT = (1/27l")Y gK/W,
is typically 15-30 cps.
In the equation above there is some error in treating friction as being
viscous. There is always some static friction. This plus diaphragm
hysteresis leads to an overall hysteresis which under shop conditions is
rarely less than 0.25-0.33 psi. Under plant conditions overall hysteresis
may change drastically and under extreme conditions may be as high
as 4-5 psi.
b. Spring-and-Diaphragm Valve with Booster. To get faster response,
particularly from valves with large topworks, a 1: 1 booster relay may be
inserted in the controller-valve transmission line just ahead of the valve.
The free volume in a valve topworks is commonly 100 in. 3 or more whereas
the input volume of a booster is usually 1-2 in. 3 • The use of a booster
at the valve therefore raises the controller-valve, transmission-line ter-

7-54

CHEMICAL PROCESS CONTROL INSTRUMENTATION

minal impedance as well as the transmission line driving-point impedance.
Speed of response between controller and valve is therefore much faster.
Furthermore, boosters usually have much greater air handling capacity
than controllers, are less likely to saturate with a low-impedance load,
and can therefore fill or dump the dome of a valve faster than an unaided
controller.
c. Spring-and-Diaphragm Valve with Positioner. To an increasing
extent positioners (valve stem positioner controllers) are used to position
spring-and-diaphragm valves. The advantages are: (a) very little stem
position offset due to coercive, axial stem forces, (b) More precise positioning of the valve, and (c) better impedance match between controller
and valve. As an example, consider the Mason-Neilan Series 7400 valve
positioner (see Fig. 45). The signal pressure from the controller, P p , is

Xp

Spring ~
rate ~
~vp

=

Bellows
spring rate

= kB

FIG. 45. Spring-and-diaphragm valve with positioner schematic.

multiplied by the end area, A B , of the input bellows to create a signal
force PpAB on one end of a lever. This moves the lever about the fulcrum
or pivot, thereby deflecting the pilot valve. The pilot valve is of the
three-way, or bleed type. Air is admitted to or exhausted from the valve
topworks and causes the valve stem to go up or down. This motion varies
the tension of the positioner spring in such a way as to create a balancing
force at the opposite end of the lever from the input bellows.
d. Positioner-Operated Spring-and-Diaphragm Valve with Booster.

INSTRUMENTATION SYSTEMS

7-55

The ability of a conventional positioner to drive at high speed a valve
with a moderate or large size topworks is limited by pilot valve capacity.
As mentioned previously a three-way or bleed type pilot cannot have high
capacity without a high bleed rate. This has led to various positionerbooster combinations for high-speed stroking of the control valve.
A typical hookup which has been popular is shown in Fig. 46. The
bypass from the booster input to the booster output is for the purpose of
stabilization. The farther open the needle valve, the greater is the damping. The reasoning which leads to this arrangement is as follows.

Adjustable
bypass
restriction

~

Signal----'----i~

t

Xv

f
FlO. 46. Schematic arrangement of spring-and-diaphragm valve driven by positioner

plus booster.

A pneumatic valve positioner normally is loaded by a low impedancethat of the connecting tubing and valve topworks. The positioner-valve
loop gain, under these conditions, is set to give reasonable stability. The
insertion of a booster, however, presents to the positioner output a relatively high impedance. Furthermore, the input-output pressure transfer
function of the tubing from the positioner to the booster is apt to be
highly resonant. The result is that the static loop gain, which is unchanged, is too high, and the system is oscillatory. Since there is no
convenient way to alter the static loop gain, one must modify the loop
dynamics. Reducing the booster input impedance, as by providing a
bypass around the booster, will accomplish this. This booster-positioner
combination permits performance which is five to six times faster than
that obtained with a positioner only.
e. Piston-Operated Valve with Integral Positioner. In recent years
the piston-operated valve with integral positioner has become a serious
competitor to the spring-and-diaphragm operated valve. The following
discussion refers to the actuator and valve made by the Annin Company
(see Fig. 47) but, with minor modifications, may be applied to those
made by several other manufacturers.

7-56

CHEMICAL PROCESS CONTROL INSTRUMENTATION
Loading pressure

_--"",y
__adjustment

Dome

pressure

Actuating
pressure

FIG.

PL

47. Schematic diagram of domotor. (Courtesy of Annin Company.)

7-57

INSTRUMENTATION SYSTEMS

The signal pressure Pp from the controller or manual loading station
enters a double bellows unit. The free end of the bellows is fastened to
a plate which is also attached to the upper side of the positioner spring.
In addition, the stem of a three-way (bleed type) pilot valve is fastened
to the plate. The output Po from the pilot goes to the lower side of the
power cylinder.
The upper side of the power cylinder is maintained at a constant loading
or reference pressure, P R , which is supplied from a built-in regulator.
The driving force for the piston is therefore furnished by PL. As it varies
and moves the power piston, the compression on the positioner spring;
whose lower end is attached to the power piston, also varies. This is so
arranged that an increase of P p in the double bellows unit is balanced by
an increased compression force in the positioner spring.
FQ.r high performance, piston actuators have an advantage in that
higher differential pressure may be applied across a piston than across
a diaphragm, which might rupture.
J. Piston-Actuators with Integral Positioners and Boosters. To get
maximum performance out of a piston actuator with positioner it is. necessary to add two boosters, one in the loading line, the other in the reference
pressure line (see Fig. 48). An alternate which provides somewhat greater
Sig~ _ _~_ _
P_P-l

60

si

Po

Kendall 1: 1 booster

Annin
domotor
\
60 psi

[>(]

Reference (loading)
pressure - 30 psig

t·

FIG. 48. Annin valve .with dual 1: 1 boosters.

speed and power is to use one booster and one reversing booster (see Fig.
49). This has the effect of do.pbling the driving force across the piston
for a given signal.
Miscellaneous Pneumatic Devices
Booster Relays. Booster relays are commonly used in pneumatic
circuits for either or both of two functions: (a) isolation amplifier and

7-58

CHEMICAL PROCESS CONTROL INSTRUMENTATION
Sign_a_'--P-P~..r-~
60 psi

------:~

t--~~~""-I

Kendall 1: 1
reversing booster
60 psi

.----'---"'-----'L....,

Annin
domotor
~---60psi

Kendall 1: 1
booster

FIG. 49. Annin valve with booster and reversing booster.

(b) power amplifier. In either case the basic design is that of the general
transmitter (see General Pneumatic Transmitter Design).
As an isolation amplifier, a booster relay is designed to maintain an
accurate static output-input ratio (usually 1:1 within ±O.lro), and to
have low hysteresis, less than 0.1 roo Air-handling capacity is a secondary
consideration and does not exceed 1-3 scfm. An example of this kind of
device is the Moore Products Company Model 61F, Fig. 50.
The power amplifier type of booster relay is used to improve the
impedance match between a relatively high-impedance signal source and
a low-impedance load. The most frequent application is for increasing
the speed of response of control valves (see Control Valve Actuators).
The best devices of this type maintain static gain and hysteresis within
0.5%. Air-handling capacity may be as much as 10-40 scfm. An example
of this kind of booster is that made by the Kendall Corporation (Fig. 26).

. .
FIG. 50. Moore reducing relay, Model

61.

(Courtesy of Moore Products
Company.)

FIG. 51.

66BR.

Moore reducing relay, Model
(Courtesy of Moore Products
Company.)

7-59

INSTRUMENTATION SYSTEMS

Some boosters have reversing action; a given increase in signal produces a corresponding decrease in output pressure.
Amplifying and Reducing Relays. It is sometimes desirable to insert
into a pneumatic circuit an isolation amplifier which amplifies or attenuates by a nominal, fixed ratio. If high precision is not required, relay
design can be simple. An example of this kind of relay is the Moore
Products Company Model 66 (Fig. 51). Note that output-input ratio is
determined by the ratio of the input diaphragm area to the output feedback diaphragm area. If the input diaphragm is the smaller, the relay
attenuates or "reduces." Ratios up to 6:1 or 1:6 may be attained.
Adding: P

=A

+B

±K

Subtracting: P

=A -

C ±K or P = B - C ±K

Air supply
Output

Output

3 element summation:

P=A+B-C±K

Averaging: P = A 1~

Air supply
Output

Output

Ratioing with pneumatic set point:

P

= r(A

- C)

±K

±K

Ratioing without pneumatic set point:
P = (B "!:. K)r

Air supply
Output

FIG. 52. Taylor computing relay, Model 348RFl.
Companies.)

Output

(Courtesy of Taylor Instrument

7-60

CHEMICAL PROCESS CONTROL INSTRUMENTATION

Computing Relays. To achieve more precision and flexibility than
are obtain~ble from the above devices, as well as to accomplish additional functions such as addition, subtraction, integration, and differentiation, a different class of relays is employed. These are aptly called computing or multifunction relays. They are made in a variety of different
models, depending on which groups of functions are desired.
Two different approaches to the design of computing relays are shown
in Figs. 52 and 53. Moore uses a stacked diaphragm construction while

Totalizing

T=A+B+K

~B

3~

C

S&T
P.V.

Differential

T=B-C+K
A

3-:>~

2

C

S&T
P.V.

s

Averaging

T=

A+B+K
2

~B

3~

S

~2T
P.V.

FIG. 53. Moore M/F (multifunction) relay: three examples of different functions
produced by the Model 68 relay. In the formulas, J( is the suppression, / / indicates
a vent to the atmosphere, and A, B, C, and D are the pressure chambers. (Courtesy
Moore Products Company.)

Taylor uses bellows. Only a small number of the computing functions
achievable with these :relays is shown.
Snap-Acting Relays. Pneumatic on-off action is sometimes required
for interlock circuits, alarms, or sequential operation of control valves
used .for batch or cyclic process operation. An example of a snap-acting
relay'with adjustable set point.is the Moore Model 67 (see Fig. 54).

INSTRUMENTATION SYSTEMS

7-61

Limiting and Selector Relays. Limiting relays are used to limit the
output from a controller. Some models have either a high limit stop or
a low limit stop; others have both high
and low stops (see Fig. 55).
Selector relays compare two pressures and transmit only one of them.
A high-pressure selector passes the
higher of two pressures while a lowpressure selector passes the lower of two
pressures (Fig. 56).
Pulsation Dalnpers for Pneu111atic
Circuits. In principle, the full range

of filter theory as developed for electric
Exhaust
circuits may be applied to the attenuation or reduction of undesired signals in
pneumatic circuits. One may use either
active or passive filters. In practice,
pneumatic filters are usually single section, low-pass RC filters. The resistance R is commonly an adjustable
needle valve, whereas the capacitance
may be only that of the tubing or else
a volume pot is added.
An exception to the above is the FIG. 54. Moore snap acting relay,
Taylor pressure pulsation damping Model 67. (Courtesy of Moore
unit. As shown by Fig. 57 it is a tenProducts Company.)
section, low-pass RC filter. It may be
used for both gas and liquid service but is more effective on the former.
7. ELECTRIC AND ELECTRONIC COMPONENTS

In general, most of the primary measuring elements which can be used
with pneumatic transmitters also can be used with electric or electronic
circuits to produee electric signals. Conversely, primary measuring elements which are inherently electrical in nature can, by translation, be
used to produce pneumatic signals.
Transmitters
Differential Pressure and Pressure. The Swartwout pressure and
differential pressure transmitters consist of a measuring diaphragm across
which the pressure or differential pressure appears, a mechanical linkage
and bias spring, and a differential transformer. NIinute movements of
the diaphragm are thereby converted to motion of the transformer core
and hence to proportional a-c voltage output changes. A coarse span

7-62

CHEMICAL PROCESS CONTROL INSTRUMENTATION
Adjust low limit

Output

1" N.P.T.

~I

Air supp1v1-

iff N.P.T.

Adjust
high limit---'--.,...-,

d

j

3-in.::--

Air supply

D
Master
cantralle.·

FIG. 55.

Lor----~)I
High-low
limit relay

Taylor high- and low-limit stops relay.
Companies.)

I

"
Pneumatic set
controller

(Courtesy of Taylor Instrument

adjustment is provided by a linkage ratio adjustment while a fine span
adjustment is accomplished electrically.
The Robertshaw-Fulton pressure transmitter works on a considerably
different principle. The pressure detecting element is a bourdon tube
or bellows whose free end is connected to a spring which in turn is connected to the beam of an electromechanical amplifier (Microsen balance).
As the loading on the beam changes, the end of the beam moves toward
or away from an oscillator coil. This changes the amplitude of oscillation
and the amplifier puts out a direct current proportional to beam motion.
Part of the output is f.ed back to a balance coil and magnet to offset the
initial torque.
Another method converting pressure or differential pressure to electrical
signals is by means of strain gages. The Baldwin SR-4 fluid pressure
cell is a commercial instrument of this type (see Fig. 58). It consists of
a metal block with a hole drilled in one end and Baldwin SR-4 strain
gages bonded to the block. An increase in pressure causes the block to
expand, thereby stretching the metal filaments of the strain gages and
changing their electrical resistance. The strain gages are connected to-

dia'h

INSTRUMENTATION SYSTEMS
3-in.
[
"""

"""

Output
L
N PT~--

A

--

111

Input

i" N.P.T.

J

~~1",,- ?::1~

• .. , jn
~

7-63

'B'

@

Inpul
111

"8 N.P.T.

'B'

High Pressure Selector

L
'~
111

Input 4' N.P.T.

Output

~

~

i" N'P'T~~-::
-:::I~

~
---

.

cY)

Air supply

I

Input
til N.P.T.

3'

-In,

I

la~

d'

111

"8 N.P.T.

Low Pressure Selector
Controller A
1----.:;------.., -

--,

I High (-) or low (--)

'f
Air supply

pressure selector

-~-

~
I -_ _

~

_ _----l

__

I

..J

Diaphragm
motor

Controller B

FIG. 56. Taylor high- and low-pressure selectors.
Companies.)

(Courtesy of Taylor Instrument

gether in a Wheatstone bridge arrangement and have a nominal full-scale
output of 1 mv per volt of bridge supply. This type of instrument may
be used for pressures up to 50,000 psi and is capable of following pressure
pulsations with frequencies up to several thousand cycles per second.
Temperature. A common means of measuring temperature is by
means of thermocouples. Since thermocouples provide low-level, d-c
voltages proportional to the difference in temperature of the hot and cold
junctions, it is necessary to amplify these signals. For a control system
such as Swartwout's, it is also necessary to convert from dc to ac. As
shown by Fig. 59, this is done with two d-c to a-c conversions; the first

7-64

CHEMICAL PROCESS CONTROL INSTRUMENTATION

I
I IlL

fk<:'-------6"--~--~>

~

I&.-..----L..-----L..-----L..-I/1-.1...-1--L..----L.....---L.....---1I---lI-,--J!~ Q

0

Q i ----;.-

Baffles With!
small orifices

CYlindricaV
barrel

I I I TI I TI

I I

(b)

FIG. 57.

Taylor snubber (pulsation damping unit): (a) schematic arrangement;
(b) equivalent circuit.
Threaded pressure

Brass diaphragm
{pressure relief seal

(filling.

Tapered pipe thread for
conduit-carrying cable

1k:-----7:~"-;-

Pressure
tube cavity

FIG. 58.

Hermetically
sealed terminal
plate

Special B~kelite SR-4
strain gages on pressuresensitive tube

Baldwin SR-4 fluid pressure cell. (Courtesy of Baldwin-Lima-Hamilton
Corporation.)
Zero suppression
and compensation
voltages
A-c filter

Contact
modulator

High-gain
a-c amplifier.

Phase-sensitive
rectifier

Cathode
follower

O-c -a-c
converter

+

t

Thermo-couple
input

tI

0-2 volts d-c

(2-S0-millivolt)
span

O-O.S-volts rms
GO-cycle ac
@ 58°
phase-reversible
output

{

1..-_ _-<)

Output isolated from1
[ thermocouple dc

J

FIG.

59.

T2C thermocouple converter block diagram.
Company.)

(Courtesy of Swartwout

INSTRUMENTATION SYSTEMS

provides voltage gain while the second provides conversion and isolation
from the thermocouple circuit.
In one type of Robertshaw-Fulton temperature transmitter, the thermocouple is used to generate current rather than voltage. This current
flows through an input coil wound around a magnet core. A change
in temperature causes a ehange in input current flow and the electromagnet deflects one end of a pivoted beam. The other end of the beam
moves in the field of an oscillator coil (see Pressure Transmitters and Differential Pressure Transmitters in Sect. 6), and causes an amplifier to
put out a proportional dir.ect current. Part of this current is fed back to
another coil on the same cor~ as the input coil, thereby providing a torque
balance on the beam.
Liquid Level. a. Capacitance Bridge. Although either differential
pressure or displacer type instruments described earlier may have an
electrical instead of a pneumatic output, there are ways of measuring
level which are inherently electrical in nature. The capacitance bridge
.
.
is an e x a m p l e . ,
If a rod is inserted into a vessel partly filled· with liquid, the rod may
function as one plate of a capacitor while the vessel itself serves as the
other plate. Since air and most gases have dielectric constants much
smaller than those of most liquids, a rise of liquid level increases the
capacitance. The rod is usually protected from the liquid by suitable
insulation.
In the' Telstor, manufactured by the Robertshaw-Fulton Controls Company, the bridge circuit is ·supplied with an RF voltage modulated by a
60-cycle power supply. Two inductance coils and two capacitors constitute the basic bridge circuit: One capacitor serves as a zero adjustment
while the other is the vessel-probe combination. Bridge unbalance is
detected by a -rectifier; the d-c output is then applied to an indicating
meter or recorder.
b. Nuclear Radiation. Several methods of measuring liquid or SOlids
level by nuclear radiation have been devised. One of these is based on
a cell manufactured by the Ohmart Corporation. A typical model cell
is a small cylinder 7 in. long by 4 in. in diameter. It may be regarded
as a type of ionization chamber with two chemically dissimilar electrodes,
and therefore requires no external potential to maintain a signal current.
It generates 2 X 10- 12 amp when exposed to a field of one milliroentgen
per hour from radium.
To measure level, the cells are stacked to an appropriate height and
a source is installed so that the material in the tank or bin partially
absorbs the radiation which would otherwise fall on the cells (Figs. 60
and 61).

'7-66

CHEMICAL PROCESS CONTROL "INSTRUMENTATION

[QJ
Electrometer

-----1
~
HeI
storage

Ohmart
cell
stack

I

I
I

I
I

I

I

I

I

I

Compe~sating

l___

II

-&__ J
Unit

~

Radioactive source stack

----->-'
FIG. 60. Measurement of liquid level is across the chord of the tank with all components exterior to the tank. (Courtesy of the Ohmart Corporation and Minneapolis.
.
Honeywell Regulat"or Company.)

Coal
hopper

Star
feeder

Source
holder

Pneumatic
controller

FIG. 61. Application of Ohmart cell and ElectroniK recorder to control level of
crushed coal fed to a pulverizer. Note: Fas = filtered air supply. (Courtesy of the
Ohmart Corporation and Minneapolis-Honeywell RegUlator Company.)

INSTRUMENTATION SYSTEMS

7-67

Flow. a. Turbine Flow Meter. The turbine flow meter has the characteristic that speed of rotation of the turbine is linearly proportional to
volumetric liquid flow rate. By magnetizing the blades or by inserting
a magnet in the rotor, one may cause an a-c voltage to be induced in a
pickup coil external to the conduit containing the flow. The frequency
of this voltage is proportional to flow rate. This voltage may then be
discriminated to obtain flow rate, or it may be treated as a train of pulses
which may be totali~ed to obtain a measure of total flow. A sectional
view of the turbine element made by the Potter Aeronautical Company is
shown in Fig. 62. A feature of this particular design is that for turbine

FIG. 62. Potter turbine type flowmeter. (Courtesy of Potter Aeronautical Company.)

speed above a certain minimum the rotor "floats" without slippage or
thrust friction, and thereby eliminates the need for thrust bearings.
b. Electromagnetic Flow Meter. lVIost flow meters depend on the ,use,
of either fixed or variable restrictions in the conduit. To a¥oid the use
of any obstructions, an electromagnetic flow meter may sometimes be
used. Only the so-called a-c type will be discussed here.
This flow meter is based on Faraday's law of electromagnetic induction.
If a conductor moves through a magnetic.field, there is induced in it a
voltage proportional to its velocity. A conductive fluid flowing through :,a,.
conduit may be regarded as a series of conductors. If, then, a magnetic
field perpendicular to the direction of flow is imposed on the conduit and
its contents, a voltage will be generated which is perpendicular both'to
the magnetic field and the direction of flow. This voltage which is directly:

7-68

CHEMICAL PROCESS CONTROL INSTRUMENTATION

FIG. 63. Foxboro electromagnetic
flowmeter. (Courtesy oi Foxboro
Company.)

proportional to volumetric flow rate may be picked up by a pair of electrodes which just barely protrude through the walls of the conduit.
An example of this kind of flow meter is that manufactured by the
F'oxboro Company. The transmitter, consisting of tube, coils, core, electrodes, cover, and end connections, is shown in Fig. 63. The overall
circuitry, which requires a special Foxboro Dynalog receiver, is shown
in Fig. 64.
Controllers

A number of electronic controllers are now on the market, but their
designs are quite different and no one of them may be considered typical.

INSTRUMENTATION SYSTEMS

7-69

115 volts
60 cycles
Differential
transformer

Chart
Transmitter

FIG. 64.

Dynalog instrument

Foxboro electromagnetic flowmeter circuit arrangement.
Foxboro Company.)

(Courtesy of

In Fig. 65 is presented a simplified block diagram of the Swartwout
Autronic controller. The phase-sensitive rectifier stage between the proportional circuit and the rate circuit is not shown, since it is not pertinent
to the analysis to be presented. The transfer function of each stage and
of the complete controller may readily be formulated as follows (Ref. 14).
Proportional Circuit

since G1 and G2
1.
If Kl is very large,
t'..J

Proportional
circuit

Signal
voltage
VI

Rate
circuit

Reset
circuit

~(x}-~.(x}-+.!

Set point
voltage
V2

FIG. 65. Block diagram of Swartwout Autronic controller.

Controller
output
voltage

l'4

'7~70

CHEMICAL PROCESS CONTROL INSTRUMENTATION

Rate Circuit
1

K

+

3

+ TDS

1

+ TDS)
1 + K3 + TDS
K 3 (1

1

K3

1+

K3

1

Reset Circuit
K5 G5
KrG r = - - - - 1
K5G5K6G6

+

(since (15

I'.J

1 and K 6Gfi =

+

(

+ TDS
TD

1 + K3

) S

K5 T rS

1+--1 + TrS

TrS)

1 + TrS

+ TrS)

K 5 (1

1 + (1

+

K5)TrS

Thus for complete controller:
V4

-

V3

4

V
V3

=

=

[K5
K 2 •

K3]

1

+ K3

1+
K

[1

+

1

l

=

KpG1)KDGDKrGr!
.

1
-

TDS
TD

+ K3

1

+

] [

+ TDS

] [

1

TD

1 + K3

1 + TrS
]
+ (1 + K 5)TrS

S

1 + TrS
]
1 + (1 + K 5 )Tr S

S

•

.

According to manufacturers' data:
K3 =

15;

K5 =

200,

V4

Va = K

[1++G~)
TDS

1

1+

] [
S

1

TrS

+ (200)r,s

]

•

INSTRUMENTATION SYSTEMS

7-71

J(

is adjustable from 0.5 to 38,

TD

is adjustable from 0.003 to 10 min,

Tr

is adjustable from 0.026 to 10 min.

The frequency response 9f the Swartwout Autr(),nic controller is given
in Fig. 66. The cutoff frequency We results from the bandwidth limitation
of the phase-sensitive rectifier and usually has a value of-approximately
7 cps.
o
~

1000
100

Q)

-g ~ 10
~;;,;.
E
co

b.O

..9

0.1

..L..L

1

Tn(Ks

+ 1)

T

ID

1'\

We

log

W __

I "'- K~: 1

~+90~ I I I
~~ a

. I

-90

\

All

~ll
0..

I

I~w-

,\

\

FIG. 66. Frequency response diagram for Swartwout Autronic controller.

Electronic Recorders

One of the earliest applications of electronics to process control was the
use of the potentiometer recorder for thermocouples. As developed by
:Minneapolis-Honeywell and by Leeds and Northl],lp, two of the chief
manufacturers of this equipment, it consists of a potentiometer input circuit followed by what is essentially a position servo system. The thermocouple signal and a feedback signal are combined in a d-c bridge circuit.
Bridge unbalance is amplified electronically, causing a two-phase servomotor to rotate in a direction determined by the polarity of the unbalance.
Rotor position is fed backto the input circuit by a ~~riable resistor whose
slider is mechanically linked to the rotor. The recorder pen is also linked
to the rotor. The pen is sometimes replaced by a rotating printing
mechanism, and the recorder becomes multipoint by a switching circuit
which selects in turn each of a number of input signal~.
Several miniature electronic recorders are now avaUable which work
on the same basic principle outlined above. Figure 67 shows the Microsen
recorder made by Robertshaw-Fulton.

7-72

CHEMICAL PROCESS CONTROL INSTRUMENTATION

(a)

Rotary solenoid

Vertical
scale

Amplifier section

Line
(b)

FIG. 67. Miniature electronic recorder: (a) miniature recorder with controller installed; (b) schematic diagram of recorder. (Courtesy of Robertshaw-Fulton Controls Company.)

Valve Actuators
Electropneumatic Valve Actuators. An electropneumatic valve positioner, such as those manufactured by Evershed & Vignoles or by
Robertshaw-Fulton, uses electricity primarily for signal transmission.
The positioner is otherwise quite similar to a conventional pneumatic
positioner. As shown by Fig. 68, the input circuit compares a force

7-73

INSTRUMENTATION SYSTEMS
Valve topwork
Exhaust port
Poppet spring

Magnet
Supply
air

Input
Nozzle
Linkage

Orifice

Air relay

FIG. 68. Electropneumatic valve positioner. (Courtesy of Robertshaw-Fulton Controls Company.)

produced by the transmitted electrical signal with a feedback force produced by a calibrated spring which detects valve stem position. Any unbalance in these forces causes a pivoted beam to move, thereby changing
the displacement between a flapper and a nozzle. The corresponding
change in nozzle back pressure actuates a pneumatic booster stage which
increases or decreases the pressure in the dome of a spring-and-diaphragm
valve actu'ator. This pressure change in turn repositions the valve stem
until there is no unbalance force in the positioner input circuit.
, Electrohydraulic Valve Actuators. For military purposes, high-performance (50-100 cps bandwidth) electrohydraulic servos have been de'veloped. In principle these may be adapted to process control valves, but
in practice their complexity and expense are prohibitive for all except' a
few applications which require maximum performance. Several manufacturers have, however, produced highly simplified versions which are,'competitive in price with pneumatic actuators when the savings in instrument air facilities ,are taken into account.
An example is the Askania electrohydraulic valve actuator (see ,Fig.
69). The input circuit compares a force produced by the transmitted
electrical signal with, a feedback force produced by a spring which' detects valve stem position. An unbalance of these forces deflects the' jet
pipe hydraulic preamplifier. This causes the power piston to move until
the feedback force balances the electrical force, and thereby causes the
jet pipe to return to it~neutral position. The only power requirements
are 110 volt, 60 cycle.

7-74

CHEMICAL PROCESS CONTROL INSTRUMENTATION

Cover

p

Permanent
magnet
Power spring
for feedback
linkage

Moving coil

Oil sump

Jet pipe

(b)

FIG. 69.

(a) GPE electrohydraulic valve actuator and (b) diagram showing its

operation. (Courtesy of GPE Controls Inc.)

INSTRUMENTATION SYSTEMS

7-75

8. SELF-ACTUATED CONTROLLERS

When control requirements are not tight and when it is desired to minimize first cost, self-actuated controllers are often used. As a class, these
devices are rugged, dependable, and simple in design. In comparison
with the control'equipment previously described, they are more specialized, less flexible,' less precise, and require no external source.
Temperature

An example of a self-actuated temperature controller is one made by
the Leslie Company (Fig. 70). A vapor-filled temperature-sensing bulb
is inserted in the process and causes a force to be exerted on the diaphragm of a spring-and-diaphragm actuator which is proportional to

FIG. 70. Self-actuated temperature controller.

(Courtesy of the Leslie Company.)

7-76

CHEMICAL PROCESS CONTROL INSTRUMENTATION

temperature. The actuator stem moves a distance proportional to the
applied force and, through a linkage, moves the stem of a pilot valve
connected to the high-pressure side of the process valve. The position of
the pilot valve then determines how much pressure is applied to the piston of a spring-and-piston actuator which positions the . process valve.
The process valve position is therefore proportional to temperature.
Pressure

Self-actuated pressure regulators are used to control gas streams, steam,
and air. An example of a small regulator is that made by Fisher for air or
inert gases (Fig. 71). The principle of operation is that the downstream
(~ontrolled) pressure must provide a force against the under side of adia;.
phragm which will balance the force on the top side due to compression
of the main adjusting spring. If the downstream pressure drops, the
diaphragm is moved downward, and the supply valve is opened to admit
upstream gas or air. If the downstream pressure bec9mes too high, the

FIG. 71. Self-actuated pressure regulator.

(Courtesy of Fisher Governor Company.)

INSTRUMENTATION SYSTEMS

7-77

diaphragm is moved upward, and thereby opens the exhaust valve which
bleeds off the pressure. The diaphragm is isolated from the controlled
fluid' by a feedback chamber connected by a small port to downstream
pressure. This provides stabilization and reduces the tendency of the
regulator to buzz or chatter.
Flow Regulators
Small Flows. Regulators for small flows are widely used in laboratories, pilot plants, and for such applications as purge flows. They are
available for gas or liquid service. A typical instrument in this category
is the Moore Products Company Model 62 gas flow controller which will
regulate gas flows in the range 0.2-2 scfh (see Fig. 72). It is designed to

FIG.

72.

Moore Model 62 gas flow controller.
Company.)

(Courtesy of Moore Products

hold flow constant in spite of fluctuations in either upstream or downstream pressure. The principle of operation is as follows.
The adjustable needle valve serves as a set-point adjustment. The
regulator then attempts to maintain a constant differential pressure of
1.5 psi across this restriction, thereby maintaining flow constant. If,
however, upstream pressure increases (or downstream pressure decreases),
the differential pressure across the diaphragms increases, the diaphragms
lift away from the exhaust valve, and the lower or inlet valve tends to
close. The pressure drop across the inlet valve is therefore increased and
the increased exhaust opening permits bleeding off the pressure under the
lower diaphragm until the required 1.5 psi across the diaphragms is established again. A decrease in upstream pressure (or an increase in downstream pressure) causes the diaphragms to close down on the exhaust valve
and to open the inlet valve ,wider, until the 1.5 psi differential is reestablished.

7·78

CHEMICAL PROCESS CONTROL INSTRUMENTATION

Rather than attempt to calibrate the needle valve precisely, most users
insert a small rotameter or bubbler bottle in series with the regulator.
Large Flows. For the larger flows commonly encountered in chemical
and petroleum plants, self-actuated regulators are sometimes used if control requirements are not too severe or if remote control and signal transmission are not required. An example of this kind of instrument is the
Kates flow rate regulator for liquids which is available in ranges from
0.1-1.5 gpm up to' 10-100 gpm. The principle of operation is as follows.
The flow enters at the bottom (see Fig. 73), passes into the inlet tube,
then emerges through the control valve into the lower chamber. The
control valve is a sleeve valve in which the inlet tube with its ports is
fixed, while the sleeve with its matching ports is movable, thereby varying the effective valve port area. The flow is then split into two sections.
The major portion goes through the adjustable orifice while the controlling
flow goes through the fixed' orifice. Both flows pass into the upper chamber and from there into the downstream piping. Any change in differential pressure between the upper and lower chambers is multiplied by the
Calibrated dial

Adjustable
orifice

Renewable
seat

_-l:*----Sleeve
Fixed
orifice
~---Inlet

port

"',.----Inlet tube

Weight

FIG. 73. Kates flow rate regulator for liquids. (Courtesy of W. A. Kates Company.)

INSTRUMENTATION SYSTEMS

7-79

area of the disk to produce a force which moves the sleeve until the differential pressure between the two chambers is restored to its proper valve.
The desired flow is then obtained by adjusting the calibrated dial on top
of the instrument that is connected to the adjustable orifice. The regulator shown is primarily suited for low flows; for higher flows the manufacturer furnishes an instrument which uses a spring rather than gravity
for a driving force.
9. CONTROL PANELS

The following discussion will be limited to central control room practice where one or perhaps several central control rooms serve as nerve
centers for an entire process. In large chemical and petroleum plants this
is virtually standard practice, and should be distinguished. from the custom in some industries of decentralizing instruments and controls and
scattering them throughout the process. The central control room has the
advantages of more convenient, unified process control and usually lower
operating labor cost. Its chief disadvantage is somewhat higher investment cost due to the necessity of transmitting measurements from the
process into the control room, and control signals back out again.
Conventional. Prior to the advent of miniature, unitized instruments,
the major case recorder and recorder-controller were standard. Customarily they were arrayed on the panels in a geometrically regular fashion.
Some users still prefer this kind of instrumentation and this arrangement
(see Fig. 74). Since its chief disadvantage is its large space requirement
(the major case instrument is typically 14 in. by 16 in. in contrast to a
typical figure of 4%6 in. by 4%6 in. fur miniature case instruments),
some users retain the linear, geometric arrangement of instruments but
use miniature case equipment. In either case, the panel is referred to as
"conventional."
Graphic. Although there are a number of different kinds of graphic
panels, the type which has been most popular consists of a large, pipture
flowsheet-control diagram on which miniature case recorders, indicators,
and manual-automatic stations are appropriately located (see Fig. 75).
By means of color coding and suitable symbols, the process streams and
instrument functions are identified with a minimum of labeling. Although this kind of panel requires slightly more space than a conventional
panel with miniature case instruments, it requires vastly less space than
a conventional panel with maj or case instruments.
The big advantage of the graphic panel is the ease with which an operator may scan the board and tell how the process is doing. The possibility of the operator turning the wrong knob or switch in an emergency
is greatly reduced. In addition, new operators are more rapidly trained
on graphic panels than on conventional panels.

/

7-80

CHEMICAL PROCESS CONTROL. INSTRUMENTATION

FIG. 74. Conventional control room panels using major case instruments. (Courtesy
of E. I. duPont de Nemours & Company.)

FIG. 75. Graphic panel using miniature case instruments. '(Courtesy of E. I. duPont
de Nemours & Company.)

INSTRUMENTATION SYSTEMS

7-81

REFERENCES
1. R. P. Bigliano, Pneumatic controller dynamics, unpublished E. 1. duPont de
Nemours report.
2. G. F. Brockett and C. F. King, Dynamic Force Reactions in Double-Ported
Control Valves, Fisher Governor Company, Marshalltown, Ia., 1950.
3. P. S. Buckley, Cost vs. performance in process control systems, IB.A. 9th Annual Conference, Philadelphia, Pa., Sept. 13-24, 1954, Paper No. 54-20-3.
4. P. S. Buckley, Dynamics of pneumatic control systems, IB.A. 10th Annual
Conference, Los Angeles, Calif., Sept. 12-16, 1955, Paper No. 55-6-2.
5. D. P. Eckman, Phase plane analysis: a general method of solution for twoposition process control, Trans. Am. Soc. M echo Engrs., 76, 109-120 (1954).
6. D. P. Eckman and R. B. Werey, Control valve body design, Instruments, 22,
269-273 (1949).
7. D. P. Eckman, Principles of fluid flow through control valves, presented for
I.8.A. at Newark, N. J., April 1,1952.
8. R. J. Kochenburger, A frequency-response method for analyzing and synthesizing contractor servomechanisms. Trans. Am. Inst. Elec. Engrs., 1, 270-284 (1950).
9. R. C. Oldenbourg and K. Sartorius, The Dynamics of Automatic Control, American Society of Mechanical Engineers,N ew York, 1948, pp. 115-182.
10. H. F. Olson, Dynamical Analogies, Van Nostrand, Princeton, N. J., 1943.
11. H. F. Olson, Elements of Acoustical Engineering, 2nd edition, Van Nostrand,
Princeton, N. J., 1947.
12. R. A. Rockwell, Unbalanced force reactions in control valve plugs and their
influence on diaphragm motor design and operation, presented at Texas A. and M.,
College Station, Texas, Oct. 13, 1950.
13. C. W. Sanders, Improving a level control process, I.S.A. 10th Annual Conf.,
Los Angeles, Calif., Sept. 12-16, 1955, Paper No. 55-6-3.
14. C. J. Swartwout, An electronic approach to process control, Instruments, 26,
728-732 (1953).
15. W. E. Vannah and A. R. Catheron, Improved flow control with long lines,
I.S.A. 6th National Conference and Exhibit, Houston, Texas, Sept. 10-14, 1951,
Paper No. 51-6-2.
16. D. P. Campbell, Prucess Dynamics, Wiley, New York, 1958.
17. D. M. Considine, Editor, Process Instruments and Controls Handbook, McGrawHill, New York, 1957.
18. J. Truxal, Control Engineer's Handbook, McGraw-Hill, New York, 1958.
19. E. Grabbe, S. Ramo, and D. E. Wooldridge, Handbook of Automation, Computation, and Control, Vol. 1, Control Fundamentals, Wiley, New York, 1958.

CHEMICAL PROCESS
CONTROL SYSTEMS

D.

CHEMICAL PROCESS CONTROL SYSTEMS

D. P. Eckman, Editor
8.
9.
10.
11.
12.
13.
14.

Design Procedures, by E. F. Holben
Process Test Methods, by P. E. A. Cowley
Single and Multiple Loop Controls, by J. E. Rijnsdorp
Nonlinearities, by C. G. Laspe and T. M. Stout
Sampled-Data Control, by R. E. Kalman
Computer Control, by I. Lefkowitz
Data Processing, by E. M. Grabbe

D

CHEMICAL PROCESS CONTROL SYSTEMS

Chapter

8

Design Procedures
E. "F. Holben

1. Introduction and Terminology

8·01
8·02
8·02
8·05
8·20

2. Specification of Quality Control
3. Operational Factors
4. System Design
References

1. INTRODUCTION AND TERMINOLOGY

The purpose of this chapter is to outline the process control design
procedures employed in the continuous processing industries, such as the
chemical and petroleum industries. The emphasis in this treatment is on
the control of the process rather than the instrumentation. Instrumentation systems are covered in Chap. 7, and a general discuss,ion of principles
and procedures for carrying out systems design is presented in Chap. 1,
Systems Design.
This chapter serves as the introduction to Part D, Chemical Process
Control Systems. The approach in this and later chapters of Part D is to
outline the qualitative and quantitative theory now available for usc"
in the design of process control systems. Chapters 9 to 14 deal with more
specific aspects of process control system design, including test methods,
single and multiple loop controls, nonlinearities, sampled data, computer
control, and data processing. A detailed discussion of instruments, their
construction, and their operation is covered in Chap. 7, Instrumentation
Systems.
8·01

8-02

CHEMICAL PROCESS CONTROL SYSTEMS

Terminology. The terminology used throughout Part D is that employed generally in the process control industries. In flow diagrams
transmitters and controllers are shown as circles. The measuring element and the means for transmitting the measured value is called a
transmitter, and is designated by T in a circle. Pressure, temperature,
level, and flow transmitters are denoted by PT, FT, TT, and LT.
Controllers, denoted by C, are concerned with the same variables, pressure, flow, temperature, and level and are designated by PC, FC, TC, and
LC in a circle. The controller has a set point which mayor may not be
shown as an input on the flow diagram. In some flow diagrams the
transmitter is omitted, and a direct connection from the controller to the
variable measured is shown.
A valve is shown as a restriction in the line with a stem attached to a
bellows or a knob.
The block diagram symbols are those used in feedback control theory.
Lower case letters stand for functions of time. Capital letters stand for
Laplace transforms of time functions, and transfer functions are usually
given in this form. An asterisk (*) indicates that the quantity is in
sampled form. Constants may be either capitals or lower case letters.
2. SPECIFICATION OF QUALITY CONTROL

The general purpose of automatic process control is to provide a specified
finished product under a wide variety of process conditions in the most
efficient manner. The success of the automatic control system must always be evaluated in terms of the quality of the finished product. At
the beginning of every instrument design study, the process design group
must specify the desired quality of the finished product and the tolerances
of deviation from this quality. The specification can be in the form of
many physical quantities. A steam generator plant would define product
quality in terms of degrees super heat and steam pressure; a plating plant
would define it in terms of thickness of plating material; and most chemical plants would specify quality in terms of chemical analysis, acidity,
viscosity, etc. The final determination will usually be a compromise
and will, most likely, be arrived at after several design studies are made,
cost estimates presented, and alternatives considered.
3. OPERATIONAL FACTORS

Process Variables. Many external and internal conditions affect the
performance of a process. These conditions may be expressed in terms
of process variables such as temperature, pressure, flow, liquid level,
dimension, weight, volume, etc. The process may be controlled by measuring a variable representing the state of the product and automatically

DESIGN PROCEDURES

8-03

adjusting one of the other variables of the process. Ambient conditions
must always be included in the list of process variables. The controlled
variable of the process should be the one that most directly produces the
desired form or state of the product. Direct control from product quality
is most likely to insure proper performance of the process and to produce
and maintain the desired quality of the product. Indirect control from a
secondary variable of the process may be necessary when direct control is
difficult to accomplish.
The manipulated variable of the process is the one selected for adjustment by the automatic controller to maintain the controlled variable at
the desired value. The manipulated variable may be anyone of the
process variables that causes a fast response of the controlled variable and
is relatively easy to manipulate.
The load variables of a process are all other independent variables
except the controlled variable and manipulated variable. It is expected
that the automatic controller will correct for fluctuation in load variables
and maintain the controlled variable at the desired value.
Process Demand as a Load Variable. One of the most important
load variables is the rate at which the finished product is used, called the
process demand. It is necessary that the specification of process demand
be clearly defined both in magnitude and time, for this will determine the
maximum conditions for the control mechanism. Often a control system is
handicapped by being called upon to operate under conditions of large
variations in process demand for which it was not designed. The effect on
the product quality may be such that a system operating satisfactorily
with high process demand will produce undesirable results at low process
demand.
Generally, a control system should be designed for one condition of
process demand. Where variations in usage rate are expected, storage
means can be provided to maintain a supply of final product and yet
allow a constant feed from the process. In this manner, one load variable
can be eliminated and a system design reduced to the control of the manipulated variables under relatively steady-state conditions of the controlled variable. The wise use of storage methods to reduce the magnitude
of process demand variations will result in less complex control systems.
Supply Variations as a Load Variable. Although process demand
variations probably have the greatest effect on the process quality, the
supply of materials to the process may vary quite widely, thus adversely
affecting the control system. For example, the gas-fired continuous heating furnace shown in Fig. 1 may have several sources of supply change.
If the gas pressure changes, the flow of fuel will be altered; the heat content of the fuel may change appreciably and, therefore, affect the rate of

CHEMICAL PROCESS CONTROL SYSTEMS

8-04

Stack

--------01!t----------'

r

T3

DDDDDD
Ps

-,;;+ "---"'" ....----...,------------'
FIG.

1. Gas-fired continuous heating furnace; T = temperature,

U

= load variable.

heat application to the furnace. Another example is the clogging of the
burner which will decrease the flow of fuel for anyone valve setting.
Therefore, it is necessary that these changes be specified with the same
care as demand changes before the instrument design study is undertaken.
Degrees of Freedom of a Process. The complete specification of the
load variables does not imply the need for the control of each. Every
process can be defined by a set of equations, and there will be a certain
number of degrees of freedom to control specific properties of the process.
The number of degrees of freedom is derived from the following equation:
(1)

where n equals number of degrees of freedom, nv equals the number of
variables of the system, and ne equals the number of defining equations of
the system. By definition, the number of independently acting controllers
in a system or process may not exceed the number of degrees of freedom.
However, there are quite often fewer automatic controllers than degrees
of freedom and such systems are usually adequate. The number of automatic controllers to be employed will be determined by the allowable
deviation of product quality.
Process Efficiency. Although product quality is probably the most
important consideration in a design study, the efficiency with which the
product is produced is also of great importance. The best economy is
accomplished, if at all, by maintaining all process variables in a predetermined relation, such that the highest efficiency, least waste, and any
other criteria are satisfied. To insure that the maximum efficiency of the

DESIGN PROCEDURES

8-05

process is maintained, it is necessary that this efficiency be calculated
at various equilibrium conditions from maximum to minimum, considering all supply, load, and demand changes. Although an automatic controller might adequately maintain the state of the controlled variable
under a wide range of load variables, this could be done at the sacrifice
of process efficiency and, therefore, require a more complex control 'design
in order to maintain the efficiency within practical limits.
Controllability of the Process. The remaining operational factor to
be considered (preliminary to the actual system design) is the general
controllability of a process. lVfany processes are comparatively simple
and possess a certain degree of inherent stability. On the other hand,
some processes possess a confusing array of capacities, lags; and load
changes. In order to determine adequately the controller charact~ristics
necessary to maintain the controlled variable at the desired value, it is
imperative that the dynamic characteristics of the process be thoroughly
understood. For example, to maintain the temperature of a heating oven
at a fixed value is relatively simple and can be accomplished within a reasonable degree of temperature tolerances. In order to control the t~mpera­
ture of a process that contains exothermic reactions, however, the system
design becomes more complex becapse the process tends to "run away with
itself." In this case, adequate provisions in the control system must be
made to compensate for or control the exothermic reactions.
Many flow control problems can be solved by the use of storage fanks.
The proper use of storage tanks,oHen results in a self-regulated system
and, therefore, the automatic controller's job is greatly simplified.' On
the other hand, where storage tanks cannot be used and the flows are varying rapidly, the characteristics of the controller must be more ~ompli­
cated and include provisions for maintaining the desired value of the controlled variable under rapidly changing conditions.
4. SYSTEM DESIGN

Up to this point the system design has been mainly concerned with a
definition of the control problem. This has consisted of determining
the process characteristics under steady-state conditions and also under
a wide range of load changes. This information must now be translated
into a suitable control system.
Design Procedure and Flow Diagram Construction

A procedure for analyzing a process and applying instrumentation can
be given as follows:
1. Divide the plant function into the smallest operation elements or
operation units.

8-06

CHEMICAL PROCESS CONTROL SYSTEMS

2. List all variables-temperature, pressure, flow rate, composition, etc.
-that may affect each process operation element.
3. Add to this list ambient temperature, ambient humidity, barometric
pressure, sun, and wind conditions.
4. Divide this list of variables into four groups: (a) variables to be controlled automatically; (b) variables to be measured continuously; (c)
variables to be measured periodically; and (d) variables neither measured
nor controlled.
5. For each variable of the automatic control group, select (a) a method
of measurement that will provide data most indicative of the desired
process performance; (b) a style of controller, nonindicating, indicating,
or recording; (c) a mode of control that will provide the desired performance in view of the process dynamics.
6. For each variable of the continuous measurement group, decide (a)
what method of measurement will provide data most indicative of the desired process performance; (b) whether signaling, indicating, or recording
is most desirable; (c) whether a signal device, indicator, or recorder is to
be located at the control center or at the unit.
7. For each variable of the periodic measurement group, decide on a
method of performing the measurement and the frequency with which
the measurement must be made.
8. Construct a flow diagram. The purpose of a flow diagram is to provide information quickly for use in the process analysis. It should be as
simple as possible and yet pictorially describe the process unit. All information pertinent to the control problem should be indicated on the
flow diagram, including the fluid or medium being controlled, size of vessels, length and size of piping, location of control equipment, pressures,
temperatures, flows, liquid levels, and other process information. Although not necessarily indicated on the flow diagram, assignment of alphabeticalletters or symbols to the system parameters should be made at this
time. A typical flow diagram is shown in Fig. 2.
Development of Block Diagram from Flow Diagram

Having constructed a flow diagram, the block diagram of the control system should be constructed. From this block diagram will be developed the
system equations and performance. The equations for each of the controlled variables will ultimately be combined to define completely the
process control system.
The general block diagram is shown in Fig. 3. The diagram illustrates
the behavior of the system by depicting the action of the variables of the
system. The circle represents an algebraic function of addition; the rectangular box represents a dynamic function such that the output is a func-

DESIGN PROCEDURES

8-07

r--------------I<~ Recirculated water,
15-20gpm

A 2-in. pipe

I
h

f

~.-_ _ _ _ _~

r - .- - - - - - - - . . . . . ___--~

,

I-in. control valvesplit body single seat

hll :-ft :~I

Set point

= 100 in.

L

Fresh water
inlet pressure 40 psi

2-in. galvanized pipe
10 ft run to process

L--------V'~

R

FIG. 2. Flow diagram; c = controlled variable, v = set point, U = load variable, m
manipulated variable, R = restriction.

=

tion of time and is also a function of the input. Notice that the terms input and output refer to signals and not necessarily to mass and energy
flow. A block diagram is not unique, and its arrangement depends on the
point of view of the analyst. The important point is that the block diagram illustrates the relation of the variables.
The operational equations for the system shown are of the following
type:
G1 G2 Ga
N
(2)
C= - - - V +
U
1 + G1G2 Ga
1 + G1G2 G3
where C =
V =
U =
G=
N =

controlled variable,
set point,
load variable,
system transfer functions,
load transfer function.

For the moment, the transfer function H will be considered as equal to 1.

Load

Level

Transmitter

FIG. 3. Block diagram.

CHEMICAL PROCESS CONTROL SYSTEMS

The effect of the function H on the process control system will be considered later in the chapter.
These equations give a complete description of the operation of the
process unit and will be used to describe both the steady-state and dynamic performance of the process loop under a wide variety of process upsets. All the quantities are Laplace transforms.
Range of Operating Conditions and Transfer Functions

Before beginning the analysis of the process loop, it will be necessary
to determine the operating ranges and transfer functions of each block
of the diagram. The operating ranges of the controller will be dictated by
the process variations and will be straightforward.
Controller Transfer Functions. The transfer function equations for
the controllers of the continuous process control variety will be of the
following general form:
Proportional Control
(3)

I ntegral Control
(4)

Proportional plus Integral Control

X= Kc(_l + l)E.

(5)

TiS

Proportional plus Derivative Control
(6)

Proportional plus Integral plus Derivative Control
(7)

In these equations,
X = controller output,
E = error signal,
1
Kc = gain =
,
.
Proportional band
T i = integral time, seconds,
s = Laplace operator, d/dt,
T d = derivative time, seconds.

DESIGN PROCEDURES

8-09

It is often necessary to simplify the method of analysis of systems by
eliminating the mathematics and using graphical methods. The use of
sinusoidal testing systems makes it possible to plot the transfer function.
The method most often used to represent the transfer function graphically is the Bode plot of magnitude and phase versus frequency. The
Bode plots of transfer functions for the various controllers are shown in
Figs. 4 to 8. For more details of controllers see Chap. 7, Instrumentation
Systems.

0

+"

e
.a
'c

10.0
6.0
4.0

2.0
1.0
tlO 0.6
ro
::2: 0.4
C1l
"0

0.2
0.1

~

60

~

30r_-r--r-rr+-~---r~H---r_-r-r~

~

or-_r----~~+-~----~~~----~_r_r~

~-30r--r--r-rr+-~---r~H---r-~~~
-60r-~--r-rr+-~---r~H---r-~~~

-90~~---~~~~---~~~---~~~~
0000000
q-\.DO
0000
....
N
q- \.D 0

....

Frequency, cycles per minute

FIG. 4. Proportional control.

The final control -element will have to be selected to accommodate

the process variations, since this device will be doing the actual controlling
of the manipUlated variable. From the definition of the problem, the
maximum and minimum conditions within the process loop have been
determined. These must be translated into the operating range of ,the
final control element.
In good system design the range is usually selected SD that the normal
maximum condition of the manipulated variable is taken as 70% of the
full range of the final control element. This recommendation, of course,
applies in general to all types of final control elements such as c~ntrol
valves, metering pumps, rheostats, autotransformers, and so forth (see
Chap. 22, Actuators).
.
Control Valves. The most widely used final control element in the
process industry is the throttling control valve. There are many types of

CHEMICAL PROCESS CONTROL SYSTEMS

8-10

0
:;:;

~

10.0
6.0
4.0
2.0

/

Q)

'tJ
::J

:!:

c:
bIl
ro

:E

1.0
0.6
0.4
0.2

/"

/

"

0.1

J=~IIIII Mil
....

N-.:tu>O

00000000
N
~u>o
0000
....
N
~
u> 0

.-4

.-4

Frequency, cycles per minute

FIG. 5. Proportional-integral control.

100
60
40
20

E
~

OJ

'tJ

.a

'c

bIl

ro

:E

~

'\.

I\.

""

'\

'"

10.0
6.0
4.0
2.0

\
'\.

"'\.

I'\.

I\.
r\.

1.0
0.6
0.4
0.2

I"

""\

'\.

"'\.

'\.

\

\

"

'r\.

0.1

....

~

N

~

~

\.0

~~

....

N

.~

\.0

0000

Frequency, cycles per minute

FIG. 6. Integral control.

0

r-i

DESIGN PROCEDURES
10.0
6.0
:§ 4.0
l.:!
2.0
OJ

.........
.......

"

"C

.a
'ctlO 1.0
III

8-11

0.6 -

:: 0.4

.......

,

r-"

0.2
0.1

180,--r--..-,,--.-~~~--~--.-.-~

fElllllllilti
0..-1

N

<::t1.00
..-I

00000000
N
<::t1.00
0
000
..-I
N
<::t 1.0

:=:

Frequency, cycles per minute

FIG. 7. Proportional-derivative control.

120

90

./

f-OJ

0.0
~

~

/'

60

/'

/'
/'

30
./

0

~

a.. -30

-60

-90

o
o

V

--

~

......

N

<::t

o

o

o

o

./

./

~I'

f-1.0 co 0
0 0 .......

000

o

N

o

o

d

000

d~'-<

Frequency, cycles per minute

FIG. 8. Proportional-integral-derivative control.

CHEMICAL PROCESS CONTROL SYSTEMS

8-12

throttling control valves available to meet various control problems.
Those most generally used are single seat or- double seat plug valves, gate
valves, butterfly valves, plug cock valves, and slide valves. In addition
to the design parameters already mentioned, the rangeability is quite important. Rangeability is defined as the ratio of the maximum flow of the
valve to the minimum flow and generally falls between 20 and 70. For details of valve construction see Chap. 7, Instrumentation Systems.
Most manufacturers of control valves provide nomographs, slide rules,
and formulas for determining valve sizes for various conditions and
fluids. These are usually derived from the following general formulas:
Liquid

(8)
Gases
1360C

=

(9)

q

l/lp

v

IPI

~ gT ~

+ P2
2

Vapor
_ KC v V- r/lp
-

(10) -

W -

JPI- +2 P2

where K = 3 for saturated steam,
K =
v

3
1

+ O.0007Ts

for superheated steam.

= liquid flow, gallons per

mirlUte,
C v = valve factor,
IIp .=:=. vaive pressure drop, pounds
. per square inch,
g ~ specific gravity,
q = gas flow, standard cubic feet
per minute,

PI = upstream pressure, pounds
per square inch area,
P2 = downstream pressure, pounds
per square inch area,
T = temperature, degrees Rankine,
Ts = temperature, degrees superheat,
w = vapor flow, pounds per hour.

In the case of single seat or double seat plug valves, selection of the valve
characteristic is quite important because of the effect on the automatic
controller. Although many characteristics can be obtained, these generally fall into two categories, linear and equal percentage as shown in
Fig. 9.

DESIGN PROCEDURES
1.0

8-13

.----r---:---,---,..-----,--~

x

E

"?E: 0.8 I----t----+---t---x---I-/
?;-

a

~ 0.6 1----+--::J

E

.~ 0.4 I---+--~~--t--++_-__l
c

2

0.2

I----f----t-----:;>'f----t---i

u

ro
~

0.2

0.6

0.4

0.8

FractiCin of maximum lift,

1.0

X/X max

FIG. 9. Control valve characteristic; A = linear type, B = equal percentage type.

The transfer function of the final control element will be determined by the characteristics of the element itself and the response of the
actuating mechanism. Final control element mechanisms are usually
first or second order systems and can be defined by the following equations:

(11)

M=

Kv
Tvs

+1

X

(12)

where M = manipulated variable,
X = final element input,
Ktl = final element gain,
s = Laplace operator, d/dt,
Tv = final element time constant, seconds,
r = damping factor.
The Bode plots of these functions are shown in Fig. 10.
The transfer function of the process itself is usually difficult to determine before a system is actually built and tested. In some cases, pilot
plants or laboratory experiments can be used to approximate closely the
actual characteristics. On the other hand, the equations of the process
may enable the designer to calculate the expected response. The process
functions can usually be broken down into simple single or double capacitance systems. Equations for typical systems are shown as follows:

CHEMICAL PROCESS CONTROL SYSTEMS

8-14

E
~

10.0
6.0
4.0
2.0

OJ
'"0

.3 1.0

'c 0.6
bD

........

~

ro

::E 0.4

",-

0.2

i'r-....,

0.1

0

10.0
6.0
4.0

I/'r- ~

~ 2.0

,)~ ... r-. \

OJ
'"0

.3 1.0
ro

::E

\

\

\'\

'c 0.6
bD

~\'

0.4

'\\

0.2
0.1

o
o

N

Frequency, cycles per minute

FIG. 10. Final control element response.

Single Capacitance

Kp

C=---M
Tps + 1

(13)

Two Capacitance (general equation)
(14)

Two Capacitance (t
(15)

>

1)

Kp
C = -------- M
(Tp1s + 1)(Tp2s + 1)

where Kp = process gain,
T p = process time constant.
System Analysis and Stability Criteria (See Vol. 1, Chap. 20, Fundamentals of System Analysis, and Chap. 21, Stability)
Analysis Procedure. After defining the transfer function of each element of the block diagram, the system can be analyzed and the proper con-

DESIGN PROCEDURES

8-15

troller settings of T d , T I , and Kc determined for best optimum control
with stable operation. The insertion of the transfer functions of each
element of the loop in the general equations and solving for the loop
response is usually cumbersome, unless an analog computer is available for
rapid manipulation of the equations. Also, the equations are based on
linear theory by definition, and if a more accurate mathematical study
of the nonlinear system is dictated, the use of a computer study is an
absolute necessity. The graphical use of the frequency response plots of
the elements is much simpler and gives an indication of the proper settings
of the controller and the final response (see also Chap. 10, Single and
Multiple Loop Controls).
The response plots are always made on logarithmic ordinates of magnitude ratio versus logarithmic plot of frequency. By definition, then,
each plot can be graphically added together to give the final response.
Determining Optimum Stable Control. The optimum condition for
the final response is determined by adjusting the parameters of the various
elements. The optimum point is usually the fastest response just short
of instability. The stability conditions are defined as follows:
1. The phase lag should not be more than 150 0 when the magnitude
ratio is one or more. The 30 0 difference between the acceptable and unstable condition is called the phase margin.
2. At 180 0 phase lag the magnitude ratio should be equal to or less
than 0.5. For a magnitude ratio of 0.5 it would be necessary to increase
the ratio by a factor of two in order to make it unity and, hence, make the
system unstable. The factor by which the magnitude ratio has to be increased to obtain instability is called the gain margin. A gain margin
of two is, therefore, desirable for process control.
Effect of Load Changes. Graphical methods of determining system
design are simple but do not show the effects of various upsets in the system. In order to analyze the system response, several mathematical
checks can be made. The most important is the effect on the controlled
variable of changes in the load or changes in the set point of the process.
In eq. (2) for a load change, the set point V is taken as zero and the
response due to load upset can be calculated. Also, for set point deviations, the load U is taken as zero and the response due to varying the set
point can be calculated. As a general rule, process control analysis is
concerned with the effect of a change in the load U variable.
The system equation and parameters determined from the graphical
plot can now be converted to the differential form by taking the inverse
transform of the equations. The purpose of this conversion is to test for
response to a step change in the load variable. For example, consider
the control of a two-capacitance system shown in Fig. 11. Manipulation

CHEMICAL PROCESS CONTROL SYSTEMS

8-16

/11\

r----r-----..1.l~U

//\\

(a)

u

c

(b)

FIG. 11. Two-capacitance process: (a) flow diagram, (b) block diagram.

of the system equations to determine the effect on the deviation E of the
process load changes gives the following:
(16)

E =

.

+ 1)(T2s + 1) V
(TIS + 1)(T2s + 1) + GIRl
(TIS

where E = error signal,
V = set point,
U = load variable,
T I = lower tank time constant,
T 2 = upper tank time constant,
R = valve resistance,
G = controller transfer function.

DESIGN PROCEDURES

8-17

Figure 12 shows the deviation of the controlled variable from the original
set point as a result of load changes for various modes of control.
1. Proportional-derivative control provides the smallest maximum
error because the derivative part of the response allows the proportional
sensitivity to be increased to a high value. The stabilization time is the
smallest because of the derivatiye action. Offset is allowed, but is only
one-half that experienced without derivative action.
0.7
0.6

'"

/

0.5

II

0.4
c:

~

1,\

"1\
\r-,.

l~-"

o

~ 0.3

r~ I\®\
r ~\
I/
\@

'5
Q)

Cl

I---

/

\

\

0.2
0.1

o
-0.1

o

~

/ ' I--- l"-

CD~ ~ P'\ CD
-,. ,.
\. --,,'- 1' .......
......... \

10

20

30

~

40

-_

.f--- t-~

50

........

/'

60

'"

-- -

70

.......

80

C\

I:::.-~

90

rs:

100

---

110 120

Time, seconds

FIG. 12. Comparison of modes of control.

2. Proportional-integral-derivative control has the next smallest maximum deviation, and offset is eliminated because of the integral action.
Stabilization time is increased, however.
3. Proportional control has a larger maximum deviation than controllers
with derivative action because of the absence of this stabilizing influence.
Offset is also larger.
4. Proportional-integral control has no offset because of the integral
action. The unstabilizing influence of integral response is reflected in the
large maximum deviation and the persisting deviation.
5. Integral control is best suited for the control of processes having
little or no energy storage, and the results of the comparison are not representative of an integral control. Moreover, in this process, the results
indicate a large maximum error and a long stabilization time.
The selection of the mode of control and the value of the controller function K c , T I , and T d will, of course, determine the characteristics of the
deviation. Final selection will depend on the amount of deviation that
can be tolerated in view of the desired product quality. For economic
reasons, the minimum number of controller functions should be used.

8-18

CHEMICAL PROCESS CONTROL SYSTEMS

Instrument Location and Transmission Dynamics
Instrument Location. The general selection of the types of instruments to be used has been outlined (see also Chap. 7, Instrumentation Systems). Instruments and controllers are generally grouped at one location near the processing or manufacturing operation they serve. This
grouping may be termed a control center. A central grouping has the ad..,
vantage of coordination of all plant operations, and maintenance of instrumentation equipment is quickly and easily accomplished.
In small plants, all instruments can be grouped at one central control
station. However, in larger plants, there may be several control groups
for various major portions of the complete plant.
Individual units of instruments are either located in individual enclosures or, as is often the case when the plant is housed in a large building,
mounted on open panel boards.
The arrangement of the instruments in the control center or on the
cuntrol board depends on the type of process or operation being controlled.
Very often the use of miniature recording and indicating instruments
permits a graphic panel layout. This type of layout is a reproduction of
the flow diagram, with the symbols for the controllers or indicating instruments replaced by the devices themselves.
Where larger recording or indicating instruments are desired, the graphic
layout can become cumbersome. The layout will then depend upon a
grouping of the instruments in an easily read group of similar measurements which will facilitate the rapid diagnosis of plant operation.
Transmission Lags. Although the centralization of recording and
controlling instruments at one location is desirable, the distances involved
in the transmission of signals between the controlling elements may vary
from a few feet to thousands of feet. For pneumatic instruments, the
pneumatic transmission is generally operated on pressures of 0 to 20 psig.
Generally, the tubing is ~ in. or % in. o.d. The lag caused by the tubing
results from the resistance and volume of the line. The lag of transmission
is generally small,. up to 500 feet, but can be tolerated up to 2000 feet
providing the lag is reduced by the use of booster pilots. For a detailed
discussion of transmission systems see Chap. 7, Instrumentation Systems.
The selection and location of the controllers or measuring means will
affect the system dynamics, depending upon the measuring lags involved.
The effect of a large measuring lag is almost always to cause large amplitude oscillations and slow return or stabilization. The introduction of a
large measuring lag modifies the block diagram of Fig. 3 by the addition of
a time element H in the feedback line as shown in Fig. 13.

DESIGN PROCEDURES

8-19

c
B
~----------------~

H r-------------------~

FIG. 13. Process with feedback lag.

The function H can be the transmission lags of the system or the characteristics of the transmitter if one is used in the control system.
The system of eq. (2) is similarly modified to include this element as
follows:
(17)

In addition, the equation for the feedback variable or measured variable
can be shown to be
(18)

The comparison of the response of the controlled variable C and the
feedback variable B to a load upset for a given system for two measuring
lags, 2 sec and 10 sec, is shown in Fig. 14. Both variables have the same
general characteristics, but the feedback variable shows less change and
is retarded from the actual controlled variable. Therefore, changes in
the controlled variables are always larger in magnitude than those indi-

TM


\

-0

~

~c
o

U

Time

Time

FIG. 14. Effect of measuring lag.

8-20

CHEMICAL PROCESS CONTROL SYSTEMS

pated by the ,feedback. Longer measuring lags result in a larger difference
between the controlled variable and the feedback variable and also result
in a greater offset in the process from the set point. The recovery time is
also slower; l\.lthough the effect of measuring lag will depend upon the
particular system, as a general rule, the measuring lag should be at least
one-tenth the largest lag in the process system.
The effect of transmission lags between the controller and the final control element, or the final control element and 'the process, is to add another
time function in the block diagram. In the proce.dure for detennining the
controller settings, these lags will have a determining effect if they are
relatively large compared to the other lags of the process. As a general
rule, the transmission lags should be at least one-tenth the largest lag
of the system.
The complete process analysis is determined by combining the individual loop analyses, just as the individual blocks of the block diagram
were combined. The degree of success with which the control system
maintains the desired product quality and efficiency is a direct function
of the thoroughness of the system design. System analysis will many times
prevent the embarrassing situation of a violently oscillating process,
making evident the effect of a particular variable within the system.

REFERENCES
1. D. P. Eckman, Automatic Process Control, Wiley, New York, 1958.
2. D. P. Eckman, Industrial Instrumentation, Wiley, New York, 1950.
'3. W. Hii(jW)
cf>io(jW)

w

a coefficient
frequency response of a controller
an arbitrary input disturbance function
controller gain
the process time response to J( t)
process frequency response
process transfer function
process step function response
process impulse function response
constant coefficient
process frequency response
complex frequency variable of the Laplace transformation
time constants
dead time, or transportation delay
a variable of integration
delay, or shift of the correlation functions
power density spectrum at the process input
cross power density spectrum between process input and process
output
auto-correlation function of the process input
cross-correlation function of the process input and the process
output
angular frequency

2. TUNING A CONTROL LOOP

The operation of tuning a controller in an automatic control loop is in
effect a process test. This test is the simplest type of test and correspondingly yields the least information about the process. Nevertheless, the

PROCESS TEST METHODS

9-03

information is pertinent and in a form suitable to the task of adjusting
the controller to give good control of the process.
There are many procedures for making controller adjustments in tuning a control system. Some of the procedures utilize the so-called "ultimate period" which is found by setting rate and reset action to minima
and increasing the gain until the system oscillates. (Rate action expressed as "rate time" in minutes is set to the shortest time. Reset action
may be expressed as "reset rate" in repeats per minute or as reset time in
minutes. The longest reset time, or the smallest number of repeats per
minute, gives the minimum reset action.) When the control system is in
the state of just sustaining an oscillation, the product of the controller
response and the process response is equal to unity:
(1)

C(jw) P(jw) = 1.

If at the frequency of oscillation (where G is the controller gain)

00

C=-~

then
(3)

P = -l/G.

That is, the process has at the frequency of oscillation a phase shift of
180 0 and an amplitude ratio l/G. Many of the controller adjustment
procedures (Ref. 1) then give rules of thumb whereby the controller knobs
are set, using only the information gained thus far together with the
desired degree of system damping.
To obtain further information about the process, reset or rate action
may be introduced to shift the frequency of oscillation. The controller
gain is adjusted so that the oscillation is just sustained. For each frequency the process response is obtained as the reciprocal of the controller
response:
1
P(jw) = - - .
C(jw)
Testing a process by this method is slow, since it may take several hours
to determine the exact critical gain required to sustain oscillation.
Accuracy is poor since controller knob calibration cannot be relied upon
to better than a factor of two. The only advantages of this method of
testing are that no additional instruments are necessary and that the
process is not taken "off control" for testing.
3. STEP FUNCTION TESTING
Procedure. The open loop step function test is extremely useful for
determining process dynamics when the greatest accuracy is not required

9-04

CHEMICAL PROCESS CONTROL SYSTEMS

and when testing time is restricted. First the process is allowed to "line
out" with the air pressure to the control valve at the normal operating
value. Then the air pressure is suddenly altered by an increment D.p, and
the transient response at the "controlled" variable is recorded. Thus far
the test has been conducted without the need for special (test) instrumentation, the assumption being that the regular plant instrumentation has
been utilized. The manual loading station can be used to apply the step
function in the air pressure to the control valve, and the increment of
pressure D.p can be obtained from successive readings of the air gauge at
the manual station. This procedure is satisfactory where step amplitudes
of 1 to 2 psi are permissible, and the best accuracy of the method is not
sought. When circumstances are such that small step amplitudes must
be employed, a special setup for testing such as that shown in Fig. 1 is
almost essential.
Air supply

DP

Process strea m

FIG. 1. Equipment setup for step function disturbance; DP = differential pressure,
G = pressure gage, P = positioner, R = regulator.

Instrumentation. As recorded on the regular plant instruments, the
transient response will in general yield only the crudest information about
the process dynamics. The recording instrument that would be ideal for
step function testing differs from the regular plant recorders in having
(1) greater sensitivity, (2) narrower span (i.e., a large range suppression),
(3) faster chart speed, (4) rectilinear recgrding, (5) less hysteresis, (6)
greater linearity, and (7) faster response time. Although improvements
in all these characteristics are not necessary for measurements on all
processes, the first four are essential to the fullest exploitation of the
step function test. For both the input disturbance to the process (i.e., the
step function change in valve air pressure) and the process output response
(i.e., the step function response of the process) to be recorded simultaneously, a two-channel recording system is desirable.

9-05

PROCESS TEST METHODS

Graphical Analysis of Step Function Response
Oldenbourg and Sartorius Method. A great deal of information
about the process may be gleaned from a quick visual inspection of the
step function response. A number of step function responses together
with the process characteristics usually determined from them are given
in. Fig. 2. When the· step function response is other than a simple exponential curve, it is necessary to analyze the response to determine
the time constants. A useful graphical method of analyzing the response
of a system having two time constants is the Oldenbourg and Sartorius
method (Ref. 2). The method depends upon finding the point of
steepest slope and the slope itself. More convenient for analysis are
the quantities T A and To which may be obtained graphically as illus-

Process Characteristics
Gain

Time
Constants

AT

Dead
Time

T

7lP

~T~

------.

T

-AT

t;;;

T

Td

AT

Two or
more

Td

Ap

FlO. 2. Process step responses.

CHEMICAL PROCESS CONTROL SYSTEMS

9-06
100

//
TC

//

75
~

/

Q)

>
0
u

~

+'

50

C

V

/

Q)

~

Q)

a..

/

/"

~V

v----

V

,....TC
TA

---

J--+--

.:.

To 100% completion

= 7.56 =0.8

/"

25

I

V
a JI
a

;11'

TA

2

4

3

5

6

7
8
9
Time, seconds

10

12

11

13

14

15

FIG. 3. Oldenbourg and Sartorius analysis of a two-time-constant system.

trated in Fig. 3. In the Oldenbourg and Sartorius diagram (Fig. 4) the
ratio To/T A is used as the intercept on each axis of the straight line. The
straight line intersects the curve in two points, either of which gives the
ratios Tl/T A and T2/T A from which Tl and T2 may be found. The graph
covers the whole range of possible ratios of Tl to T2 from infinity to unity.
Tl

1.0
0.9
0.8
0.7

~

T

K
r-

,A
T
TA
,

= I0.663.I

1
.t x I7.5 =1·4.97I sec
= 0.663

I I I I I I I I
= 0.133 x 7.5 = 1.0 sec

= 0.133

T2

1\"

'K.""-

~ 0.5

'\

0.4
Tc
-TA =

Tl
TA

-- -

a

0.1

~-

0.2

~"
~

+

0.2
0.1

Tl

I"~

0.6

0.3

I

T2
TA

Tc
TA

= 0.8

~"""- ~,

-- -

0.3 0.4

'"
--

0.5
Tl ITA

~~
~

0.6

"''

0.7

'\

['--......

0.8

r--.....

0.9

FIG. 4. Oldenbourg and Sartorius diagram.

1.0

PROCESS TEST METHODS

9-07

The case of Tl = T2 results in the straight line being tangential to the
curve.
The Oldenbourg and Sartorius method can be used for the analysis of
the step function response of processes involving integration, provided
the integral response can first be subtracted from the total response (Fig.
5) . The method cannot be applied to analyze the step function response
of processes having complex time constants, but such processes, although

Step

I

;;J ____________~) t
o

Process
response

o

Process response
less integral
action

o

) t

) t

FIG. 5. Removal of the integral response.

common in servomechanisms, have not yet been reported in process control.
The slope intercept method is useful in obtaining a rapid analysis of
step function responses when the response consists of the sum of two or
three exponential responses. It is readily applied when the time constants
are widely separated and becomes progressively more difficult and less
accurate as any two of the time constants tend to become coincident.
The percent of incomplete response (i.e., difference between the final value
of the step function response and the response at any time) is plotted on
semi-logarithmic paper (e.g., curve A, Fig. 6). One time constant Tl
is found as the time required for the asymptote to fall to 36.Sro of the
intercept. The numerical difference between the percent incomplete response and the asymptote is plotted in curve B, and the process is repeated
to extract the second time constant T 2 • If curve B deviates appreciably

9-08

CHEMICAL PROCESS CONTROL SYSTEMS
300

Percent incomplete response

200 1--+,-.-+-\-+---+ ~e-t/Tl _
1

Tl - T2

t

I II I

,~ymptote
100

~ """ Curve A, Tl - 5.0 sec

~

=

e-t/T2-

Tl - T2

--t-+--+----j

70
Cll

50

Ul

c:

~

30

~

.!!:l 20
Cll

a.
E

0

u

.::

10

'E
Cll

7

~
Cll
0-

5
3
2

\

"""betw~

\

........
Curve B is the numerical difference
~T2~~
curve A and the asymptote to curve A

'. II

\

I
I

\

I
I

I---+--'--\- Curve B, T2

r\

= 1.1 sec ----11-+--+-+----i

\,

1~~~~~~~~~~
o
2
5
7 8 9 10 11 12
3

4

6

Time, seconds

FIG. 6. Slope intercept method of determining time constants from step response.

from a straight line, it'may be possible to determine yet a third time constant.
A method has been published (Ref. 3) which in certain cases will yield
three time constants from the step response. A number of points are
picked off from the step response, and by reference to a family of curves
the three time constants are obtained.
Mathematical Analysis of Step Function Response

vVhere graphical metho,ds of analysis are not sufficient, a mathematical
analysis may be performed:
(4)

H(s) = siooho(t) e-" dt.

The step function response ho(t) of processes involving integration contains a linear term which it is convenient to remove (Fig. 5). The integral
may then be evaluated in two parts. If
(5)

where ho (1) (t) = at, then since multiplication by s is equivalent to differentiation in the time domain and since the derivative of the step functiori

PROCESS TEST METHODS

9-09

response is the impulse response hI (t), eq. (4) becomes
H(s) = -a
s

(6)

+

i

oo

hI (2) (t) e- st dt.
0

Note. The step function response is measured and is differentiated to obtain the impulse response. The substitution s = jw may now be made:
(7a)

(7b)

H(jw) =
H (jw) =

+i
~ +i

.~

JW·

JW

oohl (2)(t)

e-iwt dt,

0

OO

hI (2) (t) cos wt dt -

0

ji

OO

hI (2) (t) sin wt dt.

0

The integrals in eq. (7b) may be evaluated numerically for discrete
values of w. If the step function response ho (t) has been carefully measured with special instrumentation under conditions nearly free of noise
and other disturbances, the numerical evaluation may give useful results
over a wide range of frequency (e.g., 250 to 1). However, from step
function tests conducted in process plants where measurement equipment
and conditions are often less than ideal, the frequency range over which
useful results may be obtained is not so wide (e.g., 16 to 1). The numerical evaluation may be performed manually but is somewhat tedious even
for simple step function responses. A digital computer is desirable to obtain the best results.
The integrals in eqs. (7) may be evaluated graphically (Ref. 11) or by
analog computation. Numerous devices and schemes have been devised
f or this purpose.
The frequency response H(jw) is obtained from eq. (7) as a number of
points which when plotted may be approximated by a smooth curve. The
plot usually results in a great deal of scatter for the higher frequencies.
This scatter may be due to (1) the effects of noise and disturbances which
occurred during the step function test, (2) sampling errors and simplifying
assumptions in the case of digital computation, (3) machine errors in the
case of analog computation.
The plot of H (jw) may be approximated by the type of transfer function
desired.
4. IMPULSE FUNCTION TESTING

The impulse function test can be used as a variation of the step function test. The ideal impulse must be approximated by a pulse of finite
amplitude and finite duration. A good choice of pulse duration cannot be
made until the process dynamics are approximately known. Furthermore, the pulse amplitude must be large if a reasonable size of impulse

9-10

CHEMICAL PROCESS CONTROL SYSTEMS

response is to be recorded. Hence the test may extend beyond the linearized "small disturbance" range which is implicitly assumed in most
discussions of process control theory and practice. Perhaps for these
reasons impulse function testing has found little application in the process
industry.
Analysis of Impulse Function Response. The impulse function response is the derivative of the step function response. Hence the graphical and mathematical methods of analysis of the step function response
may be readily adapted to the analysis of the impulse function response.
Equation (4) becomes
(8)

H(s) =

i

oo

h,(t) e-" dt.

The impulse function response hI (t) of processes involving integration
contains a constant term which it is convenient to remove. The integral in
eq. (8) may then be evaluated in two parts. If
hl(t)

=

H(s) = -a
s

+

(9)

where hI (1) (t) = a, then
(10)

h 1 (1)(t)

i

+

h 1 (2) (t),

OO

hI (2) (t) e- st dt.
0

Equation (10) is identical to eq. (6) in form. The difference lies only
in the method of obtaining hI (2) (t). In eq. (10) it is obtained directly
from the experimental measurement of the impulse function response
whereas in eq. (6) it is derived from the step function response by differentiation. The evaluation of the integral may be carried out in a
similar manner.
The frequency range over which H (jw) may be obtained is greater with
impulse function tests than with step function tests. However, to achieve
this wider range, it may be necessary to make a number of impulse function tests (using impulses of various duration). Under laboratory conditions frequency'ranges of 400 to 1 have been reported (Ref. 4), but under
field test conditions in plants the useful frequency range obtainable may
be only 32 to 1 or even less.
Arbitary Function Testing. If an arbitary input function J(t) produces a process response g (t) , the process transfer function is given by

(11)

.£00 g(t) e-"

dt

.£00 f(t) e-"

dt

H(s)

PROCESS TEST METHODS

9-11

Testing with arbitary input functions has found little application in
the process industry, although the method is used commonly in the aircraft industry, which substitutes triangular pulses for f{t).
5. FREQUENCY RESPONSE TESTING

(Ref. 5)

The frequency response test is the standard by which other test methods
are judged. The frequency response test is well established in other
industries, notably communications and servomechanisms, where it has
contributed greatly to the understanding of system dynamics. To carry
out a frequency response test the control loop is first put on manual control. The pneumatic sine wave generator is then set to give a highfrequency signal having a small amplitude and a mean pressure equal to
that of the air pressure at the control valve head (Fig. 7). The block

Sine wave
generator
1-----1

G

Manual
loading
station

Process stream

FIG. 7. Equipment setup for sine wave disturbance; G = pressure gage.

valve between the pneumatic sine wave generator and the control valve
is then opened, and the block valve between the manual loading station
and the control valve is closed. When the "switch" has been accomplished, the amplitude of the pneumatic sine wave may be increased to a
relatively large value.
The recording system is arranged to record the controlled variable and
also the air pressure on the control valve. Recordings are made over as
wide a range of frequency as is necessary for a complete description of
the process. The test is usually begun with a high frequency of oscillation, using the largest amplitude of oscillation consistent with obtaining
a reasonably linearized measure of the process. The frequency is reduced
in approximately octave intervals until the response of the controlled
variable becomes apparent. The amplitude ratio and phase shift are then

9-12

CHEMICAL PROCESS CONTROL SYSTEMS

measured from the recording as shown in Fig. 8. Measurements are obtained at approximately octave intervals of frequency, and the amplitude
of the sine wave disturbance is reduced if necessary in order to maintain
reasonable limits of excursion of the controlled variable. The frequency
range over which measurements are made (or attemtped) is that range
necessary for the complete description of the process. Quite often this
will be to the low-frequency limit necessary to properly locate the longest
time constant of the process and to determine the gain (or integration
rate) of the process.

Amplitude ratio A =

*

Sine wave
disturbance
Phase shift = 8

FIG. 8. Amplitude ratio and phase shift.

The measured frequency response is plotted as shown in Fig. 9. Some
scatter in the measured points is expected, but usually the best curves
drawn through the amplitude ratio points and the phase points are capable of approximation in terms of time constants and the dead time. The
measured frequency response curves of Fig .. 9 are, for example, representative of a lumped parameter system of transfer function:
(12)

H(s)

where T d is the dead time, and Tl and T2 are the process time constants.
As with step function tests, frequency response tests are easier under
laboratory conditions than under field test conditions. However, even
under field test conditions it is usually possible to make measurements
over a frequency range of two to three decades.
The upper frequency limit to which frequency response measurements
may be made is often established by process noise rather than by instrument sensitivity. There is a low-frequency limit for processes involving
an integration owing to the difficulty of introducing extremely low-ampli-

PROCESS TEST METHODS

o

--

0

~

<11

~ -10

or-

~ ....

"C

::[ -20
E
< -30

o

~

~

~

~

""""....... ~

f'l.. r-_
r-~

Q)

Q)

f.:::; ;'-:::t'-.
1'- .....

VI

~

--,

9-13

100

~

~v

i'

-....:. ~ 1:-1-

r---.r-... r--r--_

~

:.c
VI

.....

I"-..

~ 200

.c

a..

300

om

0.1

Frequency (cycles per min.)

1.0

- ---_._,1>....

.-~

Minimum phase-

~

IIIIII

~

10

FIG. 9. Measured frequency response.

tude sinusoidal disturbances into the process and the difficulty of maintaining such a process without automatic control for long periods.
Where process noise limits the frequency range of frequency response
measurements, special steps may be taken to overcome the difficulty
(Ref. 10). Such steps are necessary for the frequency response measurement of processes, such as temperature control of exothermic reactions,
which cannot be taken off control.
6. STATISTICAL METHODS FOR THE MEASUREMENT OF PROCESS DYNAMICS

(Refs. 6 and 7)
Statistical methods for the determination of process dynamics have
been reported (Refs. 8 and 9). The advantages claimed for these methods
a.re that they require no plant disturbances and that normal operation
and control need not be changed for testing.
The method involves a considerable amount of computation with data
recording, reproduction,and storage. The computation and data handling
may be in analog or digital form. General purpose digita.l computers
may be utilized, but the equivalent calculations in analog form have
been done by some special purpose computers.
It is required to find the transfer function H (jw) of a linear system
under excitation by a random stationary function having a power density
spectrum cI>ii (jw) . If the cross power density spectrum between input
and output is cI>io(jW), the following relationship applies:

9-14

CHEMICAL PROCESS CONTROL SYSTEMS

(13)

H(jw)

if.Jii(jW)

Furthermore, if if.Jii(jW) is essentially fiat over the range of w which is of
interest in cI!io(jW), then
(14)

H(jw) = cI!io(jW).

Since the cross correlation functions are more readily computed than the
cross power density spectrum, these equations may be replaced by

(15)

H(jw)
-1
27r

and

foo ¢ii(r) e- .

JWT

dr

-00

(16)

Alternately, these equations may be written as
(17)

¢io(r) =

foo h(u) ¢ii(U -

r) du.

-00

In a novel method (Ref. 8) of "deconvolution," the system impulse response h (t) of an analog is adjusted while being repetitively convolved
with the auto-correlation function, which is generated as a time function.
Adjustments are made until the result of the convolution has the shape of
the cross-correlation function. Equation (17) is then satisfied, and the
impulse response of the analog is therefore analogous to that of the
process plant on which ¢ii(r) and ¢iO(r) were measured.

REFERENCES
1. J. G. Ziegler and N. B. Nichols, Optimum settings for automatic controllers,
Trans. Am. Soc. M echo Engrs., 64, No.8, 759-765 (1942).
2. R. C. Oldenbourg and H. Sartorius, The Dynamics of Automatic Controls, American Society of Mechanical Engineers, New York, 1948, p. 77.
3. H. ThaI-Larsen, Frequency response from experimental non-oscillatory transientresponse data, Trans. Am. Inst. Elec. Engrs., 74, Pt. II, 109-113 (1955).
4. J. O. Hougen and S. Lees, Pulse testing a model heat exchanger process, Ind.
Eng. Chem., 48, 1064-1068 (1956).
5. P. R. Hoyt and B. D. Stanton, Analyzing process control systems, Petrol. Refiner,
32, No. 10, 115 (1953).

PROCESS TEST METHODS

9-15

6. Y. W. Lee, Application of statistical methods to communication problems, Technical Report No. 181, Research Laboratory of Electronics, Massachusetts Institute of
Technology, Cambridge, Mass., Sept. 1950.
7. Y. W. Lee and J. B. Wiesner, Correlation functions and communication applications, Electronics, 23, 86-92 (June 1950).
8. T. P. Goodman and J. B. Reswick, Determination of system characteristics from
normal operating records, Trans. Am. Soc. Mech. Engrs., 78, No.2, 259-268 (1956).
9. J. B. Reswick, Determine system dynamics-without upset, Control Eng., 2, No.
6, 50-57 (1955).
10. P. E. A. Cowley, The Application of an analog computer to the measurement of
process dynamics, Trans. Am. Soc. M echo Engrs., 79, No.4, 823-832 (1957).
11. A. R. Teasdale, Frequency response from transient data by adding vectors,
Control Eng., 2, No. 10,55-59 (1955).

D

CHEMICAL PROCESS CONTROL SYSTEMS

Chapter

10

Single and Multiple Loop Controls
J. E. Rijnsdorp

1. Introduction and List of Symbols
2. Block Diagram of Single Loop Control
3. Reduction of Sinusoidal Deviations

10·01
10·03

4. Transfer Function of the Controller
5. Dynamic Behavior for Some Typical Processes

10·04
10·05
10·06

6. Responses to Step and Constant Rate Disturbances
7. Adjustment of the Controller Actions

10·17
10·20

8. Feed·Forward Control
9. Cascade Control
10. Use of Analytical Instruments for Process Control
11. Multivariable Control Systems
12. Special Subjects
References

10·27
10·28
10·34
10·35
10·40
10·40

1. INTRODUCTION AND LIST OF SYMBOLS

In principle, process controls are not different from servomechanisms.
Their dynamic behavior can be described in the same way, and techniques
common to the servomechanism field have frequently been applied to the
design of process control systems.
However, there are some differences which mark the individuality of
the process control field. In the first place it is difficult to obtain clearcut specifications for the performance of the process control system,
largely because most process controls do not directly control the quality
10·01

CHEMICAL PROCESS CONTROL SYSTEMS

10-02

of the plant products, only some easy-to-measure process variable such
as temperature, pressure, level, and flow rate.
Another aspect is the lack of quantitative data on the plant disturbances. The latter are often not even random enough to apply correlation
techniques such as Wiener's optimization (see Vol. 1, Chap. 17, Smoothing
and Filtering).
In the third place, the dynamic behavior of the process varies with
process conditions (plant load, etc.), which interferes with optimum
adjustment of the controller.
All these considerations emphasize the need for a simple, qualitative
theory and semiquantitative rules of thumb. This is the line of thought
to be followed in this chapter.
List of Symbols.
A
aI, a2

C

Cl
C2
D

area of response
constants
controller (transfer function)
primary controller } .
m cascade control sys terns
secondary con t ro11er
derivative action

e

2.718 ...

F

frequency of oscillation
flow controller
flow transmitter

FC
FT
G

. ble systems
· f actor 0 f two-varIa
coup1mg

P
(P12
= P P 21)
ll

HI, H2
h

I
j

K
Kc
Kp
Kcu
K l , K 2 , Ka

LC
M
N
n
P
p
P a, Pb, etc.}
PI, P 2, etc.

PC
PT
Q

RC
S
T

22

disturbances
height of step disturbance
integral action

v'-=1

gain factor
proportional gain of controller
steady-state gain of process
ultimate proportional gain of controller (at limit of stability)
process gains
level controller
transfer function of measuring device
number of time constants
order number
process (transfer function)
proportional action
process transfer functions
pressure controller
pressure transmitter
flow rate
ratio controller
integration coefficient (see Fig. 23b)
dead time

SINGLE AND MULTIPLE LOOP CONTROLS

Td
Ti
T I , T 2, etc.

TO

v
X, Xl, X 2
Y, YI, Y2
a

f3
l'
LlPT

o
E

()

J.L

II
p

T

cf>
W

Wmax

10-03

derivative action time
integral action time
process time constants
temperature controller
slope of constant rate disturbances
controlled variables
manipulating variables
argument of complex frequency
constant
constant
pressure difference transmitter
constant
deviation
temperature
gain factor
product of
modulus of complex frequency
time constant
phase angle
angular frequency
frequency at the peak of the deviation ratio curve
complex frequency

2. BLOCK DIAGRAM OF SINGLE LOOP CONTROL

Figure 1 gives an example of a single loop control, the control of the
outlet temperature of an oil furnace. The block diagram is shown in
Fig. 2.
Inlet flow (Qi)

~

~====~========~~~~~==~~~=====~
Inlet temperature lOi)
//
J),utlet temperature (00
/

)

C Controller

I

~p
I

\

\

\

Burners ~,$..:

~~~.~~~~~~~=====

" Fuel supply (Qf)

FIG. 1. Control of the outlet temperature of an oil furnace.

Contrary to what is normal in servomechanisms, the set point is generally at a fixed value, so that the process control system is usually a regulator. In other words, the main task of the control system is to reduce
the effect of disturbances on the controlled variable. The quality of
control can be judged by comparing the remaining deviations in the controlled condition to the requirements.
Sometimes noise has a strong influence on control, for instance in flow
control systems where turbulence causes a noise signal in the measuring

10-04

CHEMICAL PROCESS CONTROL SYSTEMS

Set point

FIG. 2. Block diagram of the furnace control system of Fig. 1.

device. In Fig. 2 all noise sources have been combined into one source
at the input of the controller.
3. REDUCTION OF SINUSOIDAL DEVIATIONS

The Deviation Ratio. The most powerful method of studying the
dynamic behavior of closed loop systems is by frequency response (see
also Refs. 1-7). In this chapter the frequency response of single loop controls are expressed in the so-called deviation ratio, as has been done by
Ahrendt and Taplin (Ref. 6) and by Janssen (Ref. 7). The deviation
ratio equals
Deviation with control
1
(1)
Deviation without control = 1 + P(jw)C(jw)

I

I

where P(jw) is the transfer function of the process and C (jw) is the
transfer function of the controller.
Formula (1) is based on the assumption that the system is linear.
However, by using describing function methods (see Vol. 1, Chap. 25,
Nonlinear Systems), the formula can be extended to nonlinear systems.
Figure 3 gives an example for a furnace control system similar to that
shown in Fig. 1 (see also Ref. 13). The frequency has been plotted in
dimensionless form; the yardstick is the frequency at which the deviation
ratio has its maximum value.
Westcott (Ref. 8) has found an interesting property of the deviation
ratio curve:
(2)

i

oo

o

log

I1 +1PC Idw = o.

Expressed in words, this formula says that improvement of control in one
frequency region deteriorates control in other frequency regions. Gen-

SINGLE AND MULTIPLE LOOP CONTROLS

11

10-05

+lpcl·
2

0.2
0.1
W max

~

0.06 radians/sec

FIG. 3. Deviation ratio of the furnace control system of Fig. 1.

erally good control at low frequencies is desired, namely, a small value of
the deviation ratio. The result is that a resonance zone has to be tolerated
at higher frequencies (see Fig. 3).
At veryhigh frequencies the loop gain is always small, so that control
is ineffective and the deviation ratio is roughly unity.
The most important characteristics of the deviation ratio are the value
of W max (the resonance frequency) and its values for low frequencies, where
IPCI» 1.
As long as noise and saturation do not interfere, a higher value of W max is
desirable because it means a larger bandwidth and a faster response.
The values for low frequencies are a measure of the control of slow disturbances which occur frequently in chemical and refinery processes. This
aspect of process control corresponds to the consideration of error constants in servomechanisms (see Vol. 1, Chap. 20, Fundamentals of Systems Analysis) .
The height of the resonance peak is not characteristic of the process
control system because it can be adjusted to any convenient value by
merely changing the gain of the controller. In practice the peak height
is seldom larger than 2.
4. TRANSFER FUNCTION OF THE CONTROLLER

The following controller transfer function will be used for the examples
of this section:
(3)

C(jw) = Kc ( ~ +
\jWTi

1) [1 + + Jwf3Td
+ (3)Td] ,
jw(l.

1

10-06

CHEMICAL PROCESS CONTROL SYSTEMS

where Kc is the proportional gain factor, Ti is the integral action time,
T d is the derivative action time, and {3 is a constant (here chosen equal
to 0.1).
It is interesting to compare eq. (3) with the corresponding part of the
transfer function of a servomechanism:
(4)

The first factor represents the integration of the servomotor and the
gain of the amplifier, whereas the second and the third factor stand for
phase lead networks (see Vol. 1, Chap. 23, Feedback System Compensation) .
Thus a process controller with three actions corresponds to a servo with
double lead compensation. Many controllers have transfer functions
which are different from eq. (3) (see ahm Refs. 9 and 10). For instance,

A transfer function often used in theoretical work is that of the pure
three-term controller:
(5)

However, only a few process controllers operate according to this formula.
Some controllers have only proportional action: Ti = 00, Td = 0 (P
controllers). Others have proportional and integral action: Td = 0
(PI controllers); or proportional and derivative action: Ti = 00 (PD
controllers) .
When the plant is being designed, the type of controller that can be expected to do the job is chosen. In general, the controller actions are not
adjusted before the plant is put into operation.
5. DYNAMIC BEHAVIOR FOR SOME TYPICAL PROCESSES

The line of thought folluwed in this section is the same as Janssen's in
Ref. 10. For further information see this reference and the examples
provided by Aikman (Ref. 12).

SINGLE AND MULTIPLE LOOP CONTROLS

10-07

A Process without a Predominant Time Constant

First a process transfer function of the following kind will be considered:
N
1
(6)
Pa(jw) = Kp
n=l 1 + }wTn

II

.

'

where all time constants Tn are of the same order of magnitude and Kp is
the steady-state gain of the process.
An example is a flow control where the flow is measured with a fastresponding device, such as a force balance pneumatic transmitter FT
(see Fig. 4). The dynamic behavior of the transmitter, the pneumatic

FIG. 4. Flow control system.

transmission lines, the control valve, and the flow line itself can be
represented by a combination of many time constants of the order of
a second or less. Then the process transfer function embraces everything in the closed loop except the pure controller transfer function
[eq. (3)].
Frequency Response. Figure 5a shows the frequency response of the
process and the deviation ratio for a P, a PD, an I, a PI, and a PID
controller. P stands for proportional action, I for integral action, and D
for derivative action. Figure 5a has been obtained from measurements on
an analog computer. The controller has been adjusted according to the
Offereins'method (see Sect. 7, Adjustment of the Controller Actions), with
two modifications.
In the case of a PID controller, the integral action is adjusted as if the
controller were a PI controller. Before this, the derivative action is adjusted in the normal way. The final adjustment of Kc (Kc/Ti in the case
of I control) is such that the height of the peak of the deviation ratio curve
equals 2.
Evaluation. It can be seen that proportional action as such is not
very useful. The steady-state deviation is rather large, and the application of integral action is highly desirable. On the other hand, derivative
action gives very little improvement.
Thus we can conclude that an integral controller or a proportional plus
integral controller (which is easier to construct pneumatically) is the best

....
o
6

co

n

:t:
m

3:

n

»
r-

"'tJ

(1

+ jwr)10

(1

10

+ jwr)9(l +

jw10 3 r)

1

(1

+

jwr)8(l + jw10 3 r)2

A:J

o

n

m

VI
VI

0.1

n

o
0.1

t
Ipl

(1)

z-f

0.01

A:J

o
r-

VI

0.1

0.01

-<

0.001

VI

-f

m

3:
VI

10- 3

(2)

t

Lp

10- 2

10- 1

10- 3

1

10- 2

10- 1

10- 3

-90

-90

-90

-180

-180

-180

-270

-270

-270

-360

-360

-360

I

10- 2

I

10- 1

I

101-

(3)

II

101//~-'F

/'\.

t
+1

10

pel 0.1 ~

.-

I

~

I

/

./

-,\

P

0.11-

0.01

0.011

10- 3

0.1

r--

10- 3

10- 1

10- 2

//

10- 1

10- 2

~WT

I

0.01 r
10- 3

(J)

10- 2

----:;-WT

I
10- 1
-...:;;-WT

Z

G)

~

m

»
Z

101-

(4)

/1

t
+lpcI

t

0.1

101-

\

/

I

-""

/

10- 1

10- 2

~

m

~

//

10"",3

0
0

.,

0.1

1/
I'
1/

n
0

z

I
10- 2

- . : ; - WT

(a)

~

.,
:j

.

I .

0.1

I'
IL

10- 3

/

/1

//(PID

,/\"PI

~
C

.. /:?,-V .. -

~~
/

0

101-

10- 1

10- 3

10- 2

~WT

(b)

10- 1
~WT

--I
;:c

0

~

(J)

(c)

FIG. 5. Frequency response of process with (a) no, (b) one, or (c) two predominant time constants and the associated deviation ratios.
0

6-0

CHEMICAL PROCESS CONTROL SYSTEMS

10-10

choice. In the latter case, a low proportional gain should be used. This
is in line with the experience obtained for flow control systems with fastresponding transmitters (see Refs. 42 and 43).
A Process with One Predominant Time Constant

The transfer function of the process equals
Pb(jW) =

(7)

K

N

1

II - - I + jwTl n=2 1 + jwTn
P

where all time constants Tn are of the same order of magnitude and T 1 » Tn.
An example is a flow control system for which the transmitter is a mercury
U-tube type with a comparatively large time constant.
Another example is the pressure control on a buffer vessel of a refinery
gas system (see Fig. 6). The transfer function between control valve and

To flare"
-====~

Inlet

Buffer

FIG. 6. Control of the pressure in a refinery gas system.

the pressure in the buffer is that of a large time constant, whereas the rest
of the system is practically identical to the fast flow control shown in
Fig. 4.
Frequency Response and Evaluation. Figure 5b shows the frequency response of the process and the deviation ratio for various types
of controllers. It can be seen that proportional action is essential; without
it control is very slow. On the other hand, derivative action does not
give much improvement. Thus it can be concluded that a proportional
plus integral controller is very suitable, whereas a proportional controller
may be sufficient when it can be adjusted to a high proportional gain.
It is not advisable to use a P controller when the steady-state gain of
the process is high. The effect of disturbances at the inlet of the process
is then amplified by the high process gain, and the resulting offset can be

SINGLE AND MULTIPLE LOOP CONTROLS

10·11

considerable. Thus integral action is desirable and a PI controller should
be used.
A Process with Two Predominant Time Constants

The transfer function of the process equals
I(p

Pc(jw) = - - - - - - - -

(8)

(1

lIN

1

+ jwTl)(l + jwT2) n=3 1 + jwTn

where all time constants Tn are of the same order of magnitude and Tl

»

~

T2

Tn.

An example is the heating furnace control discussed in Ref. 13 (see
also Fig. 1). The large time constant is determined by the residence time
of the oil in the furnace, the second time constant is that of the temperature-measuring element, and the small ones represent lags in the transmission lines, control valve, fuel supply, and the heat transfer from the
burners to the oil in the furnace tubes. In this particular case heat transfer is fast because a great deal of it goes by direct radiation.
Frequency Response and Evaluation. Figure 5c shows the frequency
response of a process according to eq. (8) and the deviation ratio for
various types of controllers. It can be seen that derivative action is very
effective because it increases the resonance frequency appreciably and
makes possible a much better control for very low frequencies. The
conclusion is that a controller with three actions is most suitable, whereas
a proportional plus derivative controller can be used when it can be adjusted to a high proportional gain.
Limitations of Derivative Action

In practice it often happens that derivative action does not give as
much improvement as might be expected from linear dynamic behavior.
The reasons are
1. As has been reported by Farrington (Ref. 14), Boyd (Ref. 15), and
Aikman (Ref. 41), the presence of dead zone effects ahead of the derivative action unit can have an unfavorable influence.
2. The control system should distinguish between signal and noise.
When there is much high-frequency noise, the bandwidth of the system
should be made rather narrow. Thus derivative action, which increases
the bandwidth, can be disadvantageous.
3. Derivative action gives fast corrections. This can disturb the operation of other processes and control systems.
4. The adjustment of derivative action is rather critical and adds another degree of freedom to the controller. Therefore, in practice, controllers with derivative action are not always adjusted as they should be.

10-12

CHEMICAL PROCESS CONTROL SYSTEMS

Summary of Control Systems for Processes with Zero, One, or Two
Dominating Time Constants
Approximations. The process transfer functions, considered up until
now, all contain a series of small time constants. A convenient approximation for such a series is a pure time delay or dead time:

e-jwT ,

(9)

where T is equal to the sum of the small time constants. Hence a good
approximation of many process transfer functions is one by two time constants and a dead time, as long as
second derivative action is not used.
c
When first derivative action is also
o
:;:;
ro
not used, process transfer functions
":;
a
can be approximated by a time constant and a dead time, or a reaction
rate, S, and a dead time, T (see the
Time
transient response shown in Fig. 7).
FIG. 7. Transient response showing These approximations have been used
dead time and reaction rate.
rather often in theoretical work (see
e.g. Refs. 19 and 23).
Suitable Types of Controller Transfer Functions. Figure 8 gives
a survey of the most suitable types of controller transfer functions for
control of processes with two time constants and a dead time. Its main
value lies in showing where additional controller actions do not give much
Q)

100.-------~---=~--~----~

p

I

I

I
I

1

PI
,-

I

/
0.1

I

,:
1

10

I

I

p

100

1iIT~

FIG. 8. Areas where various controller actions are must useful.

SINGLE AND MULTIPLE LOOP CONTROLS

10·13

improvement. The cases shown in Figs. 5a-c correspond to the extreme
points in Fig. 8, i.e., they correspond to the corner points. The diagram
has been constructed from measurements on an analog computer. The
adjustment of the controller is the same as that used for the construction
of Fig. 5 (see earlier subsection on A Process without a Predominant Time
Constant) .
The boundary lines of Fig. 8 are the following.
1. The borderline between I and PI is the locus of the points where
IC/T i [see eq. (4)] is two times as large for the PI controller as for the
I controller. This factor 2 is considered to give enough improvement of
control to justify the addition of proportional action.
2. The borderline between PI and PID is the locus of the points where
Kc of the PD controller is two times larger than Kc of the P controller.
The integral action has been omitted because the measurements indicated
that it makes control here very slow.
3. The dotted lines represent the loci of the points where the steadystate loop gain with a P or a PD controller equals 30.
It must be emphasized that Fig. 8 does not provide a complete guide to
the choice of controller types, which requires many additional data, such
as the pattern and sources of disturbances, specifications, prices, amount
of noise, etc. For instance, the application of derivative action can be
disappointing (see earlier subsection Limitations of Derivative Action) ;
and strong disturbances at the inlet of the process sometimes require
the application of integral action (see earlier subsections on processes with
one and two predominant time constants, and Using the Frequency Response of the Process in Sect. 7).
Processes with Different Behavior for Low Frequencies

vVhen a process has one predominant time constant, the low-frequency
part of its frequency response resembles
Fig. 9, curve a. Multiplication of the
steady-state gain Kp and of the predominant time constant Tl by the same factor
b
hardly changes the process transfer func- ~
a
tion except for very low frequencies (see .3
curve b of Fig. 9). Thus the choice and
adjustment of controller actions are hardly
affected.
It can be concluded that for proeesses
Logw ~
with one predominant time constant the
FIG. 9. Different low-frequency
actual magnitude of this time constant is behavior of processes with idennot very important. More important is
tical high-frequency behavior.

t

CHEMICAL PROCESS CONTROL SYSTEMS

10-14

K

Pd(jW) =

(10)

N

P

II

1

+ jwTI n=2 1 + jwTn

I

~

KIN
_P-

1

II - - -

TI jw n=2 1 + jwTn

when T 1 » Tn. Formula 10 is exact when the process contains a pure
integration (see Fig. 9, curve c). This is true for most liquid level processes
in buffer tanks and accumulators.
Temperature
Cooling

FIG. 10. Exothermic chemical reaction giving rise to positive feedback.

Unstable Process Transfer Functions

Instability often occurs for exothermic chemical reactions. There the
process contains a positive feedback loop (see Fig. 10) because an increase
in temperature increases the reaction rate, which in turn increases the
production of heat by the reaction and thus also the temperature.
When the steady-state gain of
the feedback loop exceeds 1, the
process transfer function has a
,,,""----- .... ,,,
positive real pole, and the process
,I
,
\
is unstable. However, the comI
\
Af
-1 B\ _
bination of process and controller
w=o
can be stable if the controller gain
is neither too high nor too low.
This can be seen from the Nyquist
diagram (Fig. 11) where the point
FIG. 11. Nyquist diagram for the process
-1 must lie between A and B.
of Fig. 10.
(The polar plot must encircle the
point -1 once in a counter-clockwise direction because of the positive real pole.) Such a control system
is said to be conditionally stable.
I

\

Process Transfer Functions with Parallel Paths

Many processes contain parallel paths between input and output (see
Fig. 12). The overall transfer function can be quite complicated, and
approximation by two time constants and a dead time might fail.

SINGLE AND MULTIPLE LOOP CONTROLS

10-15

Moreover, some peculiar phenomena
might occur, such as one or more zeros
with a positive real part. The transfer
function is then nonminimum phase (see
Ref. 16). An exam,ple is the response of
steam drum level in a boiler to variations
in heat supply. A sudden increase in
heat supply increases the formation of FIG. 12. Parallel paths between
steam in the tubes, which lifts the level in
input and output of a process.
the drum (see Fig. 13). Simultaneously,
the total amount of water in the boiler decreases at a constant rate because
of the increased steam production. The total transfer function equals

(11)

1

-1 +jwKT

jwT

jwT

K--=-----

FIG. 13. Transient response of the drum level in a boiler.

With parallel paths it is also possible that the control system is conditionally stable (see Vol. 1, Chap. 21, Stability). An example is pressure
control in a distillation column, where the accumulator level is controlled
by the vaporous top product (see Fig. 14). A block diagram of the process
is shown in Fig. 15. A change in cooling water supply to the condenser
influences the rate of condensation. This has a direct effect on column
pressure and an indirect effect via the accumulator level, the level controller LC, and the vaporous top product flow.
This parallel combination in the process gives a transfer function 1 +
K1Kdjw, which gives 90 degrees phase lag at low frequencies. \Vhen
integral action is used in the pressure controller PC, the total phase lag at
low frequencies becomes 180 degrees. Thus, the Nyquist diagram resembles Fig. 16; it is evident that the control system is conditionally
stable.

CHEMICAL PROCESS CONTROL SYSTEMS

10-16

ir=~~~~======--~

Cooling water

r;=======:f:::T<:1===== Va porous
top
product
---;>-

Column

--FIG. 14. Pressure control in a distillation column.

Condensation rate

(1
)
+ JWT;

Cooling water flow
' - - - - - - - - - - - - - - - 1 Kc 1

Pressure

Pressure controller

FIG. 15. Block diagram of the process of Fig. 14.

FIG. 16. Nyquist diagram for the process of Fig. 14.

SINGLE AND MULTIPLE LOOP CONTROLS

10-17

6. RESPONSES TO STEP AND CONSTANT RATE DISTURBANCES

In this section no exact analysis of the transient responses of process
control systems is given. Instead, rules of thumb are used, which can
help to assess performance quickly.
Response to a Step Disturbance in the Controlled Variable (Output
of the Process)

Figure 17a shows the general character of this response for a not too
conservative adjustment of the controller. It is the "mirror image" of the
response to a step change in the set point (see Fig. 17b). The following
geometric data more or less determine the form of the response.

(b)

FIG. 17. Response to a step disturbance: (a) in the controlled variable, (b) in the
set point.

I. Maximum Deviation (€max). This simply equals the height of the
step change h.
2. Subsidence Ratio (S.R.). The degree of damping of the oscillation
can be described by the ratio between two successive amplitudes in the
same direction {€2/€d, the so-called subsidence ratio. Its value depends
very much on the setting of controller actions and is often used as a
criterion for the adjustment of the proportional gain factor (see Sect. 7,
Adjustment of the Controller Actions).
3. Frequency of Oscillation (F). The frequency of oscillation is
roughly equal to the frequency at the peak of the deviation ratio curve.
4. Total Area (A). The time integral of the response or total area
equals
00
T.
edt=A=-t-h
(12)
Jo
KpKc

r

where Ti is the integral action time.

CHEMICAL PROCESS CONTROL SYSTEMS

10-18

Response to a Step Disturbance in the Manipulated Variable (Input
of the Process)

Figure 18 shows the general character of this response. The frequency
of the oscillation is the same as in Fig. 17. However, the subsidence ratio

FIG. 18. Response to a step disturbance in the manipulating variable.

is not a good measure for the degree of damping of the oscillation because
the nonoscillatory modes in the response are generally rather strong.
1. Maximum Deviation. Rutherford (Ref. 2) and Aikman (Ref. 3)
give a simple formula for the value of the maximum deviation:
(13)

Emax

(without control)

-----------------~

(with control)

Emax

KeKp.

This ratio is called the deviation reduction factor. It is often used as
an index of controllability, especially in the English literature.
The maximum deviation without control generally equals the steadystate gain of the process, multiplied by the step height:
(14)

Emax

(without control) = Kph.

Thus eq. (13) can be written in the form
(15)

Emax

(with control)

~

hiKe.

This formula is more convenient when the steady-state gain of the process
is unknown.
2. Total Area. The total area of the response equals
(16)

The ratio of the total area and the maximum deviation gives some measure of the duration of the response.
Response to a Step Disturbance Entering at an Arbitrary Point (see

Fig. 19)

1. Maximum Deviation. Janssen gives the following expression (Ref.
11):
(17)

Emax

= 'Yh IP'(j27rP) I,

SINGLE AND MULTIPLE LOOP CONTROLS

10-19

+

FIG. 19. Response to a step disturbance entering at an arbitrary point.

where 'Y ~ 1.5. It is based on the assumption that the oscillatory mode
is dominant in the response. Thus it is inaccurate when pI has much
attenuation for the resonance frequency, or

IPI(j27rF) I«I P'(O) I·
Another formula, based on Paynter's analog between pulse responses
and probability distributions (see Refs. 17 and 18), is the following:
(18)

E

max

= 0

hi P'(O) I
,
FV"');T,2
n

where the T'n's are the time constants of the transfer function pl. This
expression has been checked on an analog computer for a wide range of
processes and practical controller adjustments (Ref. 44). The average
value of 0 was 0.14, and 92% of the results were in the range 0.07 < 0
< 0.21.
When one of the time constants of response pI dominates, eq. (18) can
be simplified to
h IP'(O) I
Emax = 0 - - - (19)
F T'l
The last factor indicates that it is not necessary to know P'(O) and T'l
separately. Only their ratio must be determined. Equations (18) and
(19) are not to be used when the control loop has a double integration.
2. Total Area. The total area is given by
(20)

hT·

A = __
t P'(O).
KpKc

10-20

CHEMICAL PROCESS CONTROL SYSTEMS

Responses to Constant Rate Disturbances

These can be found from corresponding responses to step disturbances
by' means of integration. The steady-state deviation is typical. It can
be found directly from the total area of the corresponding step response:
(21)
Esteady-state = A (step) X v,
where v is the slope of the constant rate disturbance.
7. ADJUSTMENT OF THE CONTROLLER ACTIONS

The three principal approaches of setting the controller actions are
1. Using the limit of stability of the control system.

2. Using the transient response of the process.
3. Using the frequency response of the process.
However, practical considerations influence the choice of the final settings.
They will be discussed first.
Practical Considerations

In general, it can be said that no adjustment procedure is foolproof. In
most practical applications the final settings should be obtained by trial
and error, taking into account the specific requirements of the case.
Discrepancies between Theory and Practice. There are several reasons for the discrepancy between the theoretical and the practical setting
of the controller actions.
L The pattern of disturbances has a strong influence on the choice of
satisfactory controller settings, an influence not taken into account by
most adjustment procedures. For instance, for a process with one predominant time constant, a proportional controller can give low values of
the deviation ratio at low frequencies. However, when the steady-state
gain of the process (Kp) is large, disturbances entering at the inlet of the
pro(!ess can still give large offsets (see also A Process with One Predominant Time Constant in Sect. 5). Hence a fair amount of integral action
can be very desirable.
This can be generalized for all kinds of processes: low-frequency disturbances require more integral action, although the effect of high-frequency disturbances is better reduced with ~ less integral action (see also
Ref. 13). Another example is the double effect of derivative action: the
effect of increased resonance frequency is more desirable when high-frequency disturbances are predominant, whereas the effect of increased proportional gain factor is more useful when there are many low-frequency
disturbances.
2. Nonlinear effects lead to settings different from the adjustment procedures. An extreme example is the impossibility of using derivative

SINGLE AND MULTIPLE LOOP CONTROLS

10-21

action, although the process dynamics seem suitable for its application
(see Limitation of Derivative Action in Sect. 5).
3. In many cases the process dynamics change with process conditions,
such as plant load. Hence a good setting for one set of process conditions
can be unsatisfactory for another set and even lead to instability. The
practical solution is to set the controller actions conservatively to ensure
stability under all practical circumstances.
4. In many cases the controller can do the job easily, for instance in
most flow control systems. Then a conservative setting is sufficient. Also
when a strong mutual influence exists between control systems, it can be
desirable to use conservative settings (see also Sect. 5, The Dynamic
Behavior of Some Typical Processes).
In the next subsections the three principal approaches of setting the
controller actions will be discussed.
Using the Stability Limit of the Control System

This approach is by far the most important. It is much less time consuming than the frequency or the transient response approach and is very
suitable for all normal, not too critical, control systems.
Method of Ziegler and Nichols. One of the earliest recipes was developed by Ziegler and Nichols (see Ref. 23). First the integral and the
derivative action of the controller is put out of operation. Then the proportional gain factor of the controller is increased until the control system
is on the limit of stability and an oscillation is generated.
Because most control systems contain small signal nonlinearities, such
as valve hysteresis, dead zone in the measuring device, etc., it can happen
that no oscillation shows up, although the system is already in the unstable region. Therefore it is common practice to introduce small step or
pulse variations while increasing the proportional gain factor in order to
start any possible oscillations.
At the limit of stability, the period of oscillation Pu and the proportional gain factor Kcu are noted. Now Ziegler and Nichols give the following formulas:
(22)

For P control

Kc = O. 5Kcu;

(23)

For PI control

Kc = O.45K cu , Ti = O.8P u ;

(24)

For PID control

Kc

=

O.6Kcu , Ti

=

O.5Pu ;

Td = O.125Pu'
Offereins Method. Another method, proposed by Offereins (see Ref.
25) , is particularly useful when the calibration of the controller knobs is
not accurate. The proportional action is adjusted in the same way as

10-22

CHEMICAL PROCESS CONTROL SYSTEMS

with the Ziegler and Nichols method. Then the integral action is increased (for a PI controller) until again the limit of stability is reached.
The integral action time is then increased by a factor 3, and the proportional gain factor is slightly decreased to ensure stable operation.
For a PID controller, first the proportional gain factor is increased until
the limit of stability is reached. The derivative action time is then increased from zero until the limit of stability is reached again. After this,
the derivative action time is decreased by a factor 3. Finally the integral
action time is made about equal to the derivative action time. In this case,
the proportional gain factor can generally be increased somewhat, as derivative action has a stabilizing influence.
Method of Rutherford, Aikman, and Ream. Rutherford (Ref. 2),
Aikman (Ref. 3), and Ream (Ref. 24) give a method of obtaining the
settings from the frequency response of the process. However, their
method can also be used empirically.
1. The proportional gain is adjusted in such a way that the subsidence
ratio (see Fig. 17a, €I!€2) of the response to a small set point change
equals 3.
2. The integral action time is made equal to the period of oscillation of
this response.
3. The derivative action is adjusted in such a way that the proportional
gain factor of the controller has its maximum value, subject to 1 and 2.
Methods of Pessen and Clarridge. Pessen (see Ref. 27) has given a
special adjustment recipe for obtaining good operation with automatic
start-up of the process. The trouble with automatic start-up is the tendency to overshoot the set point (see Fig. 20a), which can be very undeControlled
variable

Controlled
variable
Moment of
( "s.:'~ching"

Set point

------~-~//1
Set point
/

/

Derivative
signal

Time
(a)

FIG. 20. Automatic start-up:

Time
(b)

(a)

using conventional control, (b) using the arrangement of Fig. 21.

SINGLE AND MULTIPLE LOOP CONTROLS

10-23

sirable, especially with chemical reactions. This overshooting is caused
by the integral action which integrates the large initial error until the
output of the controller reaches its saturation limit. "Then the controlled
variable crosses the set point, this saturation does not disappear immediately and overshoot is unavoidable.
This problem has been solved (see Clarridge, Ref. 26) by arranging the
controller in such a way that the derivative action element precedes the
proportional-plus-integral element (see Fig. 21). Because of the positive

Measured _ _~
variable

FIG.

Output
signal

21. Controller arrangement for avoiding overshoot.

rate of change of the controlled variable during the start-up period, the
output signal of the derivative element crosses zero while the deviation is
still negative (see Fig. 20b).
In this way the proportional-plus-integral element can recover from its
saturation before the controlled condition crosses the set point, and overshooting can be avoided. This method of avoiding overshoot resembles
the operation of so-called optimum relay servomechanisms, which also
have a derivative action element preceding the servomotor (see Vol. I,
Chap. 25, Nonlinear Systems).
Pessen gives the following formulas for setting the actions of the controller according to Fig. 21 when overshoot is to be avoided:
(25)
The adjustment of the derivative action time is very critical. Hence its
final value should be obtained by trial and error.
Using the Transient Response of the Process

Many recipes obtain the settings of the controller from the unit step response curve of the process. To this end the latter is generally approximated by a dead time T and a time constant Tl (see Fig. 22a), or by a
dead time T and an integration S (see Fig. 22b), or by a dead time and a
reaction rate (see Fig. 7). Finally, the controller settings are calculated
from T, T 1, and/or S.

10-24

CHEMICAL PROCESS CONTROL SYSTEMS
Deviation

Time

(a)

Deviation

/

/
-----------7-----

b

/

/

Time

(b)

FIG. 22. Transient response approximated by (a) a dead time and a time constant,

and (b) a dead time and an integration.

For example, Ziegler and Nichols (Ref. 23) give the following formulas:
(26)

P action only

1
K =-'

(27)

PI action

Kc = - , Ti = 3.3T;
ST

(28)

PID action

1.2
2.0
K =-to-',
c
ST ST

ST'

c

0.9 -

Ti

=

2T,

Td

=

0.5T.

A disadvantage of these recipes is the rather crude approximation of
the process response. As has been shown in Sect. 5, derivative action gives
much improvement when the process contains two predominant time constants. Thus, in order to obtain good settings for controllers with derivative action, it is desirable to approximate the process response by at least
a dead time and two time constants.

SINGLE AND MULTIPLE LOOP CONTROLS

10-25

Moreover it is often difficult to interpret the step response of a process
accurately because the plant disturbances easily spoil the result.

Using the Frequency Response of the Process
When the frequency response of the process is known, it is possible
to apply servomechanism techniques for setting the controller actions, e.g.,
phase margin, gain margin, M contours, etc. (see Vol. 1, Chap. 19,
Methodology of Feedback Control, and Chap. 21, Stability).
Method of Rutherford, Aikman, and Ream. However, there is also
a technique which has been developed in the process control field. It is
given by Rutherford (Ref. 2), Aikman (Ref. 3), and Ream (Ref. 24) and
uses the following criteria:
1. The subsidence ratio (see Fig. 17a, £1/£2) of the oscillatory component in the transient response should equal e (Rutherford), 3 (Ream), or
4 (Coon, Refs. 20 and 21).
2. The integral action time should be made equal to the period of the
oscillatory component.
3. The derivative action should be adjusted in such a way that the proportional gain factor of the controller has its maximum value, subject to
1 and 2.
Method Derived by Ream. In order to simplify the application of
the first criterion, a method has been developed (derived by Ream in
Ref. 24), based on a modification of the Bode diagram of the frequency
response of the process (see Fig. 23). In this diagram curves are plotted
to describe the response of the process to damped sine waves having the
prescribed subsidence ratio. Ream gives the following approximate formulas for the distances between the original and the new curves:
d[arg PUw)]

(29)

In IP(jw) I -In IP(jw) I = -a

(30)

._
.
d[ln IP(jw) I]
arg PUw) - arg P(Jw) = a
,
d(ln w)

d(ln w)

+

JW = -u jw = jpeia ,
a '= 0.175 rad. (10°) for a subsidence ratio 3,
arg PUw) = polar angle of PUw).

where

The right-hand side of eq. (29) equals the slope of the phase curve
multiplied by -a; the right-hand side of eq. (30) equals t.he slope of the
gain curve times a. Because both slopes are generally negative (see Fig.
23), the response to damped sine waves has a higher gain and more phase
lag than the frequency response.

10-26

CHEMICAL PROCESS CONTROL SYSTEMS
--:lp(jw)1
----: Ip(jw)

I

0.5

0.2
0.1

--:LP(jw)
- - - - : LP(jw)

w
0.02
0.05 0.1
-90 ,----,_ _--.--_--.--_--.--.:...-:-_0-.,..5_----r_ _ 27r ~
-120
-150
-180
-210
-240
-270

FIG. 23. Bode diagram of the process modified for finding the adjustment of the controller actions.

For a proportional controller the first criterion should be satisfied (subsidence ratio equal to 3), which corresponds to choosing the proportional
gain factor in such a way that
(31)

1

+ KcP(jw)

=

O.

This is very easy to do in the modified Bode diagram (see Fig. 23). First
the frequency is determined where the modified phase lag equals 180
degrees, which is the frequency of the oscillatory component in the transient response of the control system. The modified gain is then determined
at this frequency. The reciprocal of this modified gain gives the setting of
the proportional gain factor.
For a PI controller the second criterion fixes the modified gain and
phase lag of the controller at the frequency of the oscillatory component.
For a subsidence ratio equal to 3 they are 0.99 and 9 degrees, respectively.
Adding this gain and this phase lag to the modified gain and phase lag
of the process (see Fig. 23) easily leads to the setting of the proportional
gain factor and the integral action time.
For a PID controller, the settings can be found by a trial-and-error procedure in the Bode diagram (see Coon, Refs. 20 and 21) or by a calculation in the log-gain-phase lag diagram (see Ream, Ref. 24).

SINGLE AND MULTIPLE LOOP CONTROLS

10-27

Literature on Adjustment of Controller Actions

The literature on the adjustment of controller actions is very extensive.
Therefore, only some surveys will be mentioned here.
Oppelt (Ref. 19) compares the various settings for a PI controller and a
process transfer function consisting of a dead time and a time constant.
His conclusion is that the various methods are not very much different for
this particular case. The adjustments according to Ziegler and Nichols
give a good average.
Izawa and Hayashibe (Ref. 22) also compare various methods on the
base of the obtained phase and gain margins. Their conclusion is that
the adjustment procedures for process control lead to less stable operation than those for servomechanisms.
Coon (Refs. 20 and 21) compares the two methods of Ziegler and
Nichols (Ref. 23) and the one of Ream (Ref. 24). Her conclusion is that
the last method gives the best control.
8. FEED-FORWARD CONTROL

(See Refs. 28-30)

Figure 24 shows the block diagram of a feed-forward control system.
Disturbance

FIG. 24. Block diagram of a combined feedback and feed-forward system.

A source of disturbance influences the controlled variable via the transfer
function Pl. An extra device, with transfer function C l , compensates for
the effect of the disturbance when
(32)

or

It is necessary that C l conform to eq. (32), both statically and dynamically. In practice this can be difficult when the process dynamics
change much as a result of changes in the process conditions. The compensation is then nearly always imperfect, and the controller has to take
the difference into account.
Feed-forward control can be used (see Refs. 28-30) when there is a
strong source of disturbances whose effect cannot be sufficiently reduced
by normal control, and also when the process dynamics do not vary too

10-28

CHEMICAL PROCESS CONTROL SYSTEMS

Steam
~====::i)l:::1=====::;-]

~====~I~================~
Inlet stream

t

Condensate

FIG. 25. Feed-forward control applied to the inlet stream of a chemical reactor.

greatly. An example is given in Fig. 25. An inlet stream to a chemical
reactor shows large flow variations. The latter are measured by a flow
transmitter FT and added to the output signal of the temperature controller TC via the compensating device C 1 •
9. CASCADE CONTROL

A cascade control system can be defined as a system in which the output of one controller adjusts the set point of another controller (see Fig.
26) . The characteristics are:
1. The complete system has one control valve and two closed loops.
2. Generally the gain K of the (pneumatic) set mechanism can be manually adjusted.
3. C 1 is called the primary or master controller, and C 2 the secondary
or slave controller.
In the literature (see Refs. 31-35) the name cascade control system is
also used for those systems in which the primary controller is merely a

FIG. 26. Block diagram of cascade control.

SINGLE AND MULTIPLE LOOP CONTROLS

10··29

measuring unit. However, such systems can also be considered as single
loop systems with a controlled variable equal to
(33)

where Cl is the transfer function of the primary controller, M the transfer
function of the measuring unit of the secondary controller, K the gain of
the set mechanism, Xl the primary variable, and X 2 the secondary variable. Thus here the name cascade control system is somewhat misleading.
Therefore in a later section the term ps~udo-cascade control system will
be used to describe systems in which the primary controller is merely a
measuring unit.
The transfer function M has a strong influence on the dynamic behavior
of the cascade control system and can thus be a valuable degree of freedom
in the design.
True Cascade Control Systems

According to Ziegler (Ref. 34) the objects of cascade control are:
1. To maintain a desired relationship between variables.
2. To limit accurately the secondary variable.
3. To reduce the effects of disturbances and nonlinearitieR near their
source.
4. To improve the quality of control of the primary variable.

1. Maintaining a desired relationship between variables. This object applies particularly to pseudo-cascade control systems, as will be
shown later. The other three will be discussed separately, although they
often occur in combination.
2. Limiting accurately the secondary variable. Figure 27 gives an
example. A refinery furnace is heated by fuel oil. In order to guarantee
good operation of the burners, the pressure at their fuel inlet should be
within a certain range, say 150-450 psig.
By using a cascade control system where the temperature controller TC
adjusts the set point of a secondary pressure controller PC, and by careful

Burners

'C6~=:===~=t)k:J==

"-----------'

FIG. 27. Cascade control applied to a refinery furnace.

10-30

CHEMICAL PROCESS CONTROL SYSTEMS

adjustment of the set mechanism, a full-range change of the output signal
of the temperature controller can be made to give the desired range of
set points for the pressure controller. Without a secondary controller accurate limitation is impossible, for, as in this case, disturbances in the fuel
supply system change the pressure at the burners.
3. Reducing the effects of disturbances and nonlinearities near
their source. A simple example is the use of a valve positioner to reduce

the effect of control valve hysteresis (see Fig. 28). This system is so popForce exerted on
control valve stem

I

_____ J

Hysteresis

Displacement of control valve stem

FIG. 28. Valve positioner for reducing the effect of control valve hysteresis.

ular in process control that it is generally not recognized as a type of cascade control system. The valve po~itioner loop reduces the effect of
hysteresis by a factor 1 plus its loop gain, thereby improving the operation of the (primary) control system.
Another example is the system shown in Fig. 27. The effects of disturbances in the fuel supply are effectively reduced by the fast pressure
control, and this lightens the task of the slower temperature control system.
A third example is the control of the liquid level in· a buffer vessel (see
Fig. 29). It must be remarked that the expression "liquid level control"
is somewhat misleading here. The liquid level should not be kept constant but should change over the full range of the buffer vessel in order
~

==========:;-,
Buffer
vessel

t..====~~~=====W::========:::::[>kG==== ~

FIG. 29. Cascade control applied to a buffer vessel.

SINGLE AND MULTIPLE LOOP CONTROLS

10-31

to keep the outgoing flow rate as constant as possible. Liquid level controllers are therefore often proportional ones, adjusted to a low gain. The
secondary flow controller helps to keep the outgoing flow rate constant,
irrespective of disturbances in the pressure drop over the line.
4. Improving the quality of control of the primary variable. This
aspect of cascade control will be made plausible for the simple case shown
in Fig. 30 (see also Franks and Worley, Ref. 33, and Gollin, Ref. 35).

Set
point

1
1 +jwT2
FIG. 30. Improving control quality by cascade control.

The process response pertaining to the secondary controller is a first
order one. Hence the secondary controller can be of the proportional
type adjusted to a high gain /1-.
The loop gain of the primary control system equals
(34)

J.L

- - C1 - - - - - - - - - - -

1

+ J.L

(1

+ jwT

1

)

(1 + jw _T_2_)
1+J.L

Without cascade control, the loop gain would have been
(35)
This comparison shows that the secondary control effectively reduces
the time constant T 2 , thereby improving the controllability of the system.
There is a similarity between this system and the so-called tachometric
feedback in servos, where it is the purpose to reduce the time constant of
the servomotor (see Vol. 1, Chap. 23, Feedback System Compensation).
Pseudo-cascade Control Systems

A good example of a pseudo-cascade control system is a flow ratio control system (see Fig. 31). The block diagram is a special case of Fig. 26
and is shown in Fig. 32. Because most flow-measuring devices have a

10-32

CHEMICAL PROCESS CONTROL SYSTEMS
Ql~

Ratio
adjustment

Plant

Q~

2

FIG. 31. Flow ratio control system.

quadratic characteristic, the steady-state relationship between flow and
output signal can be expressed as
(36)

and

where al and a2 are constants.
According to the block diagram the deviation,

E

is given by

(37)

Using eq. (36), the steady-state deviation becomes
(38)

With integral action the steady-state deviation is zero; thus eq. (38)
reduces to
(39)

The ratio can be adjusted by changing K.
Flow ratio control systems are often applied to blending operations in
which a product stream is made up from two or more component streams.
They are also used for burners and other combustion processes, in order
to maintain the desired ratio between fuel and air flow.
Another example of a pseudo-cascade control system is shown in Fig. 33.
Here a bulb has been installed on a distillation column tray. A liquid
mixture with the desired composition is in the bulb. By measuring the
difference of the vapour pressures of the liquid mixture in the bulb and
of the liquid mixture on the tray, a measure is obtained of the deviation
from the desired composition (see Tivy, Ref. 36).
' .A simplified block diagram is shown in Fig. 34. All transfer functions
have been linearized. PI and P 2 are process transfer functions, and M2
represents the thermal lag of the bulb. The lag of the pressure measurement has been ignored.

SINGLE AND MULTIPLE LOOP CONTROLS

FIG. 32. Block diagram of flow ratio control system.

APT

Column

Reboiler

'----~

FIG. 33. Vapor pressure control applied to a distillation column.

Pressure at
the tray r---'
1M I

f------,~I

1 1-1- - - - ,

L ___ .J

Temperature
at the tray

FIG. 34. Block diagram of vapor pressure control system of Fig. 33.

10-33

10-34

CHEMICAL PROCESS CONTROL SYSTEMS

The loop gain of the control system equals
(40)

Approximation of M 2 by a single time constant leads to
(41)

2
_P2 K_
( 1 +jWT

_

PI)

C.

In general, the temperature transfer function P 2 consists of two parallel
paths, one via the pressure with transfer function PdK2 and the other
via the composition with a slow transfer P a.
Substitution into eq. (41) gives
(42)

(P aK 2

-

PdWT )C

1 +jWT
The step response will first go the other way because the second term of
this equation initially gives the strongest effect. Thus the response has
a nonminimum phase character.
The nonminimum phase factor can be obviated by elimination of the
time constant T of the bulb, or by introduction of the same time constant
into the pressure measurement at the tray (see dotted lines in Fig. 34).
In the latter case, the loop gain of the system equals

(43)

PaK2

C,

1 +jWT
which is generally much more favorable for good control than eq. (42).
Summary. It can be said that pseudo-cascade control systems are
used to maintain a specific relationship between two or more process
variables. They can be interpreted as single loop systems, although their
behavior is often more complicated than that of conventional single loop
systems.
10. USE OF ANALYTICAL INSTRUMENTS FOR PROCESS CONTROL

In addition to the conventional instruments, analytical instruments are
finding an increasing field of application in process control (see Chap. 24,
Continuous Analyzers). In many cases they give a direct measurement of
the composition of a product stream, for instance by means of infrared
spectroscopy, mass spectroscopy, etc. In other cases they measure some
important property of the product stream, such as pH, viscosity, density,
refractive index, dielectric constant, etc.
A problem with most analytical instruments is the difficulty of obtaining a clean and representative sample from the product stream. Elaborate sampling systems are often necessary. This easily leads to long time
constants and long dead times in the transfer function between product

10-35

SINGLE AND MULTIPLE LOOP CONTROLS

stream and instrument indication. Thus control by means of an analytical
instrument is often slow and gives insufficient reduction of the effects of
plant disturbances.
Another difficulty is that analytical instruments are less reliable than
conventional instruments. This often makes it desirable to leave the control action to the human operator; the instrument is then used as a recorder or as an indicator. Even when the analytical instrument is connected to an automatic controller, we must take into account the fact that
the instrument requires servicing and that the automatic control system
will often be out of operation.
Both difficulties mentioned here can be partly overcome by using
cascade control systems. The analytical control system thus adjusts the
set point of a secondary control loop equipped with conventional instrumentation. The secondary loop is able to reduce sufficiently the effects
of many disturbances and maintains automatic control when the analytical instrument is not in operation.
11. MULTIVARIABLE CONTROL SYSTEMS

Multivariable control systems contain, as the name implies, two or more
controlled variables. However, contrary to cascade control systems, the
set points of the controllers are adjusted independently of each other.
Figure 35 gives the block diagram of a two-variable system. Xl and
X 2 are the controlled variables, YI and Y 2 are the manipulated variables,
and HI and H 2 are the effects of plant disturbances on the controlled variables Xl and X 2 , respectively. An eXalnple is the control of distillation

YI

I

I

HI

I
I
I
I
I
I

IProcess

I
I
I
I

H2

L
Y2

FIG. 35. Block diagram of a two-variable control system.

10-36

CHEMICAL PROCESS CONTROL SYSTEMS

(b)

FIG. 36. Pressure and temperature control of a distillation column: (a) practical
system, (b) impractical system.

columns, where pressure and temperature control often form a two-variable control system (see Fig. 36a).
Condition for Stability of Multivariable Control Systems

First a simple condition which is of direct practical significance will
be derived.
In process control it is desirable to have stable control systems, irrespective of the fact that other control systems are in or out of operation. For
instance, when a controller is in repair, or when it is saturated or inoperative for some other reason, the process together with the other controllers
should form a stable system.
For the system of Fig. 35 this means that the loops PllCll and P 22 C22
should both have negative feedback:
(44)

But the control loop of Cl l should also have negative feedback when
controller C22 is in operation.

10-37

SINGLE AND MULTIPLE LOOP CONTROLS

By using formula (44), this leads to the condition
(45)

or

where the vertical lines stand for determinant.
The same result is obtained when the control loop of C 22 is considered
with Cl l in operation.
Formula (45) only contains the steady-state values of the process
responses. It indicates whether the two-variable system is practically
realizable. Figure 36b gives an example of a control system that does not
satisfy condition (45). 'Vhen the pressure controller is not in operation,
more cooling water through thecondensor generally gives a lower temperature. When the pressure controller is in operation, temperature
variations are directly related to composition variations. More cooling
water then gives more top product and less bottom product, and consequently heavier compositions and higher temperatures.
It can be concluded that the sign of the temperature response is different,
depending on whether C22 is operating or not, and the control system is
impractical. It should be replaced by the scheme of Fig. 36a, whose value
of P12P21/PllP22 is the reciprocal of that of the scheme shown in Fig. 36b.
Condition (45) can be generalized for application to n-variable systems.
Figure 37 shows the block diagram of an n-variable control system. X 11
X 2 , ••• ,X n are the controlled variables; [C] is the controller matrix,
y 17 Y 2, ••• , Y n are the manipulated variables; [P] is the process matrix;
and H 17 H 2, ••• , H n are the effects of the plant disturbances on the
controlled variables.
Disturbances
HI
H2

YI

++ ~

Hn

ii-ti-

12
(/)~

~~

~~

~~
I

[e]

~
~

~

[PJ

~

t: rI

~
IYn

++

1----7---+-----:~ ~

Xl

FIG. 37. Block diagram of a n-variable control system.

X2

Xn

i-ti-t

10-38

CHEMICAL PROCESS CONTROL SYSTEMS

A necessary but inadequate condition for stability of the system is

(I [P]

(46)

[G] I)w=O

>

°

where the vertical lines stand for determinant.
This formula can be derived from the equality of the signs of the first
and of the last term of the characteristic equation of the system. It is
further based on the assumption that integral action is used in the controller
transfer functions between Xl and Y b X 2 and Y 2, ••• , X nand Y n.
When all other controller transfer functions are without integral action,
and
(47)

(P 11 G11 )w=O

> 0,

(P 22 G22 )w=O

> 0,

then formula (46) can be simplified to

(P P ~ P

(48)

U

22

••

nn

I[PJI )"~.>

0

where P 11 P 22 ••• P nn is the main diagonal of matrix [Pl.
For an n-variable system condition (48) should also be applied to the
(n - 1) -variable control systems which can be formed from it, etc.
Multivariable systems in more general cases can be handled by computer control (see Chap. 13, Computer Control, and Chap. 14, Data
Processing) .
The Dynamic Behavior of Two-Variable Control Systems

The stability of two-variable systems can be investigated in the Nyquist
diagram of the equation
(49)
where
(50)

The factors

P11 (;11
1

+ P 11 (;11

and

P22 G22
1

+ P 22 G22

are easily determined. Generally

they have the character of a low-pass filter.
Before using eq. (49), first the stability of the loops PuGu and P 22 G22
should be investigated. From the practical point of view it is desirable
that both be stable in themselves.
Symmetrical Two-Variable Control System. A simple case is the
symmetrical two-variable control system, where
(51)

An exarnple is the combination of two identical units in a plant, each
with a control system manipulating a common supply of steam, water,

SINGLE AND MULTIPLE LOOP CONTROLS

10-39

or fuel (see Fig. 38). The internal impedance of the utility supply
causes the coupling and gives rise to the two-variable system.

Steam supply

-=======~

FIG. 38. Symmetrical two-variable control system.

In this particular case the characteristic equation of the system can
best be written in the form

[1
or
(52)

+ L(1 + Va)] [1 + L(1

- VG)] = 0

C+\ra + C_\;
L)

G + L)

~ O.

Formula (52) can be represented by two Nyquist diagrams, one with
-1/(1 + VG) instead of the point -1, the other with -1/(1 - VG)
instead of the point -1. Figure 39 gives the two Nyquist diagrams for
two specific cases: G is real and positive, and G is real and negative. It
can be seen that in both cases the limit of stability is reached earlier than
for the corresponding single variable control systems.
This means that the stronger the coupling, the less sensitive the settings
to which the controllers can be adjusted.
The reduction of the effect of very low-frequency disturbances is given
by the formula
(53)

(~:t~o = [2 + L;l - GlLo'

When G = 1, the reduction is only a factor 2, which is very unsatisfactory.
Two-Variable Control System with One Fast Control Loop. Another
simple case is the two-variable system in which one control loop is much
faster than the other one. The dynamic behavior of the fast loop is hardly
influenced by the slow loop. On the other hand, the influence of the fast
loop on the slow loop can be appreciable. It is given by (see also Ref. 13)
(54)

)(l

1

HI

I+PllC ll (1-G)

-- = ---------------

where P 22 C22 is fast compared to PnC n .

10-40

CHEMICAL PROCESS CONTROL SYSTEMS

1

~w
1
-1-

I

-va

1

G = -0.64

1-l+7a
-1

1

I
I
I
I
I

-l-W •

I

FIG. 39. Nyquist diagram for symmetrical two-variable control system of Fig. 38.

Thus the dynamic behavior of control loop PuC u is modified by the
factor 1 - G, which can improve or deteriorate the control of Xl. An
example is temperature and pressure control of a distillation column,
where the pressure control loop is often much faster than the temperature
control loop.
12. SPECIAL SUBJECTS

Reswick (see Ref. 37) has published the idea of disturbance response
feedback. In theory disturbance response feedback gives improved control for high-order processes, but the practical application is difficult.
Draper and Li (see Refs. 38 and 39) give a series of methods of
optimalizing control, whereby a special control mechanism searches for
the maximum value of some process condition, for instance the process
efficiency (see also Ref. 40).
ACKNOWLEDGMENT

The author wishes to thank J. M. L. Janssen and R. P. Offereins for many
suggestions and improvements and A. Maarleveld for the execution of the
measurements.
REFERENCES
1. D. W. St. Clair, W. F. Coombs, and W. D. Owens, Frequency response analysis
for industrial automatic control systems, Trans. Am. Soc. Mech. Engrs., 74, No.7,
1133-1150 (1952).
2. C. I. Rutherford, The practical application of frequency response analysis to
automatic process control, Proc. Inst. Mech. Engrs. (London), 162, 334-354 (1950).

3. A. R. Aikman, The frequency response approach to automatic control problems,
Trans. Soc. Instr. Technol., 3,2-16 (1951).

SINGLE AND MULTIPLE LOOP CONTROLS

10-41

4. A. R. Aikman, The influence of measuring and transmission lags, Automatic
and Manual Control, A. Tustin, Editor, Academic Press, New York, 1952, pp. 205-216.
5. P. S. Buckley, The A.B.C. of frequency response, [SA Journal, 1, 164-168 (1954).
6. W. R. Ahrendt and J. F. Taplin, Automatic Feedback Control, McGraw-Hill,
New York, 1951, p. 91.
7. J. M. L. Janssen, Control system behavior expressed as a deviation ratio, Trans.
Am. Soc. M echo Engrs., 76, 1303-1312 (1954).
8. J. H. Westcott, The development of relationships concerning the frequency bandwidth and the mean square error of servo systems from properties of gain-frequency
characteristics, Automatic and Manual Control, A. Tustin, EditOl', Academic Press,
New York, 1952, pp. 45-64.
9. A. R. Aikman and C. I. Rutherford, The characteristics of air-operated controllers,
Automatic and Manual Control, A. Tustin, Editor, Academic Press, New York, 1952,
pp. 175-187.
10. J. M. L. Janssen, Analysis of pneumatic controllers, Automatic and Manual
Control, A. Tustin, Editor, Academic Press, New York, 1952, pp. 189-200.
11. J. M. L. Janssen, A practical guide to plant controllability, Control Eng., 2,
No. 11,59-63 (1955); 2, No. 12,54-59 (1955).
12. A. R. Aikman, Plant controllability, five practical examples, Control Eng., 2,
No. 11, 63-65 (1955).
13. J. Endtz, J. M. L. Janssen, and J. C. Vermeulen, Measuring dynamic responses
of plant units, Cambridge Conference 4-6 April 1956, Butterworth Scientific Publicacations, London.
14. G. H. Farrington, Fundamentals of Automatic Control, Wiley, New York, 1951,
p.226.
15. D. M. Boyd, The importance of minimizing hysteresis in a process temperature
controller, Heidelberg Control Conference, Germany, 1956, Paper 41. Published in
Regelungstechnik: Moderne Theorieen und ihre Verwendbarkeit, R. Oldenbourg
Verlag, Munich, 1957, pp. 437-440.
16. H. W. Bode, Network Analysis and Feed-back Amplifier Design, Van Nostrand,
Princeton, N. J., 1945.
17. H. M. Paynter and Y. Takahashi, A new method of evaluating dynamic response
of counterflow and parallel-flow heat-exchangers, Trans. Am. Soc. M echo Engrs., 78,
749-758 (1956).
18. H. M. Paynter, On an analogy between stochastic processes and monotone dynamic systems, Heidelberg Control Conference, Germany, 1956, Paper 37. Published
in Regelungstechnik: M oderne Theorieen und ihre Verwendbarkeit, R. Oldenbourg
Verlag, Munich, 1957, pp. 243-250.
19. W. Oppelt, J{leines H andbuch Technischer Regelvorgaenge, Verlag Chemie,
Weinheim, Germany, 1954, pp. 293-309.
20. G. A. Coon, How to find controller settings from process characteristics,
Control Eng., 3, No.5, 66-76· (1956).
21. G. A. Coon, How to set three-term controllers, Control Eng., 3, No.6, 71-76
(1956) .
22. K. Izawa and S. Hayashibe, Optimum adjustment of control system, Heidelberg
Control Conference, Germany, 1956, Paper 36. Published in Regelungstechnik: M oderne Theorieen und ihre Verwendbarkeit, R. Oldenbourg Verlag, Munich, 1957, pp.
294-300.
23. J. H. Ziegler and N. B. Nichols, Optimum settings for automatic controllers,
Trans. Am. Soc. M echo Engrs., 64, 759-768 (1942).

10-42

CHEMICAL PROCESS CONTROL SYSTEMS

24. N. Ream, The calculation of process control settings from frequency characteristics, Trans. Soc. Instr. Technol., 6, 19-28 (1954).
25. H. H. Idzerda, L. Ensing, J. M. L. Janssen, and R. P. Offereins, Design and applications of an electronic simulator for control systems, Trans. Soc. Instr. Technol.,
7, 105-122 (1955).
26. R. E. Clarridge, An improved pneumatic control system, Trans. Am. Soc. M echo
Engrs., 73, 297-305 (1951).
27. D. W. Pessen, Optimum three-mode controller settings for automatic start-up,
Trans. Am. Soc. M echo Engrs., 75, 843 (1953).
28. C. H. Barnard, The A.B.C.'s of multi-element control, Instruments, 22, 179-181
(1949).
29. J. C. Farquhar, Some aspects of cascade and multi-element control systems,
Proceedings Third World Petroleum Congress, Sect. 4, Scheveningen, Holland, 1951,
pp.494-500.
30. E. We is, Die Regelungstechnik in der Chemischen Industrie, Regelungstechnik,
2, 10-17 (1954).
31. J. N. Swarr, Applications of mechanical cascade control systems, Trans. Am.
Soc. M echo Engrs., 70, 57-63 (1948).
32. H. J. Hartz, For better processing ... try cascade control, Petrol. Processing,
10, 511-515 (1955).
33. R. C. Franks and C. W. Worley, Quantitative analysis of cascade control, Ind.
Eng. Chem., 48, 1074-1079 (1956).
34. J. G. Ziegler, Cascade control systems, Instrumentation for Process Inds., Bulletin of the Agricultural and Mechanical College of Texas, 24-29 (1956).
35. N. W. GoIlin, Cascade control systems, Control Eng., 3, No.7, 94-98 (1956).
36. V. V. St. L. Tivy, Automatic control of fractionating columns, Petrol. Refiner,
27, No. 11, 123-128 (1948). See differential vapor pressure transmitter on page 127.
37. J. B. Reswick, Disturbance response feedback, a new control concept, Trans.
Am. Soc. M echo Engrs., 78, 153-162 (1956).
38. Y. T. Li, Optimalizing systems for process control, Instruments, 25, 72-77, 190193,228,324-327,350,352 (1952).
39. C. S. Draper and Y. T. Li, Principles of Optimalizing Control Systems and an
Application to the Internal Combustion Engine, American Society of Mechanical
Engineers, New York, Sept. 1951.
40. D. P. Eckman and 1. Lefkowitz, A report on optimizing control of a chemical
process, Control Eng., 4, No.9, 197-204 (1957).
41. A. R. Aikman, Frequency response analysis of a fractionating column, ISA
Journal, 3, 412-416 (1956).
42. D. P. Eckman, Frequency response analysis of flow control system, ISA Journal,
1, 11-14 (1954).
43. A. R. Catheron and B. D. Hainsworth, Dynamics of liquid flow control, Ind.
Eng. Chem., 48, 1042-1046 (1956).
44. G. Hendriks, private communication.
45. B. E. Powel, Basic concepts of feedback control, Control Eng., 4, 101-105 (1957).
46. P. Naslin, A simple theory of feedback control systems, Process Control and
Automation, 5, 6, Pts. 1 to 12 (June 1958-June 1959).
47. R. J. Kavanagh, Multi-variable control system synthesis, Tram;. Inst. Elect.
Eng., 77, Pt. 2, 425-429 (1958).

D

CHEMICAL PROCESS CONTROL SYSTEMS

Chapter

11

Nonlinearities

c.

G. Laspe and T. M: Stout

1. Introduction

11-01

2. Nonlinearities in Measurement Instruments

11-02

3. Nonlinearities in the Process

11-06

4. Nonlinearities in Control Equipment

11-09

5. Nonlinear Control Devices

11-11

6. Classiflcation of Process Nonlinearities

11-12

7. Effects and Treatment of Nonlinearities

11-15

8. Adjustment of Controller Constants

11-16
11-25

9. Use of Local Feedback Loops

11-26

10. Compensation for Nonlinearities

11-28

References

1. INTRODUCTION

This section describes the types and sources of nonlinearities frequently
encountered in process control systems and indicates how these might be
coped with. Chapter 25, Nonlinear Systems, in Vol. 1 of this Handbook,
presents a detailed treatment of the fundamental mathematical relationships as they apply to nonlinearities in general. In the paragraphs that
follow the nonlinearities are classified in a somewhat different manner.
This general treatment will give the systems engineer an insight into the
mode of attacking any process control problem involving nonlinearities.
Sources of Nonlinearity. There are at least three sources of nonlinearity encountered in process control. These arise from the measurement instruments, from the process itself, and from the control equipment.
11-01

11-02

CHEMICAL PROCESS CONTROL SYSTEMS

Each of these individual items will be discussed further in the paragraphs
that follow.
2. NONLINEARITIES IN MEASUREMENT INSTRUMENTS

Flow Measurements. Perhaps the most popular and most frequently
used flow measurement device in the process industries is the simple
orifice meter. The orifice meter, the venturi tube, and the Pitot tube
meters compose a group of fluid-measuring instruments that for the action depend upon the differential pressure or head produced across the
primary element by the fluid that is flowing. According to Bernoulli's
equation, this pressure differential is proportional to the square of the
velocity of the fluid. In its simplest form the relationship between flow
and differential pressure is as shown in eq. (1):
Q=

(1)

cv'h

where Q = flow rate,
C = discharge coefficient,
h = differential pressure.
By rearrangement of eq. (2) the head produced is directly proportional to
the square of the quantity flowing:
(2)

where A = proportionality constant.
With a differential head meter of this type the effective gain of the meter
depends upon the absolute value of the flow. This is readily seen by
differentiating the head produced with respect to the flow, giving
(3)

dh

-

dQ

=

2AQ.

As a consequence, in flow control systems using an orifice meter as the
primary measuring element, the control system stability depends upon
the absolute flow level. In most flow transducers the differential head h is
converted into a proportional and linear signal which is supplied as the
measured variable signal to conventional controllers.
A further complication in the nonlinearity of flow measurement arises
from the noncbnstancy of the discharge coefficient C in eq. (1). As long as
the flow is turbulent, C is relatively constant. However, as the flow is de. creased, which, in turn, decreases the system's turbulence, the flow patterns become more and more streamlined. This results in a gradual increase of the discharge coefficient to a certain maximum value which is a

11-03

NONLINEARITIES

function of the geometry of the system. In most commercial applications,
however, the orifice meter is so designed as to operate well out into the
turbulent region where the discharge coefficient C may be assumed relatively constant.
Temperature Measurements. Certain temperature-measuring instruments also exhibit a considerable degree of nonlinearity in converting ..the
measured variables into the control signal. This is especially noticeable in
instruments using the vapor pressure characteristics of liquids as the
motive force in the temperature sensitive element. In process control
jargon, these elements are known as Class II filled systems. The vapor
pressure-temperature relationship for most liquids can be expressed by an
equation of the form
b
(4)
10gP=a---

T+c

where P = vapor pressure,
T = temperature,
a, b, c = constants for a particular compound.
Vapor pressure data for ethyl chloride, a common filling agent, is presented
in Table 1. These data are also shown graphically in Fig. 1. Note that
TABLE

1.

VAPOR PRESSURE OF ETHYL CHLORIDE

Vapor PreRsure,
psig

Temperature,
of

60
80

1.5

9.5
20.0

100

120
140·
160

33.0
53.0

72.0

80r-'--.--r-~-r~--.-~-.--~~~

70
.gf60
Co

~~

50

::J

~
~

40

~30

a

Co

~

20
10
80

100

120

140

160

180

Temperature, of

FlO. 1. Vapor pressure curve for ethyl chloride.

11-04

CHEMICAL PROCESS CONTROL SYSTEMS

o
FIG. 2. Section of a recorder chart for a
vapor responsive temperature-sensing element.

as the temperature increases, the
vapor pressure increases at a
much more rapid rate. The gain
of such an element, of course, increases rapidly as the temperature is raised. A section of a typical temperature recorder chart
utilizing the Class II vapor-filled
system is shown in Fig. 2.
The main advantage of this
type of element lies in its sensitivity in the control region while,
at the same time, permitting the
same instrument to be used to
bring the process on stream when
the temperatures are considerably
below the normal operating point.
The Class II vapor-filled system exhibits a nonlinear gain as a
function of the temperature level.
For relatively short temperature
ranges the vapor pressure-temperature relationship may be expressed by
(5)

log P = a - bjT.

Since the transducer output signal

is normally proportional to the
vapor pressure exerted, differentiation of eq. (5) will allow an estimate to be made of the gain of the
instrument:
dP
a'b -bIT
(6)
-=-e
.
dT
T2
The exponential term in temperature by far outweighs the inverse square
term so that the gain of the system increases as temperature is increased.
Thermocouples are a second type of primary temperature-measuring
element which is commonly used in the processing industries. The thermocouple depends for its action upon the emf developed at the junction of
two dissimilar metals when heated to an elevated temperature. A typical

NONLINEARITIES

11-05

relationship between the emf developed and the junction temperature is
(7)

where kl, k2 = constants,
T r = reference temperature,
T = junction temperature,
E = emf developed.
For temperature spans of 200°F or less, the relationship is sufficiently
linear that the quadratic term may be dropped without creating an error
any greater than normal instrument error. In wide-range measuring instruments, however, this nonlinearity must be taken into account.
Speed Measurement. The rotary speed of large machines such as
the four-cycle gas engine and turbine-driven compressor is frequently
measured by devices containing a flyball mechanism as the primary
sensing element. In one commercially available speed transducer the
centrifugal force created by the rotation of the flyball mechanism is
counterbalanced by a linear and proportional air pressure. According to
the laws of dynamics, this force is directly proportional to the square of
the rotating speed:
(8)

where F = force,
M = mass,
a = acceleration,
w = rotary speed,
r = radius to center of mass.
Differentiation of this force with respect to rotary speed gives the effective
gain of the device as a measuring element:
(9)

dF

- = 2Mrw.
dw

Note the similarity between eq. (9) and eq. (3) for an orifice meter. In
fact, both systems are identical in that the measurement gain is directly
proportional to the magnitude of the measured variable.
pH Measurement. In the electrometric method of determining hydrogen ion concentration in aqueous chemical solutions (commonly called
pH measurement) there exists a logarithmic relation between the electrode

11-06

CHEMICAL PROCESS CONTROL SYSTEMS

potential and hydrogen ion concentration.
relationship:
1
(10)
pH = log-'
CH

Equation (10) defines this

where CH = hydrogen ion concentration.
Values of emf as a function of pH are listed in Table 2 for the glass-calomel
system of electrodes.
TABLE 2.

pH-EMF RELATIONSHIP FOR THE GLASS-CALOMEL ELECTRODE
SYSTEM AT 25°C

pH

Emf, p.v

3
7

-211

10

+202

+25

3. NONLINEARITIES IN THE PROCESS

Almost without exception most processes today involve at least one or
two chemical reaction stages. Since these chemical reactions are subject to
the laws governing mass transfer, invariably the reactor itself will be
violently nonlinear when considering the relationships between the input
and output quantities.
Process G~in. Consider a simple reaction such as shown in eq. (11)
where one molecule of A is transformed into a single molecule B, for example, as in butane isomerization:
(11)
Assuming that this is a first-order reversible reaction and that isothermal
conditions prevail, the rate equation governing this reaction is
(12)

dX

-

dt

= kl (l - X) - k2 X,

where kl = forward velocity constant,
k2 = reverse velocity constant,
X = mole fraction of A converted.
Upon integration this equation results in eq. (13) which relates the degree
of conversion as a function of the contact time within the reactor:
(13)

where Xe = equilibrium value of X,
K = equilibrium constant = kdk 2 •

NONLINEARITIES

11-07

In a continuous flow reactor the contact time is inversely proportional
to feed rate to the reactor. Inspection of eq. (13), therefore, will reveal
that the effect of feed rate upon yield is a function of the conversion level.
This is a simple and frequently encountered example of nonlinearity in
process gain. Most chemical reactors are even more complicated than
this in that more reactants and products are involved. For infinite values
of reactor contact time there is a definite fixed maximum yield which can
be expected for any partiCUlar system. This maximum value is a function
mainly of the thermodynamic factors involved in the process. Thus, returning to the blHane isomerization example, the maximum yield under
normal operating conditions is in the neighborhood of 50 to 60ro.
Distillation. Separation of the product from unreacted feed materials
is frequently carried out by means of fractionation by distillation. Although it is beyond the scope of this present chapter to go into the theory
of distillation, suffice it to say that the fractionating column consists of a
series of stages wherein the liquid and vapor at each stage are in thermal
equilibrium. The separation of two components is possible by fractionation owing to differences in volatility of the two constituents. Equation
(14) presents a relationship between the concentration of the lighter
constituent in the vapor and the concentration of the lighter constituent in
the liquid:
(14)

y=

Xa

1 + (a - l)x

,

where y = mole fraction of lighter component in vapor,
x = mole fraction of lighter component in liquid,
a = relative volatility.
This equation is applicable for a single plate or tray. 'Vhen a fractionating column consists of N plates counted from the feed tray to the top of
the column, this formula is repeated N times, assuming infinite reflux.
The resulting recursion formula will then describe the top composition as a
function of the composition of the feed to the column. 'Vhen the reflux
is not infinite, then, in addition, the material balance must be considered
at each tray. For feed mixtures which contain more than two components,
the problem becomes even more complex.
pH Process. Previously the nonlinearity in the pH-measuring element
'was considered. However, an even greater nonlinearity exists in the pH
process itself. Fig~re 3 represents a typical titration curve which might
be obtained when titrating a basic aqueous solution with an acid. The
nonlinearity becomes even more apparent when it is recognized that the
abscissa or pH values are in themselves logarithmic values of the hydrogen
ion concentration. It immediately becomes apparent that the stability of

11-08

CHEMICAL PROCESS CONTROL SYSTEMS
13r---------------------------~

11
~

.3
x 9

"E

....c
2

7

"5
VI

....~
0

5

tI:

~

3

Volume acid/Volume base

FIG. 3. Typical titration curve.

the pH control system will depend entirely upon the level of the pH
value which is to be maintained. Further, the presence of salts which in
themselves may contain ions common either to the acid or to the basic
material in the system may cause a buffering effect which will effectively
change the curvature of the titration curve presented in Fig. 3.
Liquid Level. Another frequently encountered nonlinearity exists in
the measurement of liquid level in horizontal cylindrical tanks. Although
quite obvious, this effect is frequently ignored when designing liquid level
control systems. This particular type of nonlinearity is most annoying
when applying control to maintain a level in the upper or lower portion
of the horizontal vessel. In the central regions of the vessel the nonlinearity can normally be ignored. The problem is graphically shown in
Fig. 4, and the capacity of the tank is shown in Table 3 as a function of the
liquid depth.
TABLE

\l
D

----~--t

--------------

--==-=
- - -=::=.---

d

FIG. 4. Illustrating the variation
of capacitance of horizontal cylindrical vessels as a function of liquid depth.

3.

CONTENTS OF HORIZONTAL
CYLINDRICAL TANKS

Per Cent Depth

o
10
20
30

40

50
60
70

80
90
100

Per Cent Capacity

o
5.2
14.2
25.2
37.3
50.0
62.7
74.8
85.8
94.8
100.0

NONLINEARITIES

11-09

4. NONLINEARITIES IN CONTROL EQUIPMENT

Perhaps the most common piece of control equipment having nonlinear
characteristics is the familiar diaphragm-motor control valve. Many
excellent papers have been written which concern themselves with the
practical aspects of valve characteristics in process control. The control
valve or final control element is a device by which compensation for other
nonlinearities may be made by the control engineer. For example, by
proper selection of control valve characteristics it is possible to eliminate
the nonlinear characteristics introduced by the primary transducing element, such as an orifice meter or the flyball type speed control mechanism.
Valve Characteristics. There are many practical valve characteristics
in use today. However, the wide majority of these characteristics can be
classified in one of three categories: (1) linear, (2) parabolic, and (3)
exponential. Mathematically, these characteristics may be described by
eqs. (15), (16) and (17) in which the fraction of maximum flow is given
as a function of the actuating signal or valve stroke position:
(15)

Linear, w = u,

(16)

Parabolic, '" =

(17)

Exponential, w =

~ + (1 - ~) ,,2,
pu-I,

where w = fraction of maximum flow,
u = fraction of maximum stroke,
p = rangeability of valve,
= maximum flow/minimum flow.
As noted above, the rangeability of a control valve is expressed as a ratio
of the maximum to minimum controllable flow. For the parabolic characteristic value is approximately 25 to 1, whereas with the exponential
valve a rangeability of 50 to 1 is common.
The basic law relating the flow of fluids through control valves is qUIte
similar to that governing flow through an orifice. For liquids, this flow
relationship may be simply expressed as

(18)

Q =

c·lf·

C v , the valve discharge coefficient, is a function of the maximum valve
capacity, the valve characteristic, and the percentage of valve closure.
Equation (19), along with eqs. (15) through (17), will allow an estimation

11-10

CHEMICAL PROCESS CONTROL SYSTEMS

to be made of the discharge coefficient provided the maximum capacity of
the valve is known:
(19)
Equations (15) through (19) are based upon the assumption of constant
pressure drop across the control valve. In practical control systems this
is not generally the case. Since valve pressure drop represents wasted
power, good engineering practice is to keep this value at a minimum consistent with good control. As a rule of thumb, approximately one-third to
one-fourth of the total system pressure drop should be absorbed by the
control valve. Assuming a constant pressure source, because the pressure
drop in the system vades as the flow changes, a variable pressure drop is
observed across the control valve. The valve and the system may be
considered as two flow restrictions hooked in series. The equivalent discharge coefficient of the combination may be computed· with the aid of
eq. (20):
(20)

where CE = equivalent discharge coefficient,
C v = valve discharge coefficient,
CL = line (or system) discharge coefficient.
The effective characteristics of the valve are altered considerably by the
presence of flow resistance in the remainder of the system. When it is
necessary to design a control system which requires that only a small
fraction of the total available pressure drop be taken across the cbntrol
valve, the exponential characteristic is the logical choice. It can be shown
that the overall control valve effectiveness is more nearly independent
of load level in the exponential valve than in any other type.
Stiction and Unbalanced Stem Forces in Valves. Before leaving the
subject of control valves, several other idiosyncrasies are worthy of mention. These include the effects of stiction and unbalanced stem forces.
The term "stiction" applies to the Coulomb friction between the stem and
the valve-packing gland. The effect of stiction is to require a rather large
change in the activating signal in order to overcome the friction that is
present. Once the valve stem has begun to move, however, the stroke is
nearly proportional to the applied force. There are several services in
which stiction is particularly annoying. These include (1) large valves;
(2) valves with long stuffing boxes, such as those in steam service or those
in -refrigerated service; (3) valves under high pressure; and (4) valves in

NONLINEARITIES

11-11

a service where slurry or other gum-forming materials in the process
stream may find. their way into the packing gland. Stiction in any of these
in'stances can oe remedied through the proper use of a valve position controller.
The question of unbalanced stem forces arises only in those applications in which there is a large pressure drop across the valve itself. In the
diaphragm motor control valve, a force applied to the diaphragm motor
is opposed by means of a compression spring. Assuming that Hooke's law
is applicable, the position which the valve stem will take is directly proportional to the applied diaphragm pressure. However, due to the unequal areas on which the upstream and downstream pressures operate,
unbalanced forces result which tend to alter the motion imparted by the
diaphragm motor. The final valve stem position is not a direct or linear
function of the diaphragm motor pressure. A valve stem position controller can often be used to compensate for the undesirable effects of unbalanced stem forces.
5. NONLINEAR CONTROL DEVICES
On-Off Cont!ollers. A great majority of controllers currently used
in process control systems are linear devices. However, occasionally we
find the nonlinear on-off controller in use. The common home thermostat
is a good example of this type of controller. In process control systems
its use is normally limited to very simple systems in which the ratio of
system capacity to supply is rather large. A very excellent discussion of
the on-off control system is presented in Ref. 1.
In some systems, such as the speed control of reciprocating compressors,
it is desirable to place limit stops upon the maximum possible excursion of
the set point. This is essential where a master controller, such as a pressure controller, will reset the set point of the speed control loop. In still
another instance it may be desirable to limit the minimum closure position
of a valve because of safety reasons. In this case a low-limit stop would
be placed in the signal line from the controller to the valve. Both of the
foregoing examples are illustrative of linear systems which have imposed
upon them an arbitrary nonlinearity when a certain value is reached.
This is essentially equivalent to saturation of an element in the control
system.
Pneumatic Transmission Lines. Perhaps one of the more interesting
nonlinear elements in control systems are pneumatic transmission lines.
Since air is a compressible medium, the control relationships are nonlinear. Therefore it is meaningless to speak of the time constant of a
pneumatic transmission line. When dealing with small signal changes,
however, it is permissible to linearize the flow equation about the operating

CHEMICAL PROCESS CONTROL SYSTEMS

11-12

point and to determine an effective time constant at that particular pressure level. If we restrict ourselves to small perturbations and, further, if
we define the time constant as the time required for the system to reach
63% of its final value, then for a deflating system eq. (21) will hold:
(21)

e

-AT
k

=

0.63

+ 0.37r + V (0.63 + 0.37r)2
r + Vr2 - 1

- 1

,

where r = absolute pressure ratio of initial to final values of pressures,
Tk = 63% response time,
A = geometric factor.
The apparent time constant is a function of the absolute pressure ratio of
initial to final pressure, and also a function of the geometry of the system,
including diameter and length of tubing as well as terminal volume,
molecular weight, and temperature of the gas. A simpler form of this
expression is presented as eq. (22) and plotted in Fig. 5:
(22)

As the absolute pressure ratio approaches unity, the effective time constant
will approach zero. If the effective
time constant is known at any particular pressure ratio r, Fig. 5 will
allow the estimation to be made of
the effective time constant at a different p:vessure ratio.
0.3
6. CLASSIFICATION OF PROCESS
NONLINEARITIES

Process nonlinearities may be classified either in accordance with their
effect upon the static response or the
dynamic response. Under the static
response category the effects may be
further divided into continuous and
discontinuous nonlinearities.

0.1

Static, Continuous Nonlinearities. Static, continuous nonlinear12345
Pressure ratio, Pi

/p

FIG. 5. Effect of pressure ratio upon
effective time constant of deflating
pneumatic systems.

ities are those in which a smooth
continuous relationship exists between the input and output quantities of a system and in which the
derivative of this relationship with

NONLINEARITIES

11-13

respect to the input variable is continuous within the region of interest.
This particular type of nonlinearity can be characterized by a variable
system gain which is a function of the signal level.
Static, Discontinuous Nonlinearities. Static, discontinuous nonlinearities can be conveniently classified on the basis of the signal size.
Small signal discontinuities, as far as process control is concerned, are
principally (1) dead zone, (2) backlash or hysteresis, and (3) stiction.
Graphical representations of these effects are shown in Figs. 6, 7, and 8.
Output
/

/

Output

Input

FIG. 6.

Graphical representation of
dead zone.

FIG. 7. Graphical representation of hysteresis.

Total
friction
force

/

/

/

Coulomb friction

~

Stiction

7 /

T/

7f

Viscous friction
Velocity

FIG. 8. Graphical representation of stiction.

11-14

CHEMICAL PROCESS CONTROL SYSTEMS

The main static discontinuity
caused by large signal changes
is
the effect known as saturation,
High limit
such as complete opening or closing
of a control valve. Saturation is
graphically depicted in Fig. 9.
Input
Dynamic Nonlinearities. Dynamic nonlinearities depending on
Low limit
signal amplitude and level were
mentioned briefly in a prior disFIG. 9. Graphical representation of sat- cussion of pneumatic transmissiori
uration.
lines. Another good example is the
effect of flow rate upon the effective
time constant ~f temperature control system. The time constant of a
thermal-measuring element may be estimated through the use of eq. (23)
in which h represents the overall heat transfer coefficient:
Output

a

C
Tk =-,

(23)

Ah

where C = thermal capacity = mass X specific heat,
A = area across which heat transfer is effective,
h = overall heat transfer coefficient.
N ow according to eq. (24) the heat transfer coefficient for fluids flowing
outside of a tube is a function of the 0.6 power of the mass velocity. The
reason now becomes apparent from the following equation why some temperature control systems are sensitive to changes in flow rate:
(24)

G)O.6 ,

hDo
(CpJ.L)~ (D o
-=0.33 k

k

J.L

where Do = diameter of tube,
. k = ~hermal conductivity of metal,
J.L = viscosity of the fluid,
Cp = specific heat of the fluid,
G = mass velocity of the fluid.
There is still another dynamic effect which is" p'eculiar to processes
themselves. This 1s the result of degradation of process performance as a
function of usage or time owing to catalyst activity decline, heat exchanger
fouling, compressor valve wear, etc. The rates at which these changes
occur are functions of process variables. The effects therefore constitute
a kind of nonlinearity. In most cases, however, they can be regarded as

NONLINEARITIES

11-15

long term time variations in process parameters which do not affect the
short term linearity or nonlinearity of the process. These items in general
are quite unpredictable, and compensation for them is best obtained by
periodic adjustment of the control system.
7. EFFECTS AND TREATMENT OF NONLINEARITIES

Process systems are always nonlinear to some extent. For this reason
it might appear that numerous examples could be found in the published
literature to illustrate the performance characteristics of such systems,
the various analytical tools, and the techniques for circumventing or using
nonlinearity. This is not the case.
The primary explanation is economic. Process control instruments are
sold in great numbers and at relatively low prices. Neither the manufacturer nor the user can expend much time or effort in an engineering
analysis to discover the best way to fit a controller to a process. Ordinarily, therefore, standard, off-the-shelf controllers are installed, and their
adjustments are determined by trial and error, guided by experience or
possibly by more systematic procedures having some theoretical basis
(Refs. 2 and 3). If the control system cannot be made to operate properly
by these procedures and if the incentives are great enough, a more rigorous
analysis may be undertaken. Advanced analytical techniques (see Vol. 1,
Chap. 25, Nonlinear Systems) may be used, or the assistance of computers may be enlisted. A number of papers have been published describing such studies (Refs. 4 to 22).
The second explanation for the shortage of published material on process
nonlinearities is technical. The analysis of nonlinear systems is not an
easy matter. Many methods are available, but none of them is universally
applicable or quickly mastered. Few of the methods are taught in undergraduate courses, with the result that most instrument men have not
been exposed to them. Computing facilities adequate for realistic probl~ms are somewhat expensive. Only comparatively large companies have
had people or equipment capable of detailed investigation of process control problems. These deficiencies are being remedied by education, formal
and informal, and by more widespread availability of computers. Subject to the economic constraints mentioned, increasing amounts of data
can be expected on nonlinearities in process systems.
Because the variety of process nonlinearities is so great and the analytical techniques are so numerous, it is impossible to treat them all in an
encyclopedic fashion. However, a few examples may serve to show some
of the phenomena that can be expected, to illustrate some of the techniques
presented in Vol. 1, Chap. 25, Nonlinear Systems, and to suggest some cures
for undesirable effects of nonlinearities.

CHEMICAL PROCESS CONTROL SYSTEMS

11-16

8. ADJUSTMENT OF CONTROllER CONSTANTS

In a process that operates at widely different conditions from time to
time, noticeable variations in its static and dynamic characteristics may
be encountered. Since extreme changes might result in instability of the
process and its control system, preventive measures are clearly necessary.
The simplest measure that can be taken is an adjustment of the controller
constants so that some degree of control is maintained under the worst
possible conditions. This solution, by far the commonest method of
attacking nonlinearities, will be illustrated by two examples.
Variable Static Gain
Control Valve. In nearly all control systems encountered in chemical
processes a valve is manipulated at some point. The controlled variable
may actually be the flow of an important raw material. In many cases a
flow is varied in order to regulate a temperature, pressure, level, concentration, or some other significant process condition. By suitable interpretation of the diagram, Fig. 10 can therefore be applied to a great many
process situations.
Valve

Controller

Process

Reference

R

Controlled
variable

c

+

Transducer
H

FIG. 10. Typical nonlinear process involving control of a valve.

In Fig. 10 the symbols G I , G2 , and H represent the characteristics of
the controller, process, and feedback transducer, respectively. These elements are assumed here to be described by linear differential equations
or, as a kind of shorthand, by transfer functions in the Laplace transform
variable s. The symbol GD denotes the nonlinear relation between tlie
valve position X and the flow M. This relationship is sketched in Fig'. 11
for a typical valve.
For small variations about specified operating points, the valve characteristic can be linearized. For example, when x = 0.25, the curve can
be approximated by a straight line having a slope
(25)

dnil
dx x=O.25

~

11m
I1x

0.075

= 0.25 = 0.3.

NONLINEARITIES

11-17

1.0 r - - - - - - y - - - - - - - . - - - - - - - , - - - - - ,

0.75

dl

~ 0.50

e

0.25

0.50

0.25

0.75

1.0

X, relative valve position

FIG. 11. Relation between valve position and valve flow (G D in Fig. 10).

When x = 0.75, the slope is
(26)

dm
dx

I
x=O.75

~

6.m
6.x

0.375

=

0.25

=

1.5.

The 5: 1 variation in slope can have a significant effect on the performance
of the control system. An example will illustrate this point. Take
(27)

G1

=

K,
e-S

G =
2

(s

+

.

1) (lOs

+

,
1)

H=1.
The expression for G 1 implies that a simple proportional controller is
being used; G 2 describes a process having a pure time delay of 1 sec (not
in itself a nonlinearity) and two first-order transform factors with time
constants of 1 and 10 sec; H = 1 is assumed for convenience. The frequency response corresponding to G 2 H is plotted in Fig. 12.
As can be seen from Fig. 12, the phase shift is -180° at a frequency
of 0.15 cps; the magnitude ratio at this frequency is 0.08. It follows that
the controller constant K is limited by
(28)

KGD = 1/0.08 = 12.5

since, at this value for KG D , the system is on the verge of instability.
In practice, of course, a smaller value must be used to obtain a response

CHEMICAL PROCESS CONTROL SYSTEMS

11-18

-270

2.0
1.0
0.8 t 0.6 t -

~

0.4

I-

0.2

l-

'V, ,

~,

Magnitude~
ratio

~~

='g 0.08

r,\\

t-

I-

~0.06
~

]I

0.04

,-

0.02

t-

V

V
v
V
~

Phase

0.01 r-I -I 0.001

FIG. 12.

~I""~

-

0.01

l--

vi--

~~~

--l?

-210

r,~

-180

V

Q)

-g 0.1

/

~~

~

-240

IJ

IJ
["

~

11

)

V

,

,,

J

~

Q)

no

-150~

as

,

00

-120 ~

~, ,

~v

(J)

l!!

Q)
(J)

ro

-90

~

,,
,,

if

-60

,,

0.1
Frequency, cycles. per second

Frequency response corresponding to G 2 H (see Fig. 10, H
venience).

-30

10

o

=1

for con-

with a satisfactory damping and to allow for variations in Gn . The value
of K must be determined to accommodate the largest expected value of G n .
In this example, K = 3 might be satisfactory.
Closed loop frequency response curves are plotted in Fig. 13 for
Gn = 0.3 and G n = 0.5, using K = 3 as suggested above. vVhile the
system would be stable and operate fairly satisfactorily at both operating
points, the dynamic behavior changes. At x = 0.25, the system would
show a slow and nonoscillatory response; at x = 0.75, the system would
have a faster and more oscillatory response. For the specified value of K,
the system would be stable as the operating point approached x = 1 where
the slope of the valve characteristic is greatest. With a larger value of K,
however, say K = 10, the system would be stable for small values of x
and unstable at large values of x.
Variable Dynamic Characteristics
Processes Involving Storage. In systems involving storage of materials, process dynamic characteristics can be expected to vary with the
amount of material stored. A simple example is presented in Fig. 14.
One stream from a previous processing step enters the.mixing tank at a
rate of Fl gal/sec, and it contains a low and variable concentration al
of some important ingredient. The second stream is added at a controlled
rate of F 2 gal/sec and contains the same ingredient at a high and fixed
concentration a2. Because of the thorough mixing provided by an agita-

NONLINEARITIES
2

Illl

1l - GD = 0.3~
0.8
GD = 1.5 ..
0.6 I-

0.4
~

0.2

~

i..-

-

I--

r-

\

t'--I'-

II--

:Etl.O 0.06

At x = 0.25

0.04

l-

0.02

I-

0.01

I-

\

1\

I--

Q)

~ O%~

11-19

1\

1\

At x = 0.75

~

K=3

T

0.001

0.01

0.1

10

Frequency, cycles per second

FIG. 13.

Closed loop frequency response curves for Gn = 0.3 and G n = 1.5, with

K=3.

tor, the contents of the tank are assumed to reach instantaneously a uniform concentration ao. Material of concentration ao is removed from
the tank at a rate of F ° galjsec. The quantity of material in the tank
at any time is V gal.
The function of the control system is to maintain the outlet concentration at a fixed value aOd despite changes in the inlet concentration ai. The
composition analyzer measures the actual outlet concentration. The
measured concentration aO m is compared with the desired concentration
Controller

Set poin
aOd

FI,al

F2 ,

~

IJ

a2

"'~

'"

aO m

Mixing
tank

t cb
\. Volume (V)
FIG. 14.

Composition.
analyzer

Fo,ao

Process involving storage of materials having nonlinear dynamic characteristics.

11-20

CHEMICAL PROCESS CONTROL SYSTEMS

in the controller, generating an error signal which actuates the valve
governing the flow rate F 2 •
The total material balance equation for the mixing tank is

aOd

(29)

dV

-

dt

= FI

+ F2

- Fo.

The material balance equation for the ingredient of interest is

d(ao V)
- - = alF I + a2F2 - aoFo.
dt
If F2 is small and Fo is almost equal to F I , the rate of change of V given by
eq. (29) will be small. Hence, over short time intervals at least, the quantity V in eq. (30) can be regarded as a constant. With this simplification
eq. (30) can be written
(30)

(31)

In transfer function notation the process can be represented as shown
in the area bounded by the dashed lines in Fig. 15. For ease of analysis,
the composition analyzer will be characterized by a simple constant Ka;
the dynamic characteristics of the analyzer, as well as the time required
for material to travel from the tank to the analyzer, will be ignored. The
controller will be assumed to be a pure integral or "reset" device with the
transfer function Kc/s.
For variations in aI, the block diagram can be reduced to the form

r------------------------,

-------------------------~
Mixing tank

Composition
analyzer

FIG. 15. Block diagram of process of Fig. 14. The process is bounded by the dashed
lines.

NONLINEARITIES

11-21

K G
K -- Ka Foc 2

(a)

~r------;)r:I__TS_2_+_SS_+_K_-J~
(b)

FIG. 16. Simplification of the block diagram of Fig. 15, assuming that the composition
analyzer can be characterized by a simple constant Ka and the controller is a pure
integral device represented by Kcls: (a) reduction for variations in a v (b) further
reduction.

shown in Fig. 16a. A further reduction gives Fig. 16b (see Vol. 1, Chap.
20, Fundamentals of System Analysis for theorems covering transformation and reduction of block diagrams), corresponding to the overall transfer relation
8
Fl~al(8)
~a (8) - - - - - - - - - (32)
o
- T8 2 + s + K
F0
where

(33)
(34)

and

V
T =-,
Fo
K
Ka ca 2

K=

Fo

.

The variation of T and J( with V and Fo is a manifestation of the nonlinear nature of the process. By virtue of the various assumptions, the
complete system has been represented by a standard second order transfer
function with the following parameters:

-viKIT,

(35)

Undamped natural frequency

= Wo =

(36)

Damping ratio

=

r = 2VKT'

(37)

Damped natural frequency

=

Wn

1

= wo~.

11-22

CHEMICAL PROCESS CONTROL SYSTEMS

Examples of Response Curves. By application of the final value
theorem to eq. (32), it is found that there is no steady-state change in ao
for step disturbances in al; this behavior is a direct result of the use of
an integrating controller. There are transient changes in ao, however,
whose size and duration are dependent on the system parameters. To
demonstrate the variation in dynamic behavior of the system with changes
in V, three response curves will be calculated. In all three cases the following values will be assumed:

Fo = Fl = 4 gal/sec,
al = 0.05 (t = 0-),

= 0.03 (t = 0+),
= 0.08,
a2 = 1.00,
K = 0.25.
aOd

When steady-state conditions are reached in the linearized representation
of the system, the flow F 2 will be

I _ (0.08) (4)

F

(38)

2

88 -

- (0.03) (4)
1.00

= 0.20,

from eq. (30). The rate of change of V from eq. (29) is therefore

dVI
-

(39)

dt

= 4 + 0.20

- 4

88

= 0.20.
The validity of ignoring this small rate of change can be judged better
after the duration of the transients is established.
Case 1, V

= 16. For V = 16 gal:
T = \6 = 4 sec,
Wo

= YO.25/4 = 0.25 radians/sec,
1

t

=

Wn

=

2y (0.25) (4)

=

050
.,

0.25Y 1 - (0.5)2 = 0.217 radians/sec.

For a step change in al from 0.05 to 0.03, the change in ao is a damped
sinusoid with a period of 27r/0.217 = 29 sec and a damping ratio of 0.50
(one-half critical damping), shown in Fig. 17.

NONLlNEARITIES

11-23

0.02

v = 16
Fl = Fo = 4
K = 0.25
Aal = -0.02

0.01

o

~ ----,-----~~~~~~~~~-=====d-------

-0.01

-0.02

FIG. 17. Response curve, change in concentration Aa o with time, for case 1, V = 16.

Case 2, V = 100. If the same disturbance occurs when the tank contains 100 gal, we obtain:
T = l¥ = 25 sec,
Wo

= YO.25/25 = 0.10 radians/sec,

r=
Wn

1
= 020
2Y (0.25)(25) ,~ .. ' ,

= 0.10Y 1 - (0.2? = 0.098 radians/sec.

The change in ao is now a damped sinusoid with a period of 2'17/0.098 =
64 sec and a damping ratio of 0.20 (two-tenths critical damping), shown
in Fig. 18. Because of the greater dilution of the incoming flow in the
material contained in the tank, two effects are observed: the maximum
change in ao is smaller and the transient lasts longer.
Case 3, V = O. For an empty tank the-change in al is felt immed~ately
and completely by the composition analyzer, and the controller acts
promptly to return ao to its desired value. Examination of eq. (32) shows
that the process transfer function reduces to a first order form with a
single time constant:
(40)

1

1

I{

0.25

t = - = - - = 4 sec.

The response is therefore a simple exponential, shown in Fig. 19.

11-24

CHEMICAL PROCESS CONTROL SYSTEMS

0.02

v = 100
Fl = Fo = 4
K
0.25
~al
-0.02

=

0.01

=

-0.01

-0.02

FIG. 18. Response curve, change in concentration Lla o with time, for case 2, V

= 100.

The desirability of any of the response curves cannot be judged without a knowledge of the requirements of downstream processing steps receiving the flow Fo. It is clear, however, that the inventory V has a noticeable effect on the dynamic behavior of the system. Using more realistic
0.02

Fl
0.01

4

8

V=o
= Fo = 4
K = 0.25
~al = -0.02
12

.

16

20

-0.01

-0.02

FIG. 19. Response curve, change in concentration Lla o with time, for case 3, V =

o.

NONLINEARITIES

11-25

characteristics for the composition analyzer and its associated sampling
system, it is likely that the control system would be unstable for large
values of V (or T). This difficulty might be alleviated if Fl or Fo could
be varied to maintain a constant level in the tank; whether this step
could be taken would depend on the requirements of the upstream or
downstream processes. Varying F 0 would introduce further nonlinearities
which, although they would complicate analysis of process behavior, would
not necessarily be detrimental to system performance.
Although the example treated here was a mixing process, similar problems arise in heating and cooling processes. If hot and cold materials
are combined to produce a mixture at a specified temperature, the temperatures appear in a manner analogous to concentration in this example.
However, these problems can be complicated by the phenomena of condensation and vaporization, differences in specific heats, and heat losses.
Tubular heat exchangers are further complicated by the necessity for considering space as well as time variations. For a discussion of some problems of this kind, the reader should see Ref. 3. There are, of course,
many other situations in which the dynamic characteristics of the process
vary with changes in the important process variables.
9. USE OF LOCAL FEEDBACK LOOPS

The transfer function for a feedback system is
(41)

C

G

R

1

+ GH

where C is the transform of the controlled variable, R is the transform of
the reference variable, and independent G and H are the transfer functions of the forward and feedback paths, respectively. If GH is made
very large, the system transfer function becomes
(42)

C
R

1

-:::::::-.

H

Under these conditions the system behavior is independent of G. Where G
includes a nonlinearity, its importance is effectively minimized, and the
system characteristics are determined primarily by the elements in the
feedback path (represented by H). This principle is not easily applied to
complex systems in which numerous time delays limit the attainable loop
gain, but it can be used to advantage on a smaller scale by placing feedback paths around individual nonlineaflties.
An example, already mentioned, is the valve positioner. This device
is used to counteract the nonlinear frictIon forces acting on the valve stem,

11-26

CHEMICAL PROCESS CONTROL SYSTEMS

generally a combination of stiction and Coulomb friction as suggested in
Fig. 20a. Without a valve positioner the valve stem does not move until
sufficient force is developed to overcome the stiction force. With a valve
positioner, as shown in Fig. 20b, the stem position is measured and com-

Valve
charaCteQstic

Spring force

(a)

Position transducer

K
(b)

FIG. 20. Block diagrams of valve control illustrating (a) stiction and Coulomb friction and (b) valve positioner employing local feedback loop to control valve stem
position in accordance with the actuating signal.

pared with the actuating signal. The difference signal is sent to a controller (acting as the valve positioner) and amplified. Since the controller gain can be relatively high, sufficient force is easily developed to
move the valve stem in spite of the friction forces.
10. COMPENSATION FOR NONLINEARITIES

Another treatment for the harmful effects of a nonlinearity is the deliberate introduction of a second nonlinearity. In other cases nonlinearities are introduced into linear systems to (a) reduce response time or (b)

NONLINEARITIES

11-27

minimize overshoots by better utilization of power elements. In process
control, this approach is employed most frequently in connection with
the square and square root relationships arising in the regulation of flow
rates.
Three methods for compensating for the nonlinear characteristics of a
valve are shown in Fig. 21 (Ref. 23). In the first method, Fig. 21a, a
Amplifier;;,:;;;".

Actuator

Valve

c
+
b

(a)
Amplifier

Mechanical
linkage

Actuator

-1H

Valve

M~HLL=f-!
(b)

Electronic
function
generator

Amplifier

~~H

Actuator

Valve

H'-----JH LC ~
(c)

21. Methods of compensating for the nonlinear characteristics of a valve: (a)
use of a nonlinear element in a feedback loop around the valve, (b) nonlinear mechanical linkage in series with valve, and (c) nonlinear electronic function generator
in series with the valve.

FIG.

nonlinear element having a characteristic like that of the valve is placed
in a feedback path around the-valve actuator and its amplifier. Because
of the ,veIl-known property of feedback systems, that is, to have a transfer
characteristic which is approximately the reciprocal of the characteristic of
the feedback element, the feedback loop preceding the valve will have a
characteristic which roughly cancels the nonlinearity of the valve. This
approach has the disadvantage that the dynamic properties of the feedback loop vary with the signal levels in the system.
The second and third methods use a nonlinear element, in series with
the valve, which has a characteristic selected to compensate directly for
the effects of the nonlinear valve characteristic. In the system of F,ig. 21b

CHEMICAL PROCESS CONTROL SYSTEMS

11-28

the nonlinear device is a mechanical linkage, whereas the system of Fig.
21c can use an electronic function generator.
An example of the use of deliberate nonlinearity is found in a pressure
control system for a jet engine test cell (see Fig. 22 and Ref. 24). In this
system the pressure level may change over a 15: 1 range, and the nonlinear flow position characteristic of the butterfly valves causes a further
Gain adjustment
,--------,
Set

Valve
servo

Inlet

To
atmosphere

~

Test cell

Butterfly control
valve

Exhauster

FIG. 22. Deliberate use of nonlinear function generator for pressure control of jet
engine test cell.

variation in loop gain. To compensate for these variations, the pressure
set point is mechanically coupled to a potentiometer which determines
the controller gain, and a nonlinear function generator is used to furnish a
signal to the valve servo.

REFERENCES
1. 1. Flugge-Lotz, Discontinuous Automatic Control, Princeton University Press,
Princeton, N. J., 1953.
2. J. H. Ziegler and N. B. Nichols, Optimum settings for automatic controllers,
Trans. Am. Soc. M echo Engrs., 64, 759-768 (1942).
3. D. P. Campbell, Process Dynamics, Wiley, New York, 1958.
4. Proceedings of the 1957 PGAC Symposium on Nonlinear Control, I.R.E. Trans.
on Automatic Control, PGAC·5, 41-72 (1958).

NONLINEARITIES

11-29

5. C. J. Stukas, Designing a control system for a jet engine environmental test
facility, ISA Journal, 2, 184-186 (1955).
6. T. F. McGrath and G. J. Fiedler, Control of surge in centrifugal compressors,
ISA Journal, 2, 234-240 (1955).
7. R. L. Ford, Electrical analogs for heat exchangers, Proc. Inst. Elec. Engrs. (Lon~
don), 103, Pt. B, 65-82 (1956).
8. R. A. Phillips, Analysis of tandem cold reduction mill with automatic gauge
control, Trans. Am. Inst. Elec. Engrs., 73, 355-363 (1956).
9. N. Ream, R. H. Tizard, and D. S. Townend, An analog computer applied to the
study of an operating process control loop, Plant and Process Dynamic Characteristics,
Academic Press, New York, 1957.
10. T. L. Batke, R. G. E. Franks, and E. W. James, Analog computer simulation
of a chemical reactor, lSA Journal, 4, 14-18 (1957).
11. T. J. Williams and R. T. Harnett, Automatic control in continuous distillation,
Chemical Eng. Prog. 53, 220-225 (1957).
12. R. Aris and N. R. Amundson, Stability of some chemical systems under control,
Chem. Eng. Progr., 53, 227-230 (1957).
13. C. W. Worley, R. G. E. Franks, and J. F. Pink, Process control problems yield
to the analog computer, Control Eng., 4, 97 (1957).
14. L. G. Lewis, Simulation of a solvent recovery process, Instr. and Automation, 31,
644-647 (1958).
15. R. G. E. Franks, Maximizing control performance and economy with analog
simulation, lSA Journal, 5, 80-84 (1958).
16. F. A. Woods, Simulation of process control with an analog computer, Ind. Eng.
Chern., 50, 1627-1630 (1958).
17. C. W. Worley, Simulation of industrial processes with the analog computer,
Automatic Control, 10, 44-52 (1959).
18. W. B. Field, Design of a pH control system by analog simulation, ISA Journal,
6, 42-50 (1959).
19. J. E. Samson, The control of axial flow compressors ... , Proceedings Joint
Symposium on Instrumentation and Computation in Process Development and Plant
Design, Institution of Chemical Engineers, London, May 11-13, 1959, pp. 49-55.
20. E. Muller and D. C. F. Pratt, A system for the control of volume balance and
chemical composition of a process solution ... , ibid., pp. 67-72.
21. J. E. Rijnsdorp and A. Maarleveld, Use of electrical analogues in the study of
the dynamic behavior and control of distillation columns, ibid., pp. 135-143.
22. K. 1. Mumme and L. W. Zabel, Analog computer simulation of a complex level
control system, Tappi, 43(sup), 188A-192A (1960).
23. G. V. Schwent, W. K. McGregor, and D. W. Russell, Control valve requirements for gas flow systems, ISA Journal, 3, 323-329 (1956).
24. Controls harness a giant test center, Control Eng., 3, No.2, 18-22 (1956).

D

CHEMICAL PROCESS CONTROL SYSTEMS

Chapter

12

Sampled-Data Control
R. E. Kalman

12·01
12·03
12·04
12·07
12·07
12·09
12·09

1. Introduction
2. Application Considerations
3. Design Pro(edures
4. Examples
5. Special Purpose Computer
6. Future Systems
References

1. INTRODUCTION

At present, there are but a few sampled-data systems in process control.
Such systems have important advantages, however, over conventional controllers and may be expected to be used more frequently in the future.
The block diagram of a sampled-data system for the control of a single
input, single output process is shown in Fig. 1 (Ref. 1). We use terminology
of the z-transform theory discussed in Vol. 1, Chap. 26, Sampled Data Systems and Periodic Controllers. The error signal el (t) is converted by the
sampling switch into el *(t), which is a sequence of narrow pulses, spaced at
intervals of T seconds; the area of the pulse at t = leT is el (kT). The sampled signal el *(t) is converted by the sampling controller into another pulse
train e2*(t), which, after passing through a hold circuit, becomes the input
signal met) to the process. ""The sampling switches shown in Fig. 1 are used
only for mathematical convenience.
The sampling controller performs the function of converting a sequence
of numbers el (0), el (T), "', el (leT), ... into another sequence of numbers,
12·01

12-02

CHEMICAL PROCESS CONTROL SYSTEMS
~---------- K*(z) -----------~

I
I

~ D*(z) ---':>-~+1~(- - - . . - - - - G*(z) ----~)O~II

I

I

I

I

I

I

I

I
. el*(t)! ~ I

I e2(t) /
~ Digital controllerr--

.

I

I e2*(t)

C*(t)

10
I
I

FIG. 1.

Block diagram of a sampled-data system for the control of a single-input,
single-output process.

e2(O), e2(T), "', e2(kT), .... Any linear linear sampling controller is
describable by the difference equation
(1)

e2(kT) = aOel (kT)

+ aIel ((k

- l)T)

+ ... + arnel ((k

- m)T)

- ble2((k - l)T) _ ... - bne2((k - n)T)
or, equivalently, by the z-transform
ao + alz- l + ... + arnz-rn
D*(z) = - - - 1- - - - 1 + b1z- + ... + bnz-n

(2)

FIG. 2.

Schematic diagram of a sampling controller.

SAMPLED-DATA CONTROL

12-03

where z = esT. A schematic diagram of the sampling controller is shown
in Fig. 2.
It is generally assumed that the process is governed by a linear differential equation with constant coefficients, at least for small deviations about
equilibrium. Then the closed loop z-transform of the control system relating the sampled values of the output to the sampled values of the input is
given by
C*(z)
D*(z)G*(z)
(3)
K*(z) = R*(z) = 1 + D*(z)G*(z)
where G*(z) is the z-transform of the combined hold circuit and process.
2. APPLICATION CONSIDERATIONS

In process control, the principal advantages of sampled-data systems over
conventional systems appear to be the following.
Flexibility. By proper adjustment of the coefficients ao, at, "', bn in
eq. (1), the overall control system can be made to have any desired kind of
dynamic behavior subject to the limitations imposed by available power at
the control input to the process and to the assumption that the process is
linear for small deviations about equilibrium.
Physical Realizability. The sampling controller is readily realizable
by either a general purpose digital computer (which may be time-shared
to simulate many sampling controllers) or by the special purpose unit described in Sect. 5.
Tilne Scale. By proper selection of the sampling period T, the sampling
controller can be "matched" to processes having arbitrarily long time constants. (In conventional pneumatic control instrumentation an upper limit
on the time constants of the controller is imposed by the size of the equipment; in electronic control instrumentation the upper limit is due to the
cost of stabilizing operational amplifiers.) In the special type of sampling
controller described in Sect. 5, the sampling period can be set by an electric
clock.
Transportation Lags. Sampled-data systems can be used effectively
in controlling processes with large transportation lags, without sacrificing
steady-state accuracy. See Sect. 4.
Adaptability to Sampled Analysis. In many processes, measurement
of basic process variables requires chemical or physical analysis of batch
samples. This often results in time delays, which are analogous to the
transportation lags in the process. By designing a sampled-data system
to take into account the time delay involved in batch type chemical analyses, a high-performance system can be achieved in a simple way. If the
sampling is relatively slow, eq. (1), which gives the new control setting

12-04

CHEMICAL PROCESS CONTROL SYSTEMS

e2(kT) each time a batch has been analyzed, can be implemented by using
just a slide rule or a desk calculator.
Several precautions' must be observed in attempting to put a sampleddata system into operation under plant conditions.
Steady-State Accuracy. The hold circuit, relays, and other components
in the system which affect steady-state accuracy must be of good quality,
for otherwise it may be difficult to maintain required accuracy in the steady
state.
Accurate Knowledge of Process DynaInics. The dynamics of the
process to be controlled [i.e., the transfer function G*(z)] must be known
fairly accurately (1-5%) in order to obtain substantial benefits from sampled-data operation. If this is not possible, G*(z) must be computed more
accurately from input-output data of the process observed during actual
operation. Methods for accomplishing this are available (Ref. 6). Since
the dynamic characteristics of the process may change in time (scale buildup in heat exchangers, changes in ambient temperature, etc.), it may be
desirable to.repeat this step frequently. Trial and error adjustment of the
sampling controller is not recommended unless the correct values of ao, .. "
bn are known fairly accurately.
Disturbances. Measurements on the process should be performed
sufficiently fast so that the accumulated effect of process disturbances between samples docs not become too large.
3. DESIGN PROCEDURES

A variety of methods is available to determine how the coefficients of the
sampling controller should be selected. Three of these methods are illustrated here; many other methods have been discussed in the literature; see
the textbooks of Ragazzini and Franklin, Jury, and Tou (Refs. 1-3).
l\lethod of Bergen-Ragazzini (Refs. 4 and 5). Suppose we wish to
adjust the coefficients of the sampling controller in such a fashion that the
process output is related to the system input by (see Fig. 1)
C*(z)
D*(z)G*(z)
K*(z) = R*(z) = 1
D*(z)G*(z)

+

Rearranging this equation leads to
(4)

K*(z)
D*(z) = - - - - G*(z)[1 - K*(z)]

Thus if the desired response K*(z) and the process dynamics G*(z) are
known, the coefficient settings for the sampling controller may be found
directly from eqs. (4) and (2). This method has two major limitations.

SAMPLED-DATA CONTROL

12-05

1. For the z-transfol'm D*(z) to be physically realizable, it is necessary
that in the inverse z-transform of K*(z),

the terms leo = ki = ... = le q equal zero where (q - 1) T < T < qT, T being
the combined measurement and transportation lag of the process.
2. Poles of G*(z) which lie outside the unit circle in the z-plane must not
be canceled by corresponding zeros of D*(z).
'
The chief disadvantage of this method is that it controls the response of
the system only at the sampling points. It is desirable to check the behavior between sampling points to make sure that the design is satisfactory
(see Table 1).
TABLE

1.

RESPONSE OF PROCESS AT REST TO UNIT STEP INPUT

Method of
Bergen-Ragazzini

Method of
Kalman-Bertram

Time

*0
*0.5
*1.0
*1.5
*2.0
2.25
*2.5
2.75
*3.0
3.25
*3.5
3.75
*4.0
4.25
*4.5
4.75
*5.0

met)

c(t)

met)

c(t)

12.92
-7.504
7.765
-1.496
4.121
4.121
0.7142
0.7142
2.780
2.780
1.527
1.527
2.287
2.287
1.826
1.826
2.106

0
0
0
0
0
0.3161
1.000
1.298
1.000
0.8197
1.000
1.109
1.000
0.9340
1.000
1.040
1.000

8.041
0.2058
2.000
2.000
2.000
2.000
2.000
2.000
2.000
2.000
2.000
2.000
2.000
2.000
2.000
2.000
2.000

0
0
0
0
0
0.1968
0.6225
0.9272
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000

* Denotes sampling points.
Method of Kalman-Bertranl (Refs. 6 and 7). We wish to bring the
process to equilibrium as soon as possible following the application of a
prototype input signal, such as a unit step. If the input is a unit step, it

12-06

CHEMICAL PROCESS CONTROL SYSTEMS

can be shown (Ref. 3) that
(5)

D*(z) =

Q*(z)

where

Po + PIZ- 1 + ... + Pm z- m
P*(z) = - - - - - - - - Po + PI + ... + Pm

1 - P*(z)

Q*(z) =

qo

+ qlZ-1 + ... + qnz-n
Po + PI + ... + Pm

and G*(z) = P*(z) /Q*(z). Formula (5) is valid only if all poles of G*(z)
are inside the unit circle. If one pole is located at z = 1, eq. (5) still applies
but it is necessary to factor out the term 1 - Z-l from the numerator and
denominator of D*(z). An extension of this method, which is not subject
to the limitations just mentioned, is also available (Ref. 7).
The main advantage of the Kalman-Bertram method is that the steadystate error in response to the prototype input becomes identically zero at
the sampling points as well as between the sampling points after at most n
steps, where n is the number of poles of G*(z) plus q, q being defined earlier.
Method of Kalrnan-Koepcke (Ref. 8). IVIore freedom of design is
obtained by considering performance criteria of the type

2: a[el (kT)]2 + J3[el (kT)]2 + 'Y[m(kT)]2
k=O

and adjusting the parameters of the controller so as to minimize the value
of the particular performance index chosen.
This is the most general technique and many variations are possible.
The calculations generally require a digital computer, and the use of the
method is not recommended when knowledge of process dynamics is inaccurate.
Other Considerations. The choice of the sampling period depends on
the speed of response desired. Any of the procedures described above may
lead to unsatisfactory design if the sampling period is chosen too small in
relation to the time constants of the process, because then the required control signal met) may become excessively large, violating the fundamental
assumption of linearity (small deviations from equilibrium). In practice,
it is not recommended that the sampling period be chosen to be less than
about 10% of the smallest measurable time constant of the process. Also,
the smaller T is, the more accurately G*(z) must be measured in order to
achieve theoretically possible performance. Methods are also available for
designing sampled-data systems in which the basic sampling rate (batch
analysis, etc.) is slower than the desired response of the process (Ref. 9).

SAMPLED-DATA CONTROL

12-07

4. EXAMPLES

Suppose that the process to be controlled has the transfer function
e-28
H(s) = (s

+ 1)(s + 2) .

The transportation lag T = 2 may be associated solely with the process or
it may include also a lag due to the measurement of el (le'T). Let T equal 0.5.
Then the z-transform of a zero-order hold circuit and process combination is
(1 - z-l)e- 28 ]* (1 - Z-I)Z-4(1
2
1
G*(z) = [
=
- - -- + -- .
s(s + 1) (s + 2)
2
s
s+1
s+2

)*

Using Table 1, Vol. 1, Chap. 26, rows d, 0, Sampled-Data Systems and
Periodic Controllers, leads to
0.0774z-5 + 0.0470z- 6
G*(z)

= 1 _ 0.9744z- 1

+ 0.2231z-2

l\lethod 1. Suppose that K(z) = Z-5. This is the fastest possible response given the value of T and the requirement that D*(z) be physically
realizable. From eq. (4),
12.92 - 12.59z- 1 + 2.882z-2
D*(z) =
.
(1 + 0.6065z- I )(1 - Z-5)
Method 2. From eq. (5),
D*(z) -

8.041 - 7.835z- 1 + 1.794z-2
.
1 - 0.6225z-5 - 0.3775z- 6

The response of the control system for this process as designed above is
shown in Table 1. [The responses between sampling points are computed
by first finding G*(z) for ']1 = 0.25 and then using the known values of
met) and the difference equation corresponding to G*(z).] The system designed by method 1 responds somewhat faster but requires more control
signal power and energy and has more oscillatory transient behavior than
the system designed by method 2.
5. SPECIAL PURPOSE COMPUTER

A special purpose computer designed to act as a single sampling controller is shown in Fig. 3. The values of el(kT), "', el((k - m)T) and
e2((k - I)T), "', e2((k - n)T) are stored in the form of settings of shaft
positions of potentiometers. These potentiometers are positioned by a
common servomotor, a given potentiometer being selected by engaging a
clutch. As soon as the measured signal el (kT) is available, e2(kT) is com-

......
1'0.)

600
Sampling period

n

:::z::
m

Storage selection

~

n

»
r-u

;:c

o
Switching
network

Control
signal

n

m

VI
VI

n

o
Z

Measurement
signal

-I
;:c

or-

Feedback signal

VI

-<

VI

-I

...
bn

FIG. 3. A special purpose analog computer designed to act as a single sampling controller.

m
~

VI

SAMPLED-DATA CONTROL

12-09

puted by an electronic summing circuit in accordance with eq. (1). Since
a value el(kT) stored on a potentiometer becomes el[(lc - l)T] at the next
s~mpling point, the storage .potentiometers must be switched around in
cyclical order at each sampling point, new samples being stored by potentiometers which hold signals from eq. (1) that are no longer needed. The
time interval between samples can be changed by adjusting a timing clock
which triggers the sampling operations and the switching network.
6. FUTURE SYSTEMS

As mentioned, the chief problem in achieving high-performance operation
of a sampled-data system is to obtain an accurate description of process dynamics. For this reason future systems are expected to incorporate automatic means for determining and monitoring the transfer function from
operating data (Ref. 10). Moreover, future systems will be designed to
abstract maximum usable information from data provided by the primary
measuring elements.
REFERENCES
1. J. R. Ragazzini and G. F. FrlLnklin, Sampled-Data Control Systems, McGraw-Hill,
New York, 1958.
2. E. I. Jury, Sampled-Data Control Systems, Wiley, New York, 1958.
3. J. T. Tou, Digital and Sampled-Data Control Systems, McGraw-Hill, New York,
1960.
'
4. A. R. Bergen and J. R. Ragazzini, Sampled-data processing techniques for feedback
control systems, Trans. Am. Inst. Elec. Engrs., Pt. II, 73, 236-247 (1954).
5. J. E. Bertram, Factors in the design of digital controllers for sampled-data feedback
systems, Trans. Am. Inst. Elec. Engrs., Pt. II, 75, 151-159 (1956).
6. R. E. Kalman, discussion of Ref. 4, loco cit.
7. R. E. Kalman and J. E. Bertram, General synthesis procedure for computer control of single and multi-loop linear systems, Trans. Am. Inst; Elec. Engrs., Pt. II, 77,
602-609 (1958); also Proceedings of the Conference on Computers in Control, Atlantic City,
N. J., 1957.
8. R. E. Kalman and R. W. Koepcke, The role of digital computers in the dynamic
optimization of chemical reactors, Proceedings of the Western Joint Computers Conference, 1959, 107-116.
9. G. M. Krane, Compensation of an error-sampled system by a multi-rate controller,
Trans. Am. Inst. Elec. Engrs., Pt. II, 76, 151-159 (1957).
10. R. E. Kalman, Design of a self-optimizing controller, Trans. Am. Soc. Mech.
Engrs., 80, 468-478 (1958).

D

CHEMICAL PROCESS CONTROL SYSTEMS

Chapter

13

Computer Control
I. Lefkowitz

1. The Trend to Computer Control
2. Control Based on Computed Functions
3. Optimizing Conlrol
4. Analytical Methods of System Optimization
5. Direct Methods of Optimizing Control
6. Optimizing by Computer Control
7. Applications of Computer Control
Bibliography and References

13·01
13·03
13·04
13·06
13·10
13·16
13·17
13·29

1. THE TREND TO COMPUTER CONTROL

As a result of ever-increasing demands upon the means of production
for greater output, lower costs, and improved quality of products, industry has expanded in size and complexity and adopted faster and more
intricate processes operating within tighter specifications. These technological advances have been possible only through the prior development and application of more advanced systems for measurement and
control. For example, in such applications as the control of (1) critical
processes characterized by high-speed interactions, (2) complex, multivariable processes under dynamic loading conditions, or (3) nonlinear
processes under widely varying operating conditions and loads, the variables of the process must be maintained in proper dynamic relationships
to one another in order to satisfy modern control objectives of optimum
process performance and dynamic stability.
13·01

13-02

CHEMICAL PROCESS CONTROL SYSTEMS

Conventional process control is limited, for the most part, to simple
linear relationships involving a relatively small number of variables.
Thus, relationships of the following form are readily handled by summing
relays, ratio controllers, and the like:
n

q

2: Kimi,

=

i=l

where q = output signal,
mi = input signals, i = 1, 2, .. "
Ki = constant coefficients.

This equation may be further generalized to include dynamic functional
relationships generated by process controllers with integral and derivative
response modes:
n

Q(s)

=

2: Gi(s) Mi(s),
i=l

where Gi(s) = transfer function relating Q(s) to M i(S),
llf i (s), Q(s) = Laplace transforms of input and output signals respectively.
The Gi(s) may be of the general form
Gi(S)

= Ki

(1 + -~+ TDtS)
TItS '

I

where Ki = proportional gain,
TIi = integral time constant,
TDi = derivative time constant.
There are, in addition, many examples of simple nonlinear function's such
as the two-variable multiplication obtained by the remote set type ratio
control and the square root extraction used in flow metering.
Design Procedures for Complex Conventional Systems. The more
general requirements of complex functional interrelationships among
process variables are handled in conventional systems by combinations
of the following approaches: (1) design of a system so that essentially
steady-state operation under a very narrow range of operating conditions
is maintained. This is effected by means of storage tanks, stabilizin'g
chambers, independent control of input variables, blending operations,
etc.; (2) use of the operator (aided perhaps by operating graphs, computing devices, etc.) to manipulate the set points of the different variables
in order to maintain an acceptable performance of the system.
Computer Control. As the scale of operations becomes faster and
more complex, the human operator imposes an increasing limitation to
proper maintenance of the necessary interrelationships. This limitation

COMPUTER CONTROL

13-03

is eased by incorporating within the control loop modern computers capable of handling at high computation rates the complex mathematical
relationships. Computer control may be designed to improve system controllability and performance over wide ranges of operaJing conditions in
the following applications:
1. Feed-forward compensation for load and disturbance variations.
2. Feedback control of derived variables or performance indices computed from measurements of the process variables.
3. Adaptive control to compensate for large changes in system parameters.
4. Optimizing control which maximizes a specified performance criterion.
5. Model generation based on analysis of the process behavior.
2. CONTROL BASED ON COMPUTED FUNCTIONS

Data Logging. There is fairly extensive use of computing components
in modern data logging and reduction systems. These include: square
root extraction for orifice flowmeters, temperature and pressure compensation for fluid flow, calculation .of yields and efficiency factors from
measured data (see Chap. 14, Data Processing). Although most of
these applications are for measurement and recording purposes, there are
some extensions to control.
Composition Analyzers. Algebraic equation solvers are employed in
connection with multicompohent composition analyzers. The primary
example is the mass spectrometer which provides a set of output signals
bearing a linear relationship to the concentrations of the various components of the mixture. The composition is determined by solving a
matrix of n equations in the n unknown· component concentrations. Other
examples include analysis by infrared spectroscopy and chromatographic
methods.
Analog Computer Control. There have been several recent publications describing analog computer application to on-line control of a derived quantity. Tolin and Fluegel (Ref. 1) describe a computer applied
to the control of an exothermic chemical reactor. The control is based
upon computation of production rate and reactor concentration by means
of heat and material balances around the reactor. A constant production
rate is maintained by manipulating one of the inputs. Lupfer and Berger
(Ref. 2) describe a method of computer control of i~ternal reflux in
petroleum fractionation columns. The effective reflux is determined by a
simple heat balance computation based on measurements of the external
reflux flow rate and the temperature difference between the reflux stream
and the reflux plate.

CHEMICAL PROCESS CONTROL SYSTEMS

Digital Computer Control. An increasing number of digital computer
control applications are being reported in the literature (Ref. 50). In
general, the digital facility is more adaptable to the control of large scale
processing systems; the on-line control of a derived quantity is usually
a part of an overall control complex involving data logging and monitoring, multivariable control functions, system analysis, and optimization.
Specific applications and references are presented in Sect. 7, Applications of Computer Control. Extensive bibliographies of computer control
have been prepared by Grabbe (Ref. 50) and Freilich (Ref. 51).
Decoupling. The application of computer elements to effect noninteraction in multiple loop control systems has also been considered. This
involves compensation for any internal coupling between control variables.
Such coupling generally degrades system performance and may lead to
instability because it tends to propagate disturbances from one control
loop to another. The general method was introduced by Boksenbom and
Hood (Ref. 3) in application for the control of a turbojet engine where
the controlled variables, speed, turbine temperature, and tail pipe fuel
flow, interact. Ergin and Ling (Ref. 4) apply similar principles to a boiler
control system which compensates for the interaction between the header
pressure and drum level control loops.
3. OPTIMIZING CONTROL

The major contribution of computer control lies in the area of optimizing system performance. The objective is to maximize (or minimize) a
specified performance criterion for the controlled system subject to both
disturbing and constraining influences.
Criteria for Optimization. The performance criterion is presumably
specified by management. Most generally it will be an economic criterion
based on production costs or profit and expressed as a linear combination
of the costs of raw materials, energy, labor, maintenance, depreciation,
off-standard product, etc. These cost components will in turn be functions of the operating conditions. The process objectives will often be
expressed in more limited terms such as maximizing the yield or throughput rate or minimizing by-product formation.
It is assumed that the performance p can be expressed as a function of
the system variables (see Fig. 1) :
(1)

where

Ui

mj

= independent input variables (load or disturbance variables),
i = 1,2, "', I,
= dependent input variables (manipulated variables), j = 1,
2, .. ',J,

qk

= system output or state variables, k = 1, 2, .. " K.

COMPUTER CONTROL

13-05

Disturbance and
load variables
~

rnl

Manipulated
inputs

Output or
state variables

';1'2

Performance
computer

[
mJ

qK

FIG.!. Block diagram of process variables.

Since only a relative measure of the performance is required for optimizing purposes, elements of eq. (1) which are essentially constant over the
range of operating conditions may be conveniently suppressed, e.g., some
overhead and labor charges, research expenses, etc. Indeed, the equation
may often be simplified by considering the variables only in terms of their
deviations from appropriate reference values. The performance equation
may be simplified further by dropping terms which are small in magnitude compared to the dominant terms. Note. In practice, both system
equations and measured quantities are subject to some degree of uncertainty; consequently, there is little to be gained by refining the control
criterion beyond a certain point. This is discussed further in the section
on self-checking.
Constraint Equations. The variables of the system are assumed to be
interrelated by a set of equations of the form
(2)

l = 1,2, "', L.

These constraint equations may be derived analytically by applying
principles of physics, chemical kinetics, thermodynamics, and other disciplines. In particular, the equations may be based on material and
energy balances, heat and mass transfer relationships, laws of motion,
chemical and thermodynamic equilibria, etc. Of necessity, some of the
system equations will be determined empirically, based on experimental
observation and past experience. Examples might include the effect of
operating conditions on catalyst activity; the tendency of fouling a heat
transfer surface as a function of fluid temperature and composition; fractionating column plate efficiencies as functions of the vapor arid liquid
flow rates and compositions. A more extensive discussion of the development of system equations and performance criteria may be found in Refs.
5 and 6.

13-06

CHEMICAL PROCESS CONTROL SYSTEMS

4. ANALYTICAL METHODS OF SYSTEM OPTIMIZATION

The excess of variables over equations yields the number of degrees of
freedom of the system. By referring to eqs. (1) and (2) and assuming
that all the Ui are independently determined,
F =J

(3)

+K

- L,

where F = number of degrees of freedom.
The necessary conditions for the optimum are determined by first using
K of the L constraint eqs. (2) to eliminate qk from eqs. (1) and (2). Then
the partial derivatives of p with respect to any F manipUlated variables
are set equal to zero.
ap

(4)

-=0

ami

j = 1,2, "', F.

The F equations of (4) coupled with the remaining L - K constraint eqs.
(2) provide a total of J equations (F + L - K = J), which are sufficient to
determine the J unknowns, ml, m2, .. " mi'
Lagrangian Multipliers. The method of Lagrangian multipliers eliminates the need to solve eqs. (2) explicitly for the qk variables. If we let
L

(5)

cj>

=

P(Ui, mj, qk)

+L

AzgZ(Ui, mj, qk),

Z=l

where Az are the Lagrangian multipliers (arbitrary constants at this point),
the necessary conditions for the optimum are expressed compactly as
(6)

acj>

-'- = 0
ami

j = 1, 2, .. " J.

Note that the L Lagrangian multipliers may be eliminated from the final
result by solving eqs. (6) simultaneously with the L constraint eqs. (2).
Inequality Constraints. The analytical approach just given must be
modified if the optimizing control conditions call for violation of any inequality constraints imposed by the process or control elements. The
most common inequality constraints are the upper and lower limits imposed on each of the manipulated variables by the rangeabilities of the
respective control valves. Thus,

(7)
where

MLi = lower limit of mi,
M u j = upper limit of mj.

The constraint may also relate to one of the state variables of the process
in terms of some function of other variables as, for example, conditions

13-07

COMPUTER CONTROL

determining the flooding point in a distillation column.
constraint may be expressed in the form

This inequality

(8)

The optimization of a process with a single manipulated variable is illustrated in Fig. 2. The performance curve is plotted as a function of m for
three values of the load u. If m has the fixed upper limit J.lt u, then Pmax is
determined by the solution of eq. (4) for loads U 1 and U2 (note, however,
that pmax occurs at different peaks). As for load U3 , eq. (4) does not satisfy
the condition for Pmax which occurs at the limit M u. Thus, in general, inP

I/~

(P maX )2

,/

(Pmax)3
(Pmax)l

I

.,...... .,--- .......

'''-u = U,3

~,

,,

\

\

I

~------~--------~--------~------------~m

FIG. 2. Performance curves for different loads.

equality constraints require some trial and error operations superimposed
on the analytical solution for the optimum.
Dynalllic Processes. The foregoing is based on steady-state or quasistatic process operation and is applicable where the system inputs vary
slowly in relation to the dominant response time of the system. If, however, the inputs change relatively rapidly, the constraint eqs. (2) must be
expressed in the forms of differential or integral equations. The performance specified by eq. (1) then becomes a function of time and the objective
of the optimizing control may be more properly stated in terms of maximizing (or minimizing) the time averaged performance p. Thus,
(9)

p = -1
T

iT

f(Ui,

mj,

qk; t) dt,

0

where T represents the total duration of the batch process or the time between successive steady states in the continuous process.
Calculus of Variations

The calculus of variations may be applied to determine the necessary
conditions for a maximum (or minimum) of the integral of eq. (9) (see
Refs. 7,8, and 9). Here again, equality constraints may be incorporated

13-08

CHEMICAL PROCESS CONTROL SYSTEMS

by use of Lagrangian multipliers. Inequality constraints of the forms of
eq. (7) or eq. (8) impose restrictions on the analytical solution and
require trial and error procedures to determine the optimum. One method
of handling such constraints is based on the idea of parametric representation. This is used by Miele (Ref. 10) to derive an optimum trajectory
for a rocket missile subject to upper and lower bounds on the fuel flow rate.
A simple formulation of the calculus of variations problem is the determination of a function y (x) which satisfies prescribed boundary values
y (Xl) and y (X2) and yields an extremum for the integral (extremum refers
to either a maximum or a minimum) :

r

X2

(10)

I = J~ fey, v', x) dx,
Xl

dy
where y' = dx'

A necessary condition for the solution of this problem is

provided by the Euler-Lagrange equation,
(11)

af _ ~ af = 0
ay dx ay'

provided the function fey, v', x) has continuous second partial derivatives
with respect to x, y, and y' within the region of interest.
The integrand of eq. (10) may be much more general, including higher
order derivatives and multiple dependent and independent variables. The
necessary conditions for the extremum are then given by a set of equations
similar in form to eq. (11). For example, the necessary conditions for a
minimum of the integral,
(12)
are determined by the following:
(13)

af
d af
----=0
aYi
dx ay'i

i = 1,2, "', m

where Yi(Xl) and Yi(X2) are prescribed for all i.
The boundary values Yi(XI) and Yi(X2) need not all be prescribed. However, for each value not specified, a "natural boundary condition" must be
imposed. This requires that for the integrands of eqs. (10) and (12) the
condition
(14)

- af

ay' a

I

X=XI

=0
or X2

be satisfied for each value Ya(Xl) or Ya(X2) not prescribed.

COMPUTER CONTROL

13-09

The variables VI, V2, .. " Vm may be interrelated through equality constraints of the form
(15)

or as definite integrals of the form
(16)

where J j is a constant.
By defining

n

cp

(17)

=

f

+ L: Ak(X) gk
k=l

where Ak(X) = Lagrangian multipliers,
gk = functions of the form indicated by eqs. (15) and (16),
f = integrand of eq. (12),
the necessary conditions for an extremum of the integral of eq. (12) are
given by the set of equations
(18)

acp
d acp
----=0
aVi

dx ay'i

i = 1,2, "', m.

Equations (18) coupled with the constraint eqs. (15) and (16) provide
m + n equations, sufficient to solve for the m Yi(X) unknowns and the
n Ak(X) parameters.
Dynamic Programming

Dynamic programming provides an alternative procedure for system
optimization. The problem is formulated as a sequence of discrete decision processes and as such is particularly well adapted to digital computation. This method has the advantage of being applicable to a very
much broader class of problems than that treated by classical methods;
in particular, it is not restricted by questions of continuity and inequality
constraints. A major disadvantage, however, is that a solution of the
optimizing conditions often requires excessively large computing time and
storage capacity.
Dynamic programming is based on Bellman's principle of optimality,
which states that whatever the initial state and initial decision may be,
the remaining decisions must constitute an optimal policy with respect to
the state resulting from the first decision (Ref. 11). The application of
this principle is illustrated by means of the previous example: minimization of the integral of eq. (10) subject to prescribed boundary conditions,

13-10

Y (Xl)

CHEMICAL PROCESS -CONTROL SYSTEMS

= YI, Y (XN) = YN' First, the integral is replaced by a finite summa-

tion,
n=N

(19)

[N

=

L:

f(Yn, Y' n, xn) L1X,

n=l

where a constant interval L1X is assumed and where the subscript n denotes
an appropriate value of the variable within the nth interval. By separating
out the first term of eq. (19),
n=N

[N

= f(Y1, Y'!, Xl) L1X

+ L: f(Yn, Y' n, Xn)

L1X

n=2

(20)
Since Y1 is already specified, the only choice with regard to the first interval
is the value of y'l. Denoting [No and [N -1 as the desired minimum values
of the summations [N and [N -1 respectively, the principle of optimality
states that

°

(21)

[NO = min [f(Yb Y'!, Xl) L1X

+ [N _1°].

y'l

Thus, y'l is determined such that [N is a minimum, assuming that an optimal policy is provided for the remaining N - 1 intervals. With YI and y'l
specified, Y2 can be determined and the formulation of eq. (21) repeated:
[NO = min [fey!' y'l, Xl) L1X
y'i.y'2

+ f(Y2,

y'2, X2) L1X

+ [N-20].

This leads to an iterative procedure for the determination of the optimal
policy, Yb Y2, "', YN.
This approach may be generalized to handle either discrete or continuous functions, equality and ine.quality constraints, and rriultivariable systems. It has been considered for a number of process optimization applications: control of an exothermic chemical reactor, optimum catalyst
replacement program, optimum multistage cross-current extraction, and
optimum temperature gradients in a. chemical reactor (Refs. 12 and 13).
There are two general approaches to the implementation of optimizing
control, the direct approach and the model approach.
5. DIRECT METHODS OF OPTIMIZING CONTROL

General Approach. In the direct approach the system inputs are
manipulated according to the observed effects of previous input changes
on the system performance. This is illustrated by the block diagram of
Fig. 3 in which the control computer makes decisions regarding the
changes in manipulated variable- m based on measurements of the performance p.

COMPUTER CONTROL

13-11
u

p

q

Optimizing
computer

FIG. 3.

Block diagram of direct optimizing controller.

The performance is measured continuously or sampled, depending on
the specific control scheme employed. It may be measured directly, as in
the maximizing of engine power output, or determined inferentially from
measurements of the system variables, as in the minimizing of production
cost rate according to a specified cost function.
Single Manipulated Input. The basic technique is illustrated in Fig. 4
representing a system with a single manipulated input and negligible
dynamics. The decision rule for manipulation of input In is as follows.
If the previous change in In caused an increase in p, change 1r/; again in
the same direction; if the result is a decrease in p, reverse the direction
for the next change in In. Thus, referring to Fig. 4, the direction of change
of m is reversed at steps 4, 6, 10, . . . , according to the polarity of the
change of p in the previous step. At step 7 a load change is indicated
which shifts both the value and location of the optimum. Since the controller is continually hunting, it detects the shift in performance and immediately seeks the new optimum.

m

FIG. 4. Simple strategy for direct optimization.

CHEMICAL PROCESS CONTROL SYSTEMS

13-12

The Quarie controller represents a commercial application of this technique (Ref. 14). The size of the input step is made proportional to the
difference between the actual and desired output changes corresponding
to the previous step. The system may be controlled to any specified slope
of the performance curve; control to a maximum or a minimum is obtained by setting the controller to zero slope.
Method of Draper and Li. Several modifications of the basic method
were introduced by Draper and Li (Ref. 15). Their peak holding method,
for example, varies the input signal at a constant rate until the performance drops a preset amount from the peak value measured during the
current cycle. The direction of change of the input signal is then reversed
and the operation repeated as shown in Fig. 5.
m

FIG. 5. Peak holding optimalizing control.

Sinusoidal Perturbation Method. It is apparent from eq. (4) that a
necessary condition for a maximum (or minimum) performance is that
the slope of the performance curve be zero (assuming the function p(m)
to be smooth and continuous in the operating region). Thus, another approach to direct optimization is the manipulation of the process input to
seek the point at which the slope of the performance curve changes sign.
The system shown in Fig. 6 represents an application of this approach to
an aircraft engine for the purpose of minimizing the fuel consumption for
given engine speed and load (Ref. 16).
A continuous perturbation signal A sin wt is added to the process input
signal m. It is assumed that the performance curve may be approximated
reasonably well in the vicinity of the optimum by the parabolic function

13-13

COMPUTER CONTROL
A sin wt

~

Multiplier

v

~

~

u

w

Low-pass
filter

~

Integrator

Bandpass
filter

I+-

Performance
sensor

~ l:ro:~ r-r!

FIG. 6. Direct optimization by means of sinusoidal perturbation signal.

(22)
where K is a constant and lVI and P are the optimum values of the manipulated variable and performance, respectively. Referring to Fig. 6,
m = ml

+A

sin wt.

By inserting into eq. (22) and expanding,

p = P

+ K(ml

KA2

- M)2

+ -- (1
2

- cos 2wt)

+ 2KA(ml -

M) sin wt.

A bandpass filter in the feedback rejects all the components of p except
the fundamental. Thus,

u = 2KA(ml - M) sin wt.
The fundamental is then multiplied by the perturbation signal,

v = KA 2(ml - M)(1 - cos 2wt).
A low-pass filter rejects the harmonic to yield

w = KA2(ml - M).
This is integrated with respect to time to produce the main component of
the in pu t signal,
(23)

ml = M

+

(mlO - M) e- KA

2

Bt,

where mlO = initial value of ml,
B = integrator constant.
Thus, ml approaches the optimum exponentially with an effective time
constant of 1/KA 2 B.

CHEMICAL PROCESS CONTROL SYSTEMS

13-14

OptiInization without Perturbation. Direct optimization may proceed without employing a perturbation or test signal; one such method is
shown in Fig. 7 (Ref. 17). The divider in effect generates the derivative of
the performance with respect to the manipulated variable. This derivative
x

~

Divider

Performance
~
sensor

Differentiator

z

m

Integrator

~

l=~;S

,

p

FIG. 7. Direct optimization by means of divider circuit.

is integrated with respect to time to yield the process input m. The relationships are readily established by reference to Fig. 7:
x
Z=Z

but

x = T1

dp
-

dt
dm

Z

= T2 - ,
dt

where Tl and T2 are the differentiator and integrator time constants, respectively. By combining these equations,
(24)

dm

Tl dp

dt

T2 dm

Thus, the rate of change of m is proportional to the slope of the performance curve, and m is forced in the direction to reduce the slope to zero.
This method has the great advantage of simplicity and easy realizability. It has been applied effectively to a pilot plant fractionating column. Analysis of the dynamics shows that the system is stable for a
number of practical applications (Ref. 18).
Extensions to Multiple Manipulated Inputs. The various techniques
outlined above may be extended' to systems with multiple inputs. The
inputs may be manipulated sequentially; that is, ml is first varied until p
is maximized, then m2 is varied, then m3, etc., with the cycle repeated

COMPUTER CONTROL

13-15

." until the performance is maximized with respect to all the inputs. This
procedure tends to be very slow and inefficient.
Method of Steepest Descent. Various strategies have been developed
to improve the efficiency of the exploration procedure; one such strategy
is the method of steepest descent (Refs. 19 and 29). In terms of N
manipulated inputs, this is expressed as
(25)

n

(aam

dm
--k -

dt

-

v

p
n

)

I

n = 1,2, "', N,

operating point

w?ere k is a negative or positive constant depending upon whether the
performance is to be a minimum or a maximum, respectively. The
gradient apia 1nn may be determined either analytically if the function
is known or experimentally by basing calculations on the measured
changes in p resulting from the preceding manipulations of the mn variables. For manipulation in discrete steps of fixed duration T, eq. (25)
yields
p
(26)
Amn = kT ( -a-) I
.

am n

operating point

The value of k yielding the faste'st approach to the optimum depends on
both the operating point and the 'nature of the performance contour.
Design of an optimizing controller based on the method of steepest
descent is presented by Feld'baum (Ref. 20). A detailed experimental
study of a two-channel optimizer based on similar methods is :given by
Stakhovskii (Ref. 21).
The Gpcon controller represents a commercial application of the direct
method to multiple input systems (Ref. 22). The controller employs a
special strategy to determine. the next move based on the results 6fprevious moves. Applications include a catalytic process for the' dehydrogenation of ethyl benzene and a distillation unit for the binary mixture
isobutane-n-butane (Refs. 22 and 23).
Multiple Frequency Perturbations. Simultaneous manipulations of
multiple inputs may also be achieved by employing multiple frequency
perturbations. There are limitations, however, in the frequency range
that can be employed and in the resolution of the various frequency components.
Evaluation of Direct Methods of Optimization. The efficiency of
the direct method of optimizing control depends, in general, on the amount
of phase lag in the system ,and the noise level in the output signals (Ref.
24). The phase lag limits·the maximum rate or frequency of change of
the input signal and hence limits the speed with which a disturbance
ff'omthe optimum can be corrected. In particular, the transient follow-

13-16

CHEMICAL PROCESS CONTROL SYSTEMS

ing an input change must attenuate sufficiently to permit a meaningful
interpretation of the response. Where a sinusoidal perturbation signal is
used, the phase shift of the output relative to the reference sinusoid
causes the useful component of the correction signal to decrease. Indeed,
excessive phase lag causes a reversal in phase of the correction signal,
resulting in instability. System dynamics may be compensated to some
extent by use of phase-compensating networks or appropriate logic.
The controller must be able to distinguish between the indicated variations in performance caused by the manipulated inputs and those caused
by spurious signals or noise. Thus, the noise level determines the lower
limit on the hunting amplitude of the manipulated input. This introduces
a hunting loss (see Figs. 4 and 5), which is the time-averaged deviation
of the system from peak performance produced by the hunting of the input
signal about its optimum value. The hunting loss is shown to be proportional to the square of the hunting amplitude for several systems (Ref.
24) . The noise effect may be reduced by proper choice of the frequency
of hunting or perturbation. Use of dynamic filters or correlation schemes
are also effective; however, they tend to decrease response speed and increase system complexity.
6. OPTIMIZING BY COMPUTER CONTROL

System Design. The process consists of a fixed structure of elements
and interconnections supplied by a limited number of energy and material
flows. In general, only the energy and material balance relationships can
be modified by the control computer. As a result, the effectiveness of
the optimizing control is directly related to the initial plant design and
operating practice. Ideally, the system should be designed optimally
from the start; that is, the selection and design of equipment, instrumentation, and control computer should be included in the overall performance evaluation along with the determination of operating procedures
and on-line optimizing control functions. This requires a broad systems
design approach which, at the present level of know-how, can only be
applied to a very limited extent.
The underlying theories of repetitive control, continuous processoptimization, and self-checking are discussed in Sect. 7, Applications of Computer Control, in connection with specific applications.
Model Methods of Optimizing Control. Model methods provide an
alternate approach to optimizing control. The model refers to the set of
relationships and inequality constraints which describe the process behavior. The mathematical model is the most general form of expression;
it consists of equations in the form of eqs. (2), (7), and (8). The model
may, however, be alternatively expressed in terms of some appropriate

COMPUTER CONTROL

13-17

physical simulation or analog of the process or be represented graphically
as a multidimensional surface. A further discussion of models and the
analytical and experimental methods for their determination is presented
in Chap. 14 (see also Refs. 5 and 6).
The model provides the basis for determining the optimizing conditions
for the system in terms of its present state, the desired final state, and the
specified performance criterion. In general, information defining the
present state is provided through measurements of appropriate system
variables. The results of the optimizing procedure are transmitted back
to the system through actuators of the system input (manipulated) variables.
The model may form an identifiable entity in the control loop or it may
be only an implied basis for analytical derivation of the optimizing control equations. If the former, then the system optimum can be determined
by applying to the model or analog a direct method of optimization such
as described in the preceding section. The two-time scale control of
Ziebolz and Paynter (Ref. 25) and some of the experimental methods of
Box (Ref. 26) may perhaps be considered in this category.
Many of the limitations of the direct method can be eliminated by its
application to the model rather than to the system itself. Two of the
factors involved are
1. The model may be scaled to run very much faster than the system, so
that the time required for a complete exploration of the performance contours is negligible compared to the dominant time constants of the system.
Thus, problems of unfavorable dynamics, multiple inputs, and local
maxima or minima are bypassed .
. 2. The system need not be perturbed by the optimum-seeking procedure.
Consequently, losses due to system transients and hunting are minimized.
7. APPLICATIONS OF COMPUTER CONTROL

Computation of Operating Guides. The mathematical model permits rapid extrapolatior:t- of the process performance beyond its present
state and provides the means for automatic computation of the necessary
optimizing conditions. In a large percentage of existing applications,
these conditions are transmitted to the process through the human operator. Thus, the computer serves essentially as an operating guide: it
computes periodically (or on demand) the optimum set point values for
each of the controlled variables and then displays the results in appropriate form for operator action. A diagrammatic representation of a
digital computer application as an operating guide is shown in Fig. 8.
Closing the feedback loop through the operator has the obvious advantage of greatly simplifying the computer control facility. In particu-

13.;18

CHEMICAL PROCESS CONTROL SYSTEMS

r----c-------------------B---------I

I

I
I
I

I
L

Data log

I
I
I

Process

Input switching
analog-digital
converter

L

Digital clock

Tape reader

Memory

FIG. 8. Digital computer as an operating guide.

lar, the experience, judgment, and intuitive "feel" factors of the good
operator bypass for the time being the problems of system response characteristics and stability as well as the problem of confidence in the reliability of the computed results.
A number of process applications of operating guide computers are presented in the literature. In some of these applications the computer is
designed to close the loop as soon as sufficient operating data, know-how,
and confidence are established.
Operation of a distillation column to achieve maximum operating
economy with fixed-product specifications is discussed by Engel (Ref. 27).
The computer determines optimum feed-tray, heat input, and reflux-' rate
based on a mathematical model derived from mass and energy balances
and vapor equilibrium relationships. Actual installations of computercontrolled columns include:
1. Special purpose analog computer applied to optimizing tower efficiency (Humble Oil Refinery) (Ref. 28).
2. Digital differential analyzer applied to an experimental unit for the
separation of the two-component mixture of n-butane and isobutane (Sun
Oil Refinery) (Ref. 28). This unit is referred to in Sect. 5, Direct
Methods of Optimizing Control, in connection with experimental applica.
tion of the Opcon controller.
An application of an operating guide computer for optimum operation
of a catalytic cracking unit (Esso Baton Rouge Refinery) has also been
described (Refs. 28 and 29) . Here the computer is designed to provide
information for more efficient operation, faster recovery from upsets, etc.
A computer system designed to increase open-hearth efficiency and
yield·-is described (Ref. 30) . The system scans, computes, and logs fur.-

COMPUTER CONTROL

13-19

nace data and provides the operator with scheduling guides for optimum
performance.
Economic Power Distribution. The electric power utilities have
made extensive use of the optimizing computer as an operating guide
(Refs. 31, 32, and 33). Here the objective is to allocate a given power
load among a· number of generating units in such a way that the total
cost of supplying the power is minimized. The result is to be consistent, .
of course, with the specified boundary conditions regarding frequency and
voltage variations, upper and lower limits on each unit, and allowable
rates of load change. On-line computer control of a power distribution
system is described in Ref. 34.
It is readily shown that the optimum load distribution among several
generating units is obtained when the incremental cost of received power
is the same from each source. Th~s is expressed as the following control
condition,
dF n
- L =A
n = 1,2, "', N,
(27)
dP
n
n

where F n =
Pn =
Ln =
A=
N =

cost of operating the nth power source,
power generated by the nth source,
penalty factor assigned to the nth source,
incremental cost of received power,
total number of sources.

The penalty factor is given by the expression,
(28) .

ap

Ln = ( 1 - .-!:.
.
aPn

)-1

where PL = power lost in transmission.
Equations (27) and (28) are derived by the method of Lagrangian multipliers [see eqs. (5) and (6)]. The total cost F is to be minimized subject to
supplying a given amount of power P where
N

F =

L

Fn ,

n=l

To define,
(29)

N

cp = F - XP =

L
n=1

(F n - XP n)

+ XPL

13-20

CHEMICAL PROCESS CONTROL SYSTEMS

where A is the Lagrangian multiplier; the necessary conditions for a minimum are determined by differentiating with respect to P n and setting the
result equal to zero [refer to eq. (6)]:
(30)

dF n
dP n

_

A(1 _ iJP

L)

iJP n

=

0

n

= 1,2, .'., N.

Note that use is made of the assumption that Fn is a function only of
Pn and is independent of the power outputs of the other sources. Equation

(30) is equivalent to the desired result given by eqs. (27) and (28).
A graphical representation of the incremental cost approach is given in
Fig. 9 for a simple two-source system with negligible transmission losses.

FIG. 9. Equal incremental slope method.

For every given load P the source outputs PI and P 2 must adjust themselves so that their sum equals P and the slopes of the curves at the indicated outputs are equal.
This result is applicable to a wide range of systems where there are
a number of parallel producing or consuming units, e.g., economic distribution of fuel flow through a pipeline system or optimum feed allocation
to a bank of catalytic reactors (Ref. 35) .
On-Line Computing Control. The extension of the operating guide
computer to a closed loop optimizing control application is, in concept,
fairly straightforward. As mentioned previously, there are, however,
practical difficulties with respect to the complex dynamics often encountered. These difficulties are circumvented by (1) incorporating the process
dynamics into the control equations or (2) limiting the frequency and rate
of change of control signals transmitted to the process, thereby restricting the system to a quasi-static state. Current on-line computer control
applications are, for the most part, based on the second approach.

COMPUTER CONTROL.

13-21

An increasing number of on-line computer control· applications are
being reported. The first is the optimizing control of a catalytic polymerization unit (Texaco Port Arthur Refinery) with the objectives of improving operating efficienoy and reducing catalyst replacement costs (Ref.
36; references of related interest are 6 and 35). The computer determines
optimum values for reactor pressures, catalyst temperatures, recycle flow
rate, and reactor feed rates; these values are then transmitted to the set
point inputs of process controllers in conventional feedback control loops.
The system consists of ten parallel reactors, and an important aspect of
the optimization control is the distribution of feed to the reactors according to their relative catalyst activities (Ref. 35). Similar approaches to
digital computer control of chemical processes are presented in Refs. 37
and 38.
Another on-line control application of interest is the computer control
of a continuous annealing furnace (Ref. 39). Here, the computer maintains closed loop control of the various zone temperatures and other functions, including data acquisition and processing.
There are many other areas of the steel mill considered for computer
control. One of the more challenging and potentially offering, perhaps,
the most significant returns is the optimization of the blast furnace. Some
of the results of Soviet efforts in this direction are outlined in Ref. 40.
Predetermined Program Control. The conditions for controlling to
a specified system performance may be predetermined when the model
is reasonably complete and exact. Often these conditions can be stated
explicitly; that is, the manipulated inputs may be specified in the following forms: (1) as algebraic functions of the measured system variables,
(2) as functions of time or some other independent parameter, or (3) as a
library of discrete operating procedures or practices.
It is apparent that, once computed, the optimizing conditions can be
stored on punched tape, magnetic drum or even, for a simple two-dimensional model, on a mechanical cam. The system variables are then
manipulated according to the playback of the appropriate stored program.
There are several recently announced computer control installations
for electric power generating stations which are based to a large extent
on predetermined program control. These include installations at the
Southern Californi~ ~dison Company, Huntington Beach Station, and the
Louisiana Power and Light Company, Little Gypsy Station. The stored
programs direct station start-up and shutdown operations under various
normal and emergency conditions. The main objective is to assure correct operating procedures so as to prevent costly accidents. The computer
provides, in addition, continuous logging and control of the system variables.

13-22

CHEMICAL PROCESS CONTROL SYSTEMS

Automatic control of start-up and shutdown operations,· sequencing of
cyclic operations, etc., are also important in the process control field.
The development of predetermined optimizing programs for such operationsmay prove fruitful in many computer control applications.
Repetitive Computer Control. The predetermined control scheme is
essentially open loop with respect to the desired system performance; that
is, there is no feedback of information to verify either that the process
performs as specified or that the model accurately describes the system
behavior. Accordingly, if there are any factors tending to cause the
system to deviate from the model, such as disturbances, the system performance may be expected to deviate from the computed optimum.
The predetermined optimization concept is modified by repetitive
feedback of information describing the state of the system. Thus, as
shown in Fig. 10, the qk variables are periodically sampled by the optimiz-

Optimizing
computer

Performance
computer

FIG. 10. Repetitive optimizing control scheme.

ing .computer, providing the basis for repetitive computation of the
optimizing conditions. In this way, each computation is based on the
most recent information describing the state of the process. As a result,
deviations of the system from the postulated model do not cause cumulative errors. The repetitive computer action tends to force the system to
the desired performance, despite significant inadequacies of the model.
Tl~e repetitive control concept has been applied to the optimizing control of a pilot plant scale batch hydrogenation reactor (Refs. 41, 42, and
43) . A brief description of this process is now presented.
(;
The reaction mixture is made up of three chemical components identified as X, Y, and Z. Hydrogen unde~ pressure and in the presence of a
catalyst reacts with X and Y according to the following reaction scheme,

COMPUTER CONTROL.

13 .. 23

where kl and k2 represent, kine'ti~ reaction coefficients. A reasonable approximation to the kinetic behavior of this. process is given by the following
equations:
dx

(31a)

-klX

dt
dy

- =

(31b)

dt

(31,c)

x

klx - k 2 y

+y+z =

1,

where x, y, and z represent molar concentrations of components X, Y, and
Z, respectively.
The kinetic coefficients ar~·functions of the operating conditions-pres':'
sure, temperature, catalyst, '~gitation, etc. Assuming that only pressu~e is
to be manipulated and that all other influencing factors are relatively constant, the coefficients may be expressed as
(32a)

kl = AIPNl

(32b)

k2 = A 2p N2,

where AI, A 2, N I , and N2 are assumed constant and p equals the process
pressure.
Based on a mathematical model consisting o!eqs. (31) and. (32), the
necessary conditions for optimum:process performance may be derived. In
the particular process under study, control to a specified produ'ct composition consistent with minimum processing time is established as the performance criterion.
It is convenient to transform these equations to new variables, u, v, and k
defined as follows:
y
U=(33a)
x

v

(33b)

(33c)

=

Xo

logex

_pN 2 -N 1•
. k = -k2 = A2
kl
Al

Making the substitutions in eqs. (31a) and (31b), a single equation defining
the processing path independent of the time variable is obtained:
du

(34)

-

dv

== (1 - k)u

+ 1.

13-24

CHEMICAL PROCESS CONTROL SYSTEMS

Since the kinetic coefficient ratio k may be varied during the course of
the reaction by manipulating the pressure [eq. (33c)], there are an infinite
number of operating paths which can satisfy the boundary conditions,
Xo, Yo, Zo representing the initial composition and XI, Yj, ZI representing the
desired final composition. (In terms of the u, v coordinates, these boundary
conditions are expressed as Uo, 0 and UI, Vj, respectively.) This degree of
freedom permits the introduqtion of an optimizing condition. Assuming
that the processing time is the predominant factor in the cost equation, the
optimizing problem reduces to the determination of a control path which
will minimize the time to go from the raw material state to the desired
product state.
An expression for the processing time il is derived from eqs. (31), (32),
and (33):
(35)

where

The necessary condition for minimizing this integral is derived by applying the Euler-Lagrang~ conditions [eq. (18)]. The following optimizing
~quation is obtained:, ..
(36)

dk

1k

dv

Bu

The optimizing computer is programmed to solve eqs. (34) and (36)
simultaneously for the given boundary conditions Uo, 0 and u" VI'
If eqs. (31) and (32) described the process behavior exactly, one computation based on eqs. (34) and (36) and the specified boundary conditions would suffice to define the optimum control path p (t). Thus, the
p (t) schedule could be recorded on tape or other storage medium and
played back through app:r:opriate transducers and pressure controller to
manipulate the process pressure according to the schedule. In the example
under consideration, however, the model only approximates the process
kinetics because such faCtors as variations in catalyst activity, other
components in the reaction mixture, higher order terms in the kinetic
equations, etc., are neglected. Open loop control of the process would
lead, therefore, to very significant deviati6ns from the desired end point.

COMPUTER CONTROL

13-25

\Vhen the repetitive control concept is used, eqs. (34) and (36) are
solved for the control path leading from the current state of the process
(based on the most recent composition measurement of the reaction mixture) to the specified final composition. Thus, each time a new composition measurement is made available to the computer, a new control path
is computed. This technique has been shown to be very effective in
forcing the process to the prescribed performance.
Optimizing Control of Continuous Processes with Significant Dynamics. As noted previously, the optimizing control of a continuous

process may be treated statically; that is, the control conditions are determined on the basis of the process going from one steady-state configuration to another. In general, the process performance during the
transition period is not considered, except perhaps to make sure that the
transient response of the manipulated variables are reasonably stable.
There are two factors limiting the static approach for systems whose
dynamics are significant in relation to the frequency of disturbances or
input changes:
1. Off-optimum control during the transient period may significantly
degrade overall performance.
2. Manipulation of the process inputs in seeking the optimum may in
fact continually upset the process equilibrium.

The process may be considered in terms of a succession of steady states
if the inputs and disturbance variables are normally relatively constant
except for changes occurring at discrete intervals (Ref. 44). The transition from one steady-state level to another may then be treated as a batch
operation with maximizing the performance during the transient phase,
the objective. Thus, the calculus of variations (or other optimizing technique) is applied to a performance function of the form of eq. (9) to define a control path leading the process from its present state to a new
steady-state optimum. The new steady state is determined by conventional static optimization procedures. One approach to this problem is
presented by Sandelien (Ref. 44).
Note that, except for very special cases, determination of the optimum
path requires a priori knowledge of the nature of the time variations of
the (independent) inputs. This is feasible in certain applications; for
example, a surge chamber can be employed to convert arbitrary flow
variations into a sequence of discrete step changes in flow. In general,
however, the inputs must be approximated by arbitrarily assumed time
functions (corrected perhaps by a repetitive control scheme). Alternatively, the optimum path may be based on an appropriate mean input
function arrived at statistically.

13-26

CHEMICAL' PROCESS CONTROL SYSTEMS

A generalized'chemical processing model which embodies the basic
limitations pointed out above has been formulated by Williams (ReL45).
The problem, considered representative of the process industry, involves
optimization of a continuous reactor that has unfavorable dynamics and
is subj ect to large input variations .
. Model Adaptation (Self-Checking). . In practical applications of
the model method of optimization, the postulated model will generally
deviate significantly from the actual system behavior. There are 'several
reasons for this:

1. Not enough is know'ri about 'most industrial processes to derive a
complete and accurate analytical representation. Indeed, plant design
and operation are generally based on very approximate and empirical rela tionshi ps.
2. The complexity of most systems precludes comparable detail in the
formulation of the mathematical model because the resulting computer
capacity would be prohibitive.
3.· Many. variables affecting ~ystem behavior cannot be satisfactorily
measured with existing instrumentation (e.g., catalyst activity); hence,
they cannot be employed directly in the computer control function.
4; The state of the system can generally be specified only within statisticaLlimits because of nonhomogeneity, random fluctuations of measured
quantities, etc.
'. The inadequacies of the model are compensated, in part, by the repetitive control technique described earlier. However, the effectiveness of
such compensation depends on the nature and,degree of the approximations in the model and is limited by the repetitive period, measurement
lags, dead time, and bounds on the manipulated variables.
More effective compensation for the approximations in the mathematical. model is possible through a self-checking or model adaptation technique (Refs. 46 and 47). This technique involves a periodic adjustment
of the parameters of the model in order to force a "best" fit of the model
to the observed system behavior in the vicinity of the operating point. In
essence, the parameters are adjusted to minimize the deviations between
the actual processing path, defined by appropriate system variables, and
the path predicted by the model for the same operating conditions. The
resulting parameter corrections are applied to the proper terms of the
optimizing control equations.
The self-checking operation may be considered an application of optimizing control to the model, where the performance criterion is defined
as some measure of the effectiveness of the model in describing the system

COMPUTER CONTROL

13-27

behavior. Thus, any of the available optimizing techniques may be applied to the problem.
The self-checking concept is illustrated by the block diagram or' Fig.
11. The deviations of the system variables from their respective model
variables generate error· signals (as functions of time) from which the
performance criterion is determined. An optimizing computer manipu-

Model
behavior

Parameter
corrections

FIG. 11. Self~che~king control scheme.

lates the parameter values to minimize this criterion. Storage elements
are inserted for synchronizing in time the system and model time functions. Finally, the corrective action is sampled to provide an intermittent self-checking action compromised between the rate at which· the
parameter values are changing and the limitations imposed by stability
considerations and the rate of information flow to the self-checking computer.
The formulation of the model depends on both the complexity of the
system and on how much is known of the system equations. Several possibilities may be considered:
1. The system equations are known reasonably well, with the model
based directly on these equations. Self-checking may be applied to correct for slow drifts of some of the parameter valu~s.
2. The model represents only the dominant characteristics of the system equations, because either knowledge of the system is limited or ·the
equations have been intentionally simplified. The parameter values are
then functions of the state of the system and change with changes in
operating conditions. The self-checking determines average values of
the parameters for the region about the operating point.

'13-28

CHEMICAL PROCESS CONTROL SYSTEMS

3. The model does Jlgt include the influence of one or more system
variables (because their effects are unknown or because they are not
satisfactorily measured). Here again, the self-checking determines
average parameter values for the region of the operating point.
4. The theoretical background for the system analysis is totally lacking, and a generalized expression, such as a power series, is used for the
model. The self-checking determines effective values of the parameters
in the same manner as for models 2' and 3.
The self-checking technique may be intentionally applied for the purpose oi'simplifyingthe equations or reducing the number of pertinent
variable:s. In general, the optimizing computer requirements are reduced
at the expense of the self-checking facility. Thus, as the equations become more generalized or approximate, either the number of parameters
to be adjusted is increased or the parameters must be adjusted more frequently as operating conditions change. It is expected, however, that
the overall computer demand can be minimized by a judicious compromise
between the two systems; in particular, the process equations may advantageously describe only the dominant first order effects, which relate
only the rapidly changing variables.
Computer-Controlled Pilot Plant. A promising extension of the
model adaptation concept is the application of a computer to control a
pilot plant for the purpose of automatically determining a satisfactory
process model (Ref. 48). The computer manipulates the pilot plant
through a programmed series of experiments. Measurements of the
system response are fed back into the computer for subsequent' analysis
'and correlation.
Adaptive Control. The adaptive concept has attracted a great deal of
attention in the servo field, particularly for aircraft and missile control
(Ref. 49). The major emphasis in this work has been the automatic
modification of controller parameters to achieve a desired transient response of the system under widely varying operating conditions. Thus,
the gain and perhaps the time constants of the controller function are
periodically adjusted to satisfy a performance criterion based on some
appropriate time function of the error signal. Effective implementation
of this approach in the general complex system usually requires computer
control.
The adaptive control approach may be applied to process systems in
which the nonlinearities result in very different response characteristics
under varying operating conditions. In particular, the adaptive control
approach may be coupled with the optimizing control function to assure
that the manipulated variables respond properly over the operating range.

COMPUTER CONTROL

13-29

BIBLIOGRAPHY AND REFERENCES
1. E. D. Tolin and D. A. Fluegel, An analog computer for on-line control of a
chemical reactor, ISA Journal, 6, No. 10,32-38 (1959).
2. D. E. Lupfer and D. E. Berger, Computer control of internal. reflux in fractiona..
tion columns, ISA Journal, 6, No.6, 34-39 (1959).
3. H. S. Tsien, Engineering Cybernetics, McGraw-Hill, New York, 1954, Chap. 5.
(Refer also to A. S. Boksenbom and R. Hood, NACA Technical Report 980, Lewis
Flight Propulsion Laboratory, Cleveland, Ohio, 1950.)
4. E. 1. Ergin and C. Ling, Development of a non-interacting controller for boilers,
Proceedings of the First Congress of the International Federation of Automdtic
Control, Moscow, 1960, Butterworth, London.
5. T. M. Stout, Mathematical relationships for computer control systems, paper
presented at the American Society of Mechanical Engineers semi-annual meeting in
Detroit, June 15-19, 1958.
6. E. W. James and A. S. Boksenbom, How to establish the control problem for an
on-line computer, Control Eng., 4, No.9, 148-159 (1957).
7. F. B. Hildebrand, Methods of Applied Mathematics, Prentice-Hall, New York,
1952, Chap. 2.
8. R. Courant and D. Hilbert, Methods of kI athematical Physics, Interscience
Publishers, New York, 1953, Chap. 4.
9. R. Weinstock, Calculus of Variations, McGraw-Hill, New York, 1952.
10. A. Miele, On the brachistochronic thrust program for a rocket powered missile
traveling in an isothermal medium, Jet Propulsion, 28, 675-684 (1958).
11. R. Bellman, Dynamic Programming, Princeton University Press, Princeton,
N. J., 1957.
12. R. E. Kalman, L. Lapidus, and E. Shapiro, On the optimal control of chemical
and petroleum processes, IBM Research Laboratory, Yorktown Heights, N. Y., Research Report RC-76, ,Jan. 1959.
'"
13. R. Aris, R. Bellman, and R. Kalaba, Some optimizatiol) problems in chemical
engineering, Rand Corp., Santa Monica, Calif., Report P-1798; .. Sept. 1959.
14. B. White, The Quarie optimal controller, Instr. and Automation, 29, 2212-2216
(1956).
.'
15. C. S. Draper and Y. T. Li, Principles of Optimalizing Control Systems and an
Application to an Internal Combustion Engine, American Society of Mechanical
Engineers Publications, New York, 1951.
16. G. Vasu, Experiments with optimalizing controls applied to rapid control of
engine pressures with high-amplitude noise signals, Trans. Am. Soc. M echo Engrs.,
79, 481-489 (1957).
.
17. 1. Lefkowitz and D. P. Eckman, A review of optimizing computer control,
Proceedings of the Self-Adaptive Flight Control Systems Symposium, WADC-TR-59,
Wright Air Development Center, Dayton, Ohio, March 1959.
18. J. S. Frait, An investigation of optimizing circuits using the divider-optimizer
concept, M.S. thesis, Case Institute of Technology, 1960.
19. E. F. Beckenbach, Modern Mathematics for the Engineer, McGraw-Hill: New
York, 1956, Chap. 18, pp. 448-480.
20. A. A. Feld'baum, Automatic optimalizer, Automatika i Telemekhanika (English
translation), 19, 718-728 (1958).

13-30

CHEMICAL PROCESS CONTROL SYSTEMS

21. R. E. Stakhovskii, Twin-channel automatic optimalizer, Automatika i Telemekhanika (English translation), 19, 729-740 (1958).
22. D. H. Archer, An optimizing control for the chemical process industries, Westinghouse Electric Corp., Pittsburgh, Pa.
23: J. W. Bernard and F. J. Soderquist, Dow evalua,tes optimizing control, Control
Eng., 6, No. 11, 124-128 (1959).
24. H. S. Tsien, Engineering Cybernetics, McGraw-Hill, New York, 1954, Chap. 15.
25. H. Ziebolz and H. M. Paynter, Possibilities 6f a two-time scale computing
system for control and simulation of dynamic systems, Proceedings of the National
Electronics Conference, Vol. 9, Feb. 1953, pp. 215-223.
',26. G. E. P. Box, The determination' of optimum conditions, Chap. 11 of The
L. Davies, Editor, Hafner PublishDesign and Analysis of Industrial Experiments,
ing Co., New York, 1954.
27. H. L. Engel, Computing control applied to a fractionating column; Control Eng.,
4, No.9, 144-147 (1957).
28. A. H. Freilich, Process computer control concepts, ISA Journal, 6, 47-54 (1959).
29. R. W. Schrage, Optimizing a catalytic cracking operation by the method of
steepest ascents, Operations Research, 6, 498-515 (1958).
30. Engineering Staff, G.P.E. Controls Inc., Applying the digital computer to openhearth operations, Control Eng., 6, No.8, 94-ioO (1959).
31. L. K. Kirchmayer, Economic Operation of Power Systems, Wiley, New York,
1958.
32. L. K. Kirchmayer, Economic Control of Interconnected Systems, Wiley, New
York, 1959.
33. C. D. Morill and J. A. Blake, A computer for economic scheduling and control
of power systems, Goodyear Aircraft Corp., Akron, Ohio.
34. E. J. Kompass, The "Early Bird" goes automatic, Control Eng., 3, No. 12,
77-83 (1956).
, 35. T. M. Stout, System considerations in computer control of a semicontinuous
chemical process, Tran~. A~. Inst. Elec. Engrs., Pt. II,40, 640-651 (1959).
36. Computing cont'r~l-acommercial reality, Control Eng., 6, No.5, 40 (1959).
37. T. M. Stout, Co~put~rcontrol of a butane isomerization process, paper presented at thfLCnnferenceon Analog and Digital Instrumentation, American Institute
of Electrical Engineers, Philadelphia, April 20, 1959.
38. D.B. Brandon, Digital control of an alkylation plant, Princeton University
Conference on Computer Control of Industrial Processes, Feb. 10, 11, 1959.
39. R. C. Larsen, Application of a control computer in the closed loop temperature
c~ntrol of an annealing furnace, ISA Preprin't No. 141-59, paper presented at Instrument Society of America Annual Conference in Chicago, III., Sept. 1959.
40. 1. A. Rilov, Prospects of utilizing calculating m~~.I;ines for automatic regulation of blast furnace operation, Central Laboratory on Automatics, U.S.S.R. (translated from the Russian by 1. S. Locke, Feb. 10, 1951).
41. Case Institute of Technology, Process automation, Report 1, Sept. 1956.
42. D. P. Eckman and 1. Lefkowitz, Optimizing control of a chemical process,
Control Eng., 4, No. 9, 197~204 (1957).
..
. 43. 1. Lefkowitz and D. P. Eckman, Application and analysis of a computer control
system, Trans. Am. Soc. M echo Engrs., 81, 569-577 (1959).,
44. J. F. Sandelien, An approach to dynamic optimizing control of the continuous
proce~s, AlEE Preprint No. 60-247, paper presented at the American Institute of
EleCtrical Engineers Annual Meeting in New York, February 1, 1960.

0:

COMPUTER CONTROL

13~31

45. T. J. \Villiams and R. E. Otto, Generalized chemical processing model fm; the
investigation of computer control, AlEE Pre print No. CP 60-119, paper presented at
the American Institute of Electrical Engineers Annual Meeting in New York, February 1, 1960.
46. 1. Lefkowitz and D. P. Eckman, Optimizing control by model methods, ISA
Journal, 6, No.7, 74-77 (1959).
47. D. P. Eckman and 1. Lefkowitz, Principles of model techniques in optimizing
control, Proceedings of the First Congress of the International Federation of Automatic Contl"Ol, Moscow, 1960, Butterworth, London.
48. J. K. Walker and C. K. Hines, Computer controlled pilot plant, Information
Bulletin 154, Consolidated Electrodynamics Corp., Pasadena, Calif.
49. Proceedings of the Self-Adaptive Flight Control Systems Symposium, \V ADC
TR 59-49, Wright Air Deyelopment Ccnter, Dayton, Ohio, March 1959.
50. E. M. Grabbe, Digital computer control systcms; an annotated bibliography,
Proceedings of the First Congress of the International Federation of Automatic Control, Moscow, 1960, Butterworth, London.
51. A. H. Freilich, Status of process computer control, ISA Journal, 6, No.7, 46-65,

81-82 (1959).

D

CHEMICAL PROCESS CONTROL SYSTEMS

Chapter

14

Data Processing
E. M. Grabbe

1. Introduction

14-01

2. Monitors and Data Logging Equipment

14-08

3. Process Control Computer Equipment

14-13
14-17

4. Planning for Computer Control
References

14-22

1. INTRODUCTION

Basic Principles. Emphasis on the data processing aspect of chemical
and other industrial processes has been increasing steadily. With common usage of analog and digital computers, widespread application of
automatic control theory, and increased knowledge of the behavior of
processes, it has thus become easier to mechanize much of the computing,
data manipulation, and logical decision processes associated with the
control of industrial systems so that they may be carried out by machines rather than by human operators.
Data processing is the monitoring, recording, computing, and evaluating
of important information concerning process variables in order to obtain
improved operation of the process. The computations range from simple
scaling to calculating operating guides which an operator ca,n ,use to
control the process or plant more effectively. In systems using a computer, the loop may be closed and the computer supplies signals which
automatically make calculated changes in process varia~les. Other
names applied to this type of data processing system are data acquisition,.
14·01

14-02

CHEMICAL PROCESS CONTROL SYSTEMS

dat.a logging, data recording, computing control, and computer control.
The theory and methods of computer control are covered in Chap. 13,
Computer Control.
Continuous monitoring means that all points are observed at all times.
Each variable being monitored must have its own instrumentation and
detection equipment. Scanning systems are programmed to observe or
sample sequentially a large number of points: The recording and indicating equipment is time shared, thereby reducing cost. Both standard
and special purpose data processing systems are in use. The emphasis
in this chapter will be on standardized equipment and digital systems.
Henefits of Monitoring. The fundamental benefits of monitoring are
protection of equipment and personnel. In complex systems computation
maybe required to determine whether dangerous conditions exist in a
process, for example in nuclear power plants (s~e Ref. 10). Automatic
monitoring removes the human bias and error" introduced in manual
logging or conversion of analog records into digital form. Hence, the
output information is far more reliable and accurate. The plant operators are also freed from the tedious task of gathering large quantities
of data, and they can concentrate on improving plant efficiency and in
coping with unanticipated emergencies when proper and expeditious
action is needed.
For plants which represent large capital investments and have high
production rates, data processing has beeo'tne a must. Proper data
gathering systems will provide accurate accounting data, improve maintenance procedures, reduce down time, and increase the operating life
of, industrial plants. With the trend toward larger plants the need and
value of data processing as a protective measure increase. Examples.
Individual electrical power generating plants of the future may represent investments in the order of $25,000,000. Nuclear power plants represent large investments, and personnel must be protected against radiation hazards.
Benefits of Closed Loop Computer Control. When a computer is
used in a closed loop system, substantial benefits may result from carrying,out the control functions described in Chap. 13, Computer Control.
In complex multivariable processes the computer. can improve yield, increase throughput, improve quality, and decrease operating costs. Computer control is especially useful in systems in which process variables
interact strongly, input materials vary in characteristics, output prodllctspecifications are changed frequently, environment variations are important, etc. These are situations in which. man cannot cope with the
speed and complexity of action required for optimum control. Computer

DATA PROCESSING

14-03

control has been applied to many processes in which the payout (time
to recover investment) is six months to two years.
Objectives. There are many different levels of on-line data processing
in industrial activity. The objectives, listed in order of increasing complexity and sophistication, are as follows.
'. :. 1. As a safety device to sound warnings, to provide visual indication of
malfunction, and to shut down equipment automatically when unsafe or
em.cf:gency conditions· exist.
2. To supply accurate records for cost analysis, inventory, and other
accounting functions.
3. To provide records for analyses of processes. Examples are det~r­
minations of static and dynamic behavior, recording of events during
emergency shutdown, and collection of maintenance data.
4. To compute operating guides which may then be used for adjusting
set points of controllers to obtain optimum plant operations.
5. To close the control loop and accomplish completely automatic control for optimum plant operation (feed-forward or feedback).
6. To provide for autom~tic adjustment of mathematical models of the
process to account for slow changes in the process.
TABLE 1. MONITORING AND DATA PROCESSING FUNCTIONS
1. Alarms ( off-normal conditions)
AV~diblle annu~citator} Continuous or scanned
Isua annunCla or
Equipment shutdown
Analog indication (visual)
Meter
Oscilloscope
2. Analog Recording
Chart records
Continuous
Scanned
Off-normal indication
Programmed (relays or plugboard)
3. Digital Recording (logging and simple computation)
Analog computations (scaling, zero offset, square root, etc.)
Digital indication (visual digital display)
Digital records (typewriter, punched cards, punched tape, magnetic tape)
Programmed (plugboard)
4. Digital Control Computers (computation, recording, and control)
Process Optimization
Operating guides (manual control)
Closed loop control (feed-forward or feedback)
Automatic modification of mathematical equations (computer program)
Internally stored program

14-04

CHEMICAL PROCESS CONTROL SYSTEMS

Items 4 and 5 are concerned with short-term process optimization,
whereas item 6 is concerned with long-term changes which require modification of the process transfer functions as represented by a mathematical
model (see Chap. 13, Computer Control).
Table 1 shows the types of data processing equipment which may be
used as part of control systems. The equipment ranges from simple alarms
to general purpose control computers. Figures 1, 2, and 3 illustrate three
levels of data processing. Figure 1 is a block diagram of a monitoring

Process

Audio
FIG. 1.

Automatic
plant
shutdown

Monitoring and recording system block diagram.

and analog recording system. Figure 2 shows the functions of a typical
digital data logger, and Fig. 3 illustrates the use of a digital process control computer.
The digital data logger of Fig. 2 provides all the functions of the simpler
monitoring and recording system of Fig. 1. In addition, it can provide
some analog computation and digital records such as printed data,
punched cards, punched tape, and magnetic tape. The process control
computerpf Fig. 3 adds the features of computation of operation guides,
automatic closed loop control, and automatic long time optimization

DATA PROCESSING

14~05

Process

Off-normal
limits

Alarms

cards

FIG. 2.

Punched tapes,
magnetic tapes

Typewriter
pointout
(alarms)

Typical digital data logger system block diagram.

through adjustment of mathematical models (see Chap. 13, Computer
Control, Sect. 7, Applications of Computer Control).
Loggers are employed for gathering process data for analysis ata later
time. On-line computing systems are employed for large and complicated
processes for which rapid computation and control involving many variables are required and are beyond the scope of a human operator.
Data Processing Inputs. The inputs to a data processing system
originate for the most part in physical quantities, the variables of the
process. Measuring elements (transducers) convert the signals into suitable pneumatic or electric form for monitoring and data'processing. Chap-..
ter 20, Measuring Elements and Sensors, describes the basic principles
of measuring elements and sensors with emphasis on devices that provide

14-06

.CHEMICAL PROCESS CONTROL SYSTEMS

Process

-----.,1
1
1

Automatic:
closed
loop
control
Digital process
control computer
(general purpose,
programmed)

1

1
I
- - - - - - - - - - _______ J

Off-normal
limits

Punched
cards

Punched
tapes

Typewriter
printout (alarms)

Ma ual
control

-

-

-

_.J

FIG. 3. Process computer control system block diagram.

electrical signals as their outputs. Chapter 7, Instrumentation Systems,
covers the basic types of measuring instruments used in the process industries. The most common values for variables measured in industrial
control systems are temperature, liquid level, pressure, and flow .. Other
important measurements come from strain gages, tachometers, pH~cells,
and continuous analyzers (see Chap. 24, Continuous Analyzers).
The off-normal limits must be entered into the system as constants.
For analog systems these limits are set by potentiometers. For digital
systems the information is recorded in the storage or can be read in
coded form when needed, for example, by a punched card reader.
Programming the System . . Some monitors operate continuously,
and duplicate equipment is required for each point. When large numbers
of points are to be monitored,. analog systems and digital data loggers
usually use plugboard programming for sequencing the equipment and

DATA PROCESSING

14-07

for selecting the functions to be performed on each channel. Digital
computers have internally stored p.J;ograms. Such programs may include
more sophisticated system checks as well as off-limit checks at the will
of the programmer. For example, the computer program might include·
(1) tests for computer malfunction, (2) reasonableness checks on raw or
computed data, (3) redundancy features, (4) detection of instrument failures, and (5) automatic optimization.
Data Processing Outputs. The system outputs are listed in Table 1
as the equipment functions. Alarms for emergency action or automatic
shutdown are among the basic outputs of any data processing system.
Analog and digital records provide the output under normal operating
conditions. The form and: format of the recorded output will depend
on the particular requirements. If cumulative data is required in analog
systems, the output production is recorded continuously and planimetering is necessary. On the other hand simple digital computing can provide cumulative records of production during prolonged periods. A digital computer can also extrapolate values, and in the event of instrument
or transmission system failure it can compute good estimates for quantities such as cumulative production. When analog-to-digital converte~s
are used, the output data appears in digital form. As such it may be
displayed by digital indicators, print~d out by electric typewriter, or
recorded on punched or magnetic tapes or punched cards. This recorded
information may then be used for other purposes as desired (see Vol. 2,
Computers and Data Processing).
Installation. Installation of monitoring equipment is expensive. It
includes installing transducers, fittings, conduits, wiring, alarms, etc.
For simple systems the cost of installation may be three to four times the
cost of monitoring equipment. The cost may be reduced by connecting
closely located transducers to a central point in the area or zone. A
stepping switch is used to select a desired variable, and a single pair of
wires is needed to make the connection to the control room.
Time sharing of a transducer may.. also be accomplished, as in the
Fischer and Porter multiple pressure readout system. This equipment
uses one readout detector for sampling a number of pressures from processing units located reasonably near to one another.
Installation of data logging and computing equipment will require more
detailed system planning. Control room air conditioning is usually desirable to prolong the life of electronic equipment. For computer control systems the installation may also require transducers for converting
pneumatic signals to electric signals and continuous composition or quality analyzers. For stored program computer systems, program checkout
is part of the installation procedure.

CHEMfCAL PROCESS CONTROL SYSTEMS

14-08

Maintenance. To be useful, data processing equipment must be highly
reliable and easy to maintain. Complex equipment is subject to the
rules laid down in Chap. 19, Reliability. The basic design of the system
should be such that it is fail-safe. Test procedures and test equipment
must be available to diagnose and correct any malfunctions.
Solid state electronic equipment designed for high reliability has demonstrated excellent performance. On-call maintenance personnel are
provided for computers and data loggers. It is often better practice to
avoid scheduled maintenance but to carry out preventive maintenance
only when the process being monitored is down for other purposes.

2. MONITORS AND DATA LOGGING EQUIPMENT

Table 2 shows a survey of typical monitoring and logging equipment
TABLE

2.

MONITORING AND DATA LOGGING EQUIPMENT CHARACTERISTICS

Characteristic
Number of points
Expandability
Scanning rates
Logging rates
Logging cycle
Error
Inputs (electrical)
Functions
Variables
Transducers

Typical Data
4 to 10 (continuous monitors)
60 to 100 (digital loggers)
Modular
30 to 2000 points per minute
1 to 2 points per second
1,2,5, 10, 15,30,60 minutes and off
0.1 to 2% of range
o to 100 mv, thermocouples
Audio alarms, alarm indicator light,
analog or digital indication, analog or digital recording
Temperature, pressure, force, flow,
strain, speed, pH, level, etc.
Thermocouples, strain gauges, pH
electrodes, other standard detectors (see Chap. 20, Measuring Elements and Sensors)

for production and processing operations (Ref. 1). Scanning rates become
important for systems with large numbers of variables. Only the simplest
systems monitor continuously.
Monitors. Typical alarm monitors come in modules of a small number of points, 4, 6, or 10, such as the temperature monitoring equipment
shown in Fig. 4. When the temperature reaches an alarm setting adjustable for each channel, a sensitive relay detects the condition and
closes a contact. The alarm action consists of actuating a light on the
front of the unit, lighting a direct reading designation card, and actuating
remote visual and audible anunciators. A meter may be plugged in to
read the monitored variable. External wiring can automatically shut

DATA PROCESSING

14-09

Tempera ure
sensing

, 1/

0

0

CJ -0/1'

0

0

CJ -0/1'

-?-

,1/

-?-

,1/

0

0

CJ -0/1'
CJ

pOints,~Wc::...- J

Limit set
and meter jacks

H

Audio
alarm··

~

I

,1/

-/

-

~_1

_ _ _--.-___

_--I

~

Alarm lights

Location
indicators

FIG. 4. Temperature monitoring system.

down the operating equipment if desired. Equipment of this type is
adaptable to zone or centralized installation. Its modular construction
permits panel or closure mounting.
Scanning and Recording Monitors. Scanning systems have been
developed to fill the need for compact and economical methods of displaying and/or recording large quantities of information in multivariable
systems (Ref. 2). Typical scanning systems come in modules that monitor 50 to 1000 or more variables. Scanning rates are in the range of 2 to
3 per second for mechanical switches or relays (Fig. 5). Electronic scanSensing
points

Set
points

I
/

I

Memory
relays

Scanning
indication

r-----r----------r--------'T"--I
I

I

I

I

I

/

FIG. 5. Scanning monitor block diagram.

/

Motor
magnet

I

(Courtesy Thermo Electric Co.)

14-10

CHEMICAL PROCESS CONTROL SYSTEMS

ning rates are as high as 2000 per second. In some systems displays
are on an oscillograph screen at the central receiving point. Heights of
the pulses displayed on the screen are proportional to the measured function, and a number of variables may be displayed simultaneously as a
train of pulses on the calibrated
oscilloscope.
Other scanning devices are single
pen multipoint analog recorders
with added functions. A typical
setup· such as that shown in Fig. 6
may cover 100 points. This device
operates in similar fashion to alarm
monitors and scanners but provides
a chart record of the variables. The
points are recorded sequentially on
a strip chart and an identifying
number and the time is printed by
each point. The monitoring unit
has stepping switches and controls
for program selection.
Scanning monitors are programmed to record data, say,
hourly but to scan for off-limit
values at the maximum rate between recordings. The operator
should be able to override the programming controls to select any
desired value, to initiate recording,
to omit any variable, and to reset
to the beginning of the cycle.
Digital Data Loggers
Information Recording in the
Chemical and Petroleum Industries. Large scale data loggers were

FIG. 6. IOO-channel scanning and analog recording system. Each point is
recorded with identifying code and
time. (Courtesy Leeds & Northrup.)

first developed for the chemical
processing industries (Refs. 2 and
3) . Similar equipment, often called
data processing systems or data
reduction systems, has found broad
applications in aircraft and missile
testing, nuclear and conventional

14-11

DATA PROCESSING

power generating plants, and a variety of other industries. Each new
generation of data loggers has increased computing capabilities because
of the demands of the users, and some data loggers have been discontinued by manufacturers in favor of digital control computers. It is
difficult to justify a data logger when the output is a punched tape which
is later fed into a scientific computer. The use of a process control
computer eliminates duplication of equipment and intermediate steps.
Data loggers will continue to be used when recording without too much
computation or evaluation is required.
Characteristics of Data Loggers. Typical data logger diagrams are
shown in Figs. 7 and 8. In most equipment computations such as scaling,
.

ro

"C

....
Q)

a.
Vl

~2

"0

"C
"C
C

ro

Vl

:l

o

:5 1

tf
o

Variable cost

-------t----

u

iii

~

Fixes cost

o~------------~----~--~----------~------------~------~

o

2

3

4

5

Flow rate, thousand barrels per day

FIG. 10. Representation of material costs, total cost versus flow rate.

for all the significant streams to reach realistic conclusions on how to adjust the process. In particular it is advisable to allocate all operating
costs to the product streams.
Where the process uses materials which are the outputs of previous
processes and furnish a product which becomes the feed material for

14-21

DATA PROCESSING

subsequent processes, the values of the various materials can be somewhat nebulous and difficult to determine. Even in relatively straightforward situations the systems engineer may need help from the accounting department in order to obtain suitable values of the slopes, intercepts,
and equations.
System Boundaries. The boundaries for the process considered must
be fixed, and all income-producing or cost-incurring materials which cross
these boundaries must be included in the profit equation for the process.
Hence, a multi term equation results:
!If

(3)

P =

N

L: VQiQi - L: VFjFj -

Po,

1

where P is the total profit,
Qi is the amount of the ith product,
V Qi is the unit value of the ith product,
P j is the amount of the jth raw material or utility which feeds the
process,
V Fj is the unit value of the jth raw material or utility, and
Po is the fixed cost.
If the Q's and F's in these equations are given as rates rather than

quantities, this equation gives the profit rate in dollars per hour or day.
Continuous processes can be optimized by making adjustments so that the
profit rate is always a maximum.
Batch and semicontinuous processes as well as the start-up and shutdown periods of continuous processes can be optimized only by considering the time variations of P that are due to programmed variations of
process conditions, deactivation of catalysts, etc. Although the values
of materials (V's) have been defined as independent of Q and F, they
will vary as changes in the market occur and must frequently be brought
up to date. In rare instances fiuxations in market may be sufficient to
require frequent adjustment.
Product Specifications and Production Quotas. Product specifications may vary from (1) the minimum which ensures that the desired
product is made to (2) stringent requirements on product characteristics.
Typical product specifications are
1. Physical properties of material: strength or hardness limits, viscosity, specific gravity, color, etc.
2. Chemical properties: composition, impurity limits, pH, etc.
Many of the quality specifications may appear as constraints on the

14-22

CHEMICAL PROCESS CONTROL SYSTEMS

control process conditions. An impurity limit, for example, may restrict
reaction tempera.ture. Poisoning of a catalyst may inhibit reactivity.
Equipment rating will also constrain the production rate.
Constraints. Constraints or restrictions on process operations generally take the form of inequalities. Process variables may be restricted
to have values (1) greater than some minimum value, (2) less than
some maximum value, or (3) within both minimum and maximum limits.
These constraints arise from product quality specifications or production
quotas or from material availability, equipment ratings, safety requirements, etc.
Optimization. Optimizing is performed at two levels: (1) frequent adjustment of variables to maintain operation a.s close as possible to the
desired limits set by the ~quations, (2) periodic adjustments of constants of the equations to bring the mathematical model into agreement
with process operation. The latter function may be performed every Y2
hour to 4 hours, whereas the short-term adjustments are made every 2
to 5 minutes depending on the process. ChaTacteristics of a typical operating installation with both of these types of optimization is described in
Refs. 9 and 28.

REFERENCES
1. H. Karp, Monitors safeguard industry's processes, Control Eng., 2, No.9, 80-89
(1955).
2. R. A. Anderson, Scanning instruments: control and information systems, Process Instruments and Controls Handbook, D. M. Considine, Editor, McGraw-Hill,
New York, 1957, pp. 8-34 to 8-47.
3. A. F. Sperry, An information system consolidates process control,Automatic
Control, 1,4-7 (Nov. 1954).
4. A. Freilich, Available computers and what they do, ISA Journal, 6, No.7, 55-65
(1959).
5. E. M. Grabbe, Digital control systems; an annotated bibliography, PrDceedings
of the First Congress of the International Federation of Automatic Control, Moscow,
U.S.S.R., June 27-July 7, 1960.
6. E. L. Braun, A digital computer for industrial process analysis and control, Proc.
Western Joint Computer Conf., 207-211 (March 3-5, 1959).
7. P. B. Nalleand J. M. Sauer, Application of a digital computer to cement manufacture, ISA Paper 41-59, 14th Annual Instrument Automation ISA Conference and
Exhibit, Chicago, Sept. 20-25, 1959.
8. H. Karp, Computing control-a commercial reality, Control Eng., 6, No.5, 4042 (1959).
9. J. M. Madigan, Computer controlled processing, Chem. Eng. Progr., 56, No.5,
63-67 (1960).
10. J. Auricoste and Y. Panis, Utilisation d'une calculatrice numerique universelle

DATA PROCESSING

14-23

dans une central nucleaire a reacteur a gas, La Technique Modern, 1, 62-64
(1959); in French.
11. M. Phister, Jr. and E. M. Grabbe, Fitting the digital computer into process
control, Control Eng., 4, No.6, 129-136 (1957).
12. T. M. Stout and C. G. Laspe, Digital computers for process control, Ind. Eng.
Chem., 49, 38A-42A (1957).
13. W. S. Aiken, Building reliability into digital process control systems, Control
Eng., 5, No. 10,76-79 (1958).
14. M. Phis tel', Jr., How to plan computer control, ISA Journal, 6, No.1, 51-55
(1959).
15. J. Auricoste and G. Gau, Command centralisee de processus industriels a l'aide
de calculateurs numeriques, Automatisme, 5, 2-8 (1959); in French.
16. T. M. Stout, Mathematical models for computer control systems, Proceedings
of the First Congress of the International Federation of Automatic Control, Moscow,
U.S.s.R., June 27-July 7, 1960.
17. T. M. Stout, Computer control of butane isomerization, ISA Journal, 6, No.9,
98-103 (1959).
18. D. B. Brandon, Developing mathematical models for computer control, ISA
Journal, 6, No.7, 70-73 (1959).
19. S. M. Roberts and C. G. Laspe, The development of on-line computer control
equations for a thermal cracking reaction, paper presented at Process Dynamics and
Control Symposium, Part II, American Institute of Chemical Engineers, 41st Annual
Meeting, St. Paul, Minn., Sept. 27-30, 1959.
20. R. C. Johnson et aI., Computers, mathematics, statistics, and operations research, Ind. Eng. Chem., 51, 422-431 (1959).
21. T. J. Williams, Chemical kinetics and the dynamics of chemical reactors, Control Eng., 5, No.7, 100-108 (1958).
22. W. R. Marshall and R. L. Pigford, Applications of Differential Equations to
Chemical Engineering Problems, University of Delaware Press, Newark, Del., 1957.
23. C. G. Laspe, A practical application of transient response techniques to process
control systems analysis, ISA Journal, 3, No.4, 134-138 (1956).
24. A. J. Young, An Introduction to Process Control System Design, Instruments
Publishing Company, Pittsburgh, 1955.
25. T. L. Batke, R. G. E. Franks, and E. W. James, Analog computer simulation
of a chemical reactor, ISA Journal, 4, No.1, 14-18 (1957).
26. F. A. Woods, Simulation of process control with an analog computer, Ind. Eng.
Chem., 50, 1627-1630 (1958).
27. J. J. Florentin et aI., Correlation analysis of a heat exchanger, presented at
Joint Symposium on Instrumentation and Computation in Process Development and
Plant Design, London, May 11-13, 1959.
28. R. D. Eisenhardt and T. J. Williams, Closed-loop computer control at Luling,
Control Eng., 7, No. 11, 103-114 (1960).

INDUSTRIAL CONTROL SYSTEMS

E.

INDUSTRIAL CONTROL SYSTEMS
15. Transmission Systems, by L. M. Silva
16. Nuclear Reactor Control, by W. E. Shoupp and M. A. Schultz
17. Control of Interconnected Power Systems, by Nathan Cohn

E

INDUSTRIAL CONTROL SYSTEMS

Chapter

15

Transmission Systems
L. M. Silva

1. Introduction and Symbols
2. Information
3. Transmission Systems
4. FM Demodulation and System Errors
5. AM Detection and System Errors
6. Pulse Transmission
References

15·01
15·04
15·09
15·27
15·49
15·69
15·89

1. INTRODUCTION

A measure of the effectiveness of a technological society is its ability
to effectively transfer information from the source to the user. Information may originate from instrumentation, computers, or weapon systems.
In each particular situation the effectiveness of information transfer or
transmission is determined by the rate at which information transfer is
accomplished and the degradation or loss of information in the process.
A transmission system, to perform within the limits set by the allowable
degradation and at the specified rate, is designed by selecting a configuration which is appropriate for the distances involved and in which the total
equivocation or ambiguity introduced by all the system components is
within the specified limits.
Symbols. The symbols defined in the following list are used in a consistent manner throughout this chapter. Symbols not listed are defined
where they are used.
15·01

15-02

INDUSTRIAL CONTROL SYSTEMS

A
Ao
AOt

An
Ap

Aq
As
A(w)
Ao(w)
a

ao
B

Q.

c
D
Do(t)

E2
f
fo
fe
fs
f(t)
I
K

k
M(t)

Rms amplitude.
Peak carrier amplitude.
Peak carrier amplitude, at the threshold point.
Rms noise amplitude.
In-phase carrier amplitude component.
Quadrature carrier amplitude component.
Peak amplitude of a signal voltage.
Amplitude frequency characteristic of a system, filter, etc.
An assumed or ideal amplitude characteristic for pulse transmission
systems. Also, the amplitude characteristic of a reference system
used as a standard of comparison.
Rms value of a(w) over the transmission bandwidth.
Ratio of rms carrier amplitude to rms noise amplitude.
Bandwidth in cycles per second. For high-order filters, B should be
interpreted as the half-power bandwidth or 3-db amplitude bandwidth.
3-db bandwidth of carrier circuits in cycles per second (e.g., the
bandwidth of the bandpass filter ahead of an FM discriminator).
Bandwidth of a Gaussian filter, cycles per second.
Output filter 3-db bandwidth, cycles per second.
3-db bandwidth required to track a signal in a phase lock loop.
Signal or source bandwidth, cycles per second; where signal refers
to message or information which is being transmitted.
Transmission system bandwidth, cycles per second.
R t' f Transmission system bandwidth
a 10 0
Source bandwidth
•
72 power bandwidth.
72 amplitude bandwidth, cycles per second.
Moments of a frequency distribution or spectrum around some
reference frequency (e.g., carrier frequency) or point. The zeroth
moment bo is equal to the mean noise power and is equal to N for
the message bandwidth spectrum and NT for the transmission
system bandwidth spectrum.
Rms phase deviation in radians over the transmission bandwidth,
B~a = wI!271'".
Information rate measured, bits per second.
A distortion power factor.
Time-varying angular modulation [271'" X Time-varying frequency
modulation]. For sine. wave modulation, Do sin wst. Do = 271'" X
Maximum frequency deviation.
Time-averaged mean square error.
Frequency, cycles per second.
A reference frequency, or the center frequency of a filter.
Carrier frequency.
Signal frequency.
Any function of time.
Information measured in bits.
Message dynamic range; sluggishness index; ratio of quadrature to
in-phase carrier power; a constant; a peak factor.
Number of redundancy bits; also a constant.
A modulated voltage waveform.

TRANSMISSION SYSTEMS

m=n+k
N

Pdc

Ro
R(t)

S

SIN
(SIN)eff
(SIN)r
(SIN)rr
B

Bmin

15-03

Sum of information bits and redundancy bits in a digital code
representing a single sample of the signal. Control bits are not
included. Also, modulation index of an amplitude modulated carrier.
l\1ean noise power or the noise power in the signal or message
bandwidth.
Noise power in output of AM detector when carrier is not present.
Mean noise power in the carrier bandwidth or bandwidth of bandpass filter.
Rms noise power in transmission circuit bandwidth.
The number of bits in a digital code representing a single sample of
the signal. Redundancy and control bits are not included in n.
Also, the number of identical sections in a filter.
The power component at the output of a device which contains no
information and is equivalent to a d-c bias, a fixed amplitude
carrier component, etc.
The maximum power component associated with the signal or information, P 8 = S if Pdc = O.
Maximum average transmission system power.
Maximum peak transmission system power.
Probability density function. The probability that a particular
measured value lies in an interval of length dx centered at x.
Saturation level of limiter.
The modulated signal received at the receiving end of a transmission system.
Rms signal power.
Signal-to-noise power ratio. For a specific measurement it is the
ratio of signal power to noise power. For a device or component
it is the ratio of maximum available signal power to noise power.
Signal-to-noise power ratio realizable at the output of a device,
component, or system or the signal-to-noise power ratio required
at the output of a device, component, or system.
SIN for narrow band FM.
SIN for wide band FM.
Power efficiency factor; 8 in decibels is equal to the excess power
required (8 is negative) to realize a given (SIN)eff.
Power efficiency factor for a transmission system with an average
power limitation.
Power efficiency factor for maximum decibel loss or minimum
efficiency.
Power efficiency factor for minimum decibel loss or maximum
efficiency.
Power efficiency factor for a transmission system with a peak power
limitation.
Time constant, etc. Time over which an average is taken.
Time.
Intersymbol amplitude interference (see Pulse Modulation section).
Rms intersymbol amplitude interference for pulse transmission.
Peak intersymbol interference.
Carrier envelope voltage or response as a function of time.
Input voltage.
Noise voltage.

INDUSTRIAL CONTROL SYSTEMS

15-04

Vo

Vp

Vq

V8
Vet)
W(f)

Xo
x

Z(jw)

a(w)

(jew)

r

p

1/Io(w)

Output voltage.
In-phase carrier voltage component.
Quadrature carrier voltage component.
Signal voltage.
Time-varying voltage.
Power spectrum as a function of frequency.
True value of an arbitrary quantity, a series of measurements, etc.
A measured value of an arbitrary quantity.
Amplitude characteristic of a filter as a function of frequency.
Fractional deviation of an actual amplitude frequency characteristic from that of an ideal system or of a reference system. a
is equal to the rms value of a(w) over the transmission bandwidth
B~a = wI!27r.
Fractional deviation of an ·-actual phase characteristic from that
of an ideal characteristic or reference system. b is equal to the
rms phase deviation in radians over the transmission bandwidth
B~a = wl/27r.
A ratio of rms modulation to a bandwidth factor that is a function
of the spectral distribution of the noise.
Maximum fractional error.
Deviation rate (for sine wave modulation fJ. = deviation ratio).
Mean squared value of noise
power spectrum about Wo
Bandwidth factor equal to ratio: --.:'-----.:...-----~Mean noise power
The standard deviation, root mean square error.
Rms phase jitter.
Variance.
Period or time interval.
Transmission delay time.
Phase deviation in FM systems or phase characteristic versus frequency for pulse transmission systems.
An assumed ideal linear phase characteristic for pulse transmission
systems. Also the phase- characteristic of a reference system used
as a standard of comparison.
Radian or angular frequency.
A reference angular frequency, the center frequency of a filter.
Angular frequency of carrier.
Angular detuning.
Angular signal frequency.

2. INFORMATION

Information typically originates from instrumentation and is in effect
a measure of a physical quantity or quality. It is characterized by being
continuous over a finite range and for a given measurement precision can
have a number assigned to every possible state. Typical signal sources
include voltages from transducers, pulse signals in which the information is contained as the time displacement between pairs of pulses, and
sinusoidally varying voltages, the frequencies of which contain the information.

TRANSMISSION SYSTEMS

15-05

The process of measuring or assigning a number to a particular magnitude of the signal is limited by the presence of noise or uncertainty in the
measuring system. For scientific measurements it is normal to assume a
Gaussian or normal law of errors.
Gaussian Distribution. If Xo is the true value of a quantity, the
Guassian distribution states that the probability p(x) of any particular
value is
1
p(x) = _ ; - exp [ - (x - Xo)2/2 (§.)
(§.)
N input
Nell

Modulator

Transmission
circuit""
power PT
bandwidth BT

Demodulator

Filter
bandwidth
Bs

Output
bandwidth = Bs
Dynamic range =

~1+ (*)eff

Noise

BT = effective transmission circuit bandwidth
BB = message bandwidth

p;. =

transmission circuit peak power
FIG. 5. Transmission system.

This method of normalizing system performance with respect to the
output permits describing the system performance in terms of the message
bandwidth, B s , and the effective signal-to-noise ratio, (SIN) eff, required
a t the output for a specified dynamic range.
These two specifications, output bandwidth and message dynamic
range, in conjunction with the input-output SIN characteristics for each
of the elements, will determine the signal-to-noise ratio required at the
source and the power and bandwidth requirements of the transmission
circuits. The information rate of a system which is normalized in this
manner is simply
C

=

Bs log2 (SjN)eff,

with (SjN)eff large compared to unity.
Classification of Modulation Methods. Four modulation methods
are listed in Table 2. Each of these represents a unique class of
modulating devices in the sense that information is represented in a different manner.
Direct Transmission-Amplitude Modulation. For the simplest
transmission system, direct transmission over a pair of wires, the output
signal-to-noise ratio is equal to the input signal-to-noise ratio providing

TRANSMISSION SYSTEMS
TABLE

2.

15-15

MODULATION METHODS

Method

Information Representation

Amplitude modulation

In terms of an amplitude
function
In terms of a frequency
deviation from a reference frequency (carrier)
In a pulse group as a digital code
In terms of a time interval

Frequency modulation
Pulse code
Pulse modulation

the amplifier or transmitter at the source does not have a peak power
limitation and only thermal noise exists in the trnasmission circuit. In.
practice, however, the power limitation is more likely to be a peak power
limitation than an average power limitation. Shannon (Refs. 20 and 22)
has shown that under these circumstances the effective signal-to-noise
ratio will lie within a range

2Pr ~ (8)
2Pr
N
~ Jj

7re 3 N

cff

7re

I

for SIN large,
.....-...

P T = peak power,
N = noise power in message bandwidth.

Thus if a 60-db signal-to-noise ratio is required at the output of the system, the input signal-to-noise ratio will correspond to
75 db

P

~ :- ~ 66.3 db,

where (SjN)cff = 60 db. For this example, direct transmission with a
peak power limitation, the effective signal-to-noise ratio is simply a constant times the required signal-to-noise ratio at the input to the transmission circuits. The only constraints are those of a peak power limitation
and the fact that the effective signal-to-noise ratio is substantially greater
than unity.
For the generalized amplitude modulation process, the expression for
the effective signal-to-noise ratio can be written

Pr ~ (S)
N

smaxJj

eff Smin

Pr

~N

where the s's are called power efficiency factors.

I

INDUSTRIAL CONTROL SYSTEMS

15-16

-

A measure of the excess power required for a particular system is the

-

ratio PT/P s of peak power PT to the amount of power P s required for an
ideal system. In this instance, this ratio is simply the reciprocal of the
power efficiency factors:

P;

1

1

--;;:::-;;:::--.
Smax - P s - Smin

P s is the message power or the transmission circuit power for direct trans-

mission without a peak power limitation and without losses.
These results are applicable to all transmission systems in ';Vhich information is contained in the form of an amplitude. The only differences
between individual systems are the magnitudes of the power efficiency
factors.
Frequency Modulation. In the case of FM systems, Goldman (Ref.
22) has shown that the effective signal-to-noise ratio for wide deviation FM

-

and for large PT/N is
2

Pr (BT)2

7re NBs

where N

~

(S)
N

2e P'?(BT)2

eff

~ -;

NBs

'

= thermal noise power in message bandwidth B s ,

BT = effective transmission circuit bandwidth
=

maximum frequency deviation (note transmission circuit bandwidth = (3BT > 2BT).

In this instance the effective signal-to-noise ratio varies directly as the
product of peak power and the square of the deviation ratio BT/Bs. Thus,
for a given (S/N)eff and bandwidth B s, power is exchanged as the square
of the bandwidth of the transmission medium.
It is characteristic of all systems that exchange bandwidth for power that

-

a threshold value of PT/NT exists below which performance deteriorates
rapidly. For the case of FM, the threshold occurs when the amplitude
of the carrier signal equals approximately four times the rms noise voltage
in the carrier passband. An expression from Nichols and Rauch (Ref. 7),
for the threshold power level is

(NTPr)
-

r--J

16{3,

threshold

where {3 r--J 3 for deviation ratios in excess of 4,
{3BT = RF bandwidth.

TRANSMISSION SYSTEMS

15-17

The quantity f3 is a function of the deviation ratio, dynamic range of the
message, and first derivative of the message waveform.
For the general case of a system in which power is exchanged on the
basis of the bandwidth expansion ratio squared, (S/N)cff becomes

-

s

max

(S)

P; (BT)2
-P;- >1- (Bs)2
.
Smax

- Ps -

BT

Smin

BT

Binary PCM-Direct Transmission. In pulse code modulation (PCM)
the signal is sampled periodically, and an n-bit binary code is generated
which corresponds to the amplitude level of the signal at the instant of
sampling. The device which performs the sampling is called an analogto-digital converter. For each sample, its output is a serial group of n
pulses which are transmitted over the transmission circuits. In addition
to the n pulses which carry the information, one or more additional pulses
are used to synchronize the transmitter and receiver.
If there are n binary pulses per sample, the resolution of the measurement is limited to 7f n • This quantity is called the quantizing step and
determines the accuracy of the conversion. Since the resolution is finite,
the quantized value will, on the average, be in error by plus or minus onehalf a quantizing step or 7f n +1 • This error is called quantizing noise.
If Bs is the bandwidth of the message, then 2Bs samples per second are
required by the sampling theorem. Each sample will include a group
of n pulses, where n = log2 I( with I( the dynamic range.
The transmission system will transmit 2nBs pulses per second. Since
a transmission circuit of bandwidth BT can transmit up to 2BT binary
pulses per second, then

BT = nBs = Bs log2 J( = Transmission bandwidth.
If the error rate of the transmission circuit is small, the received message
signal-to-noise ratio is independent of the transmission circuits. Error rates

of less than 10-6 (Ref. 5) can be realized with values of Pr/NT of 20 db.
The power required for PCM transmission is proportional to the number

-

of bits or the dynamic range. The power ratio PT/P s can be obtained from

P;.

1

NT

S

-=-

1

where - = 20 db for 10-6 error rate.
S

INDUSTRIAL CONTROL SYSTEMS

15-18

Then

P;

1

1

1

-=----=

n

s(Ps/N) (Bs/nBs)
Thus for PCM the bandwidth varies as the log2 of the dynamic range, and

-..

transmission power ratio PT/P s varies inversely as the square of the dynamic range.
If it is assumed that transmission will be effected at a negligible error
rate, the only source of noise in the output of the system will be that resulting from quantizing noise (Ref. 22), and the effective signal-to-noise ratio is

Pulse Modulation. Pulse modulation is the method used by another
class of modulators which have found widespread use. Their characteristics
are intermediate to the extremes represented by amplitude modulation and
frequency modulation. This can be established by considering that information is contained in the interval between two pulses or the duration
of a pulse. If the transmission circuit has a peak power limitation, then
the signal to noise ratio for the detection of a single pulse or pulse edge will

-..

be of the form, s(PT/NT). The time resolution of the system is proportional
to the ratio BT/ B s, of transmission circuit bandwidth (pulse rise time) to
message bandwidth (pulse repetition rate). The ratio BT/ B s, is an amplitude function; hence it will appear in the effective SIN as (BT/Bs)2 since
the power ratio must vary as the square of the amplitude variations. Thus,
the effective SIN will be of the form

with s the power efficiency factor. Thus, for a peak power limitation,
pulse modulation (PPM or PDM) systems exchange bandwidth directly
for power for a given effective signal-to-noise ratio.
The question of power is fundamental in this form of modulation as
in amplitude type systems. If it is assumed that an average power limitation exists rather than a peak limitation, the exchange relationship between power and bandwidth is more attractive. If the average power remains constant as the bandwidth is varied and the peak power varies
directly as bandwidth, then
-..Bs
(PT)av = PT - = Constant,
BT

TRANSMISSION SYSTEMS

..-....

PT

and (S/N)cff becomes

=

(NS)

PT

off

=

15-19

BT
-·

Bs

S

PT (BT)2
N Bs .

Thus, for the case of pulse modulation with an average power limitation,
power is exchanged directly as the bandwidth squared as in FM. This
example serves to illustrate the importance of a realistic appraisal of the
physical characteristics and limitations of a system.
Comparison of Modulation Methods. The basic power and bandwidth characteristics of the various forms of modulation provide a basis for
comparison and evaluation. A summary of these characteristics is given
in Table 3. In order to obtain a quantitative grasp of the power efficiency
of the various methods in terms of the dynamic range of the transmission,
the quantity Pr/N is used since it is directly proportional to the transmission power required for a particular system:

P;.

P;. P s

N

PsN

-=--

but

P
= (S)
N
N

=

s

I<-2 _ 1.

off

Hence,

Pr
N

P; (K 2

=-

Ps

-1).

This quantity P;'/N also appears in Table 3.
In the derivation of expressions for the effective signal to noise of the
various systems, the following assumptions or constraints were imposed:
1. There is linear superposition of signal and noise.
2. A filter at the output of the demodulator limits the noise bandwidth
of the overall transmission system to the message bandwidth Bs.
3. Excess noise contributed by system elements (modulators, receivers,
etc.) is negligible.
4. All systems receive the same noise power per unit bandwidth.
5. Noise has a Gaussian amplitude distribution.
6. No allowance for losses associated with the transmission circuits or
other system elements .
..-....
7. PT/NT» 1.
The assumption of negligible losses throughout the system is not restrictive, providing the individual elements do not contribute noise in excess

01

~

o
TABLE

Information
Coordina tes
(modulation)
Amplitude

3.

POWER AND BANDWIDTH CHARACTERISTICS FOR BASIC METHODS OF MODULATION

Power Ratio

Power Ratio
/'-.

/'-.

PT
Ps

PT

1

1
- ~[(2 - 1)

N

13 [Bs]

!(Bsy
S BT

! ( BSy([(2 _

1 (Bs)
Sp BT

~ ( B s) ([(2 _ 1)

S

BT

Remarks

A. BT = Bs
B. S < 1
C. 1 < 13

S

S

Frequency

Actual
Transmission
Circuit
Bandwidth

1)

I3BT

zo
c

(J')

---4
AI

<2

);

A. Threshold limitation
B. 13 ~ 3

o

A. Peak power limitation
B. 1 ~ 13 ~ 2

or-

r-

n

Z

---4
AI

Time

1 (Bsy
SA BT

Sp

BT

~ ( Bs)2([(2 _ 1)
SA

I3BT
I3BT

BT

A. Average power limitation

/'-.T (Bs)
B. P T = P
BT

= constant
Pulse code

1 log2 [(

S ([(2

-

1)

1

;log2 [(

Bslog2 [(

(J')

-<

(J')

---4

m
~

(J')

TRANSMISSION SYSTEMS

15-21

of that attributed to the thermal noise associated with the bandwidth of
the element. The fact that losses do exist in a system merely implies the
need for providing excess power at the transmitter or power amplification
at the receiver. The assumption of Gaussian or White noise is restrictive
in the sense that the results do not apply for impulsive or Rayleigh noise
sources which are encountered in RF transmission systems.
The inclusion of the filter at the output is typically not restrictive,
since by definition no information is contained in the message for frequencies greater than B s , the message bandwidth.
The assumption of linear superposition of noise is required for simplicity
of analysis. With the exception of binary pulse transmission, the ·assumption that P;IN T is greater than unity is not restrictive since the information content of the message will normally require that this condition be
satisfied. In the case of FM or pulse systems, the threshold condition
places a limitation on the minimum value of this quantity.
Table 4 presents the expressions obtained for the effective signal-tonoise ratio for all the systems and in addition indicates the range over
which the expressions are meaningful.
In the case of amplitude-modulated carrier type systems, no distinction
is made for synchronous systems in which the phase of the carrier is used
in the demodulator to effect a SIN improvement. The use of synchronous
detection will provide a maximum of 3-db improvement in the effective
signal-to-noise ratio of the double sideband AM systems in which a single
modulator is used at the transmission end. With more sophisticated modulation methods (two modulators or two signals per channel), it is possible
to obtain up to an additional 3-db improvement. Thus in the limit double
sideband (DSB) modulation can be as efficient as single sideband. (SSB)
modulation while avoiding the difficulties of SSB transmission.
EXAMPLE.
To illustrate exchange of bandwidth and power and the
performance of the various methods of modulation, assume that a transmission system is required to transmit 0.1 % data. This corresponds to a
dynamic range of 1000: lor 10 binary bits. If the results are plotted in
terms of PTIN versus bandwidth ratio BTIBs, the curves (Fig. 6) will indicate the actual power required for transmission over a lossless system.
This statement is not true for pulse position modulation systems in which
the actual pulse width is a fraction of the repetition period. In this instance, the actual power will be equal to the peak power multiplied by the
duty ratio.
For this particular application, if the conservation of spectrum or bandwidth is the primary consideration, then SSB-AM is the best choice. If
bandwidth is available, either PCM-DSB-AM or PCM-FM provides the
greatest power saving. Note that if the duty ratio is small for the pulse

TABLE

Symbol
AM

AM

DSB-AM

SSB-AM

FM

Binary PCM

PPM

4.

EFFECTIVE SIGNAL-TO-NOISE RATIOS FOR BASIC MODULATION METHODS

(~

Description
Direct transmission
with average
power limitation
Direct transmission
with peak power
limitation
Double sideband
amplitude-modulated carrier
Single sideband
amplitude-modulated carrier
Wide band frequency
modulation

Direct transmission
of binary pulse
code modulation
Direct transmission
pulse position
modulation

t11
t.)

PT
N

(S)
N
(S)

-2PT
-< 3
'lI"e

N -

1 p;;
2'l1"e 3

N::::;

N

<2PT
--

eff -

'lI"e

N

1 P;.

2B s = actual transmission bandwidth, upper bound uncertain
(Ref. 20)

~ 2'l1"e N

eff

1 (4) PT (S)
1 (4) P;.
1 N ~ N eff::::; 2'l1"e 1 N

~ PT (BT)2::::; (§..)

'lI"e

NBs

N

~ (~)'ff ~
PT

Ii

::;
eff

~ PT (BT)2
'lI"

NBs

[2(2K - I)]'

-I

>
r-

PT = 16,B
N

PTI
N

1

=

-;log2 K

PTBT
N Bs

Sp

N

Bs

=-;

,BBT = actual RF bandwidth
BT = max. frequency deviation
..
. BT
5
,B ~ 3 f or deVIatIOn
ratIOS 13 =
(Ref. 7, p. 51)
s
n = no. of bits = log2 K
K = dynamic range

! =
8

---PT

BT

PT

BT

N

Bs

-=16N
Bs
- = 16-

20-db, error rate

~

10-6

Peak power limitation:
Values of 8 ranging from 1 to
0.01 reported in literature
Average power limitation P T =

P;.(Bs/B T )
Pulse position modu--BT
S
lation of an ampliPT = 16,BPeak power limitation
p N '4 Bs
N
Bs
tude-modulated
carrier
S)
..
. ,
Max. signal output power
.
( -N eff = effectIve SIgnal to nOIse power ratIO of system referred to output =
Average nOIse power

P;.1 BT

zo

c:
CJ)
;;:c

2'l1"e 3

SA PT (BT)2

PPM-DSB-AM

-t..:J

Remarks

Threshold

)eff

()

o
Z

-I

;;:c

or-

CJ)

-<

CJ)

-I

m

~

15-23

TRANSMISSION SYSTEMS

I
80

>-~[I I]wIDSB-AM
I I

f-

=

Actual RF bandwidth
Effective transmission
bandwidth

/Synchronous
detection

70

-

I--

PS

r--

60

<

1\

\

Q)

"'C

40

~i~

=2

~~FM~~ "C.onv.en~ional.
(3
~% ~ ~
dlscrlmmator

\

\ I'\.

10

--.......

Average power _~
limitation

~ ~~

-~

~l--

Threshold _
peak amplitude
= 4 (I
noise)_

~>:'
~
:(~)

~ I~direct
./

Sha "V,

V

~

~~~~

<*-)
r-...

20

...............

PCM-OS8-AM
w /Synchronous
~~
detection
~
5l'-'
= 20 db
eff
·PCM·
i......,
'a. PCM I
<::

1\

30

IPPM!

@.~

\

en

OJ

.0
'(3

I'-~

ftd~

\

50

k power

.

eff

=

II
30db-

_lIc:lIl:>IIII:>:>IUIi

IUILI"]'

o
1

2

3 4 5

10

20

30 4050

100

200 300

(3B~T, transmission bandwidth
FIG.

6. Power and bandwidth exchange for transmission of signal having a dynamic
range of 1000: 1 and bandwidth B s'

position modulation system, the total power required will be comparable to
that required for the PCM systems. For PCM-FM system, a signal-tonoise ratio of 30 db was used in order to obtain a deviation ratio of 2.5 to 5.
The 30 db was necessary in order to maintain the power level above the
threshold. Note that for PCM-FM the threshold is obtained relative to
f3 (BTl Bs) = 10 since the output frequency of the PCM modulator is ten
times the input frequency. If phase lock demodulators are used for the
FM systems, the threshold can be reduced by 10 to 20 db. (See Sect. 4,
FM Demodulation and System Errors.)
An alternate method of comparing transmission systems has been proposed by Halina (Ref. 39) which relates the actual bandwidth and power
characteristics of systems to the information capacity.

15-24

INDUSTRIAL CONTROL SYSTEMS

Digital Codes

The use of digital codes other than straight binary in transmission systems can usually be identified with one of the following requirements:
1.
2.
3.
4.

Codes required to correct for apparatus limitations.
Codes which compress information into less time or bandwidth.
Codes which reduce errors due to random system disturbances.
Codes which are basically decimal for operator convenience.

Operators are accustomed to information in the decimal notation. The
trend in modern communication systems is to employ binary pulse transmission. If this is carried to the extreme, information will be coded as
a binary number, and the final user must either memorize the binary number system or have a binary-to-decimal converter at his disposal.
For a message with a dynamic range of 1000:1, a 10-bit binary code
must be used to transmit the information. If the number were transmitted
in decimal notation, then 30 bits (3 X 10) would be required and the
channel capacity would be increased by a factor of 3. A compromise between these two extremes would be to code individual decimal digits in
binary notation and to send 12 binary bits (3 groups of 4 bits) for a system
having a dynamic range of 1000: 1. The user is now required to memorize
only the ten binary numbers 0-9. This code, called binary-coded: decimal
(BCD) , is shown in Fig. 7. It requires a 200/0 increase over straight binary
in channel capacity (10 to 12 bits per sample).
Codes Designed to Compensate for Apparatus Limitations. A characteristic of the BCD code is that in going from number to number (e.g.,
3 to 4), the values of two or more of the binary bits may change. In devices such as shaft position digitizers, a group of four brushes per decimal
digit is used to read the code corresponding to the position of the shaft.
It is impossible to align the brushes so that in going from one number to
the next the binary bits all change at exactly the same time. Thus, if the
code is changing from 3 (0011) to a 4 (0100) and the "l's" bit goes to 0
before the "4's" bit changes to a 1, a reading of 2 (0010) will be obtained.
This problem can be solved by using codes in which the value of only one
bit changes in going from one number to another. Two of these codes, the
reflected binary (Gray code) and cyclic binary decimal, are illustrated in
Fig. 7. Note that the reflected binary code cannot be used as a reflected
binary-coded decimal code because of errors that can occur during change
between decimal digits 9 and 10 (00001101 and 00010000).
Thus, the reflected binary code solves the ambiguity problem, but the
decoding and visual interpretation problem are just as bad as for the
straight binary. A solution to this problem suggested by Glixon (Ref. 16)

TRANSMISSION SYSTEMS
Decimal
Number

0
1
2
3
4
5
6
7
8
9
10
11

12
13
14
15
16
17
18
19
20
100
1023

BCD
Binary

0000
0001
0010
0011
0100
0101
0110
0111
1000
1001
1010
1011
1100
1101
1110
1111
10000
10001
10010
10011
10100
1100100
1111111111

8421
0000
0001
0010
0011
0100
0101
0110
0111
1000
1001
1010
1011
1100

15-25

Reflected
Binary

Cyclic Binary
Decimal

0000
0001
0011
0010
0110
0111
0101
0100
1100
1101
1111
1110
1010
1011
1001
1000
11000
11001
11011
11010
11110
1010110
1000000000

0000
0001
0011
0010
0110
0111
0101
0100
1100
1000
11000
11001
11011
11010
11110
11111
11101
11100
10100
10000
110000
11000000
1100000110010

FIG. 7. Digital decimal codes.

is to combine the reflected and binary decimal code into a cyclic binary
decimal code that is easy both to decode and to interpret.
Error-Detecting and Correcting Codes. The impetus for the develop~
ment of codes which would detect errors was provided initially by the
need for a reliable method of teletype radio communication (Ref. 23) in
the presence of fading. Initial efforts were directed toward methods that
would detect one or two errors per code group. The development of the
digital computer and attempts to improve the reliability of communications systems led to more sophisticated codes that would detect and correct
errors.
The construction of noise- or error-reducing codes is typically approached by utilizing redundant or excess binary bits to represent a
single symbol or measurement; e.g., more than 4 bits for the decimal numbers 0-9.
These codes are called systematic codes and are based on using k out of
a total of m binary bits for error detection or correction. Thus n bits
represent the information, k bits represent redundancy (for checking),
and
Total = m = n
k binary bits.

+

The ratio min = R is the redundancy and is a measure of the efficiency
of the code (Ref. 17).

15-26

INDUSTRIAL CONTROL SYSTEMS

Parity Check-Single Error Detection. Single error detection codes
use an additional bit, called the parity bit, to detect single errors. Parity
check is defined as odd or even in the sense that the sum of one's in a
symbol code is odd or even. Thus, for example, the decimal number 7 in
BCD with even parity check would require a parity bit, but it would not
if an odd parity scheme were employed. Table 5 illustrates the use of
an odd parity check bit.
TABLE 5. ODD BIT PARITY CHECK
Decimal
Parity
Number
8421
Bit
0000
1
0
0001
1
0
0101
5
1
0110
1
6

Sum
1
1
3
3

Hamming Codes. The construction of single error correcting codes has
been described by Hamming (Ref. 17). The number of check bits k required for a given number of message bits is shown in Table 6. From the
table, for m = 4, k = 3, and thus a total of 7 bits per BCD symbol are
required to correct single errors. Hence, a total of 7 X 4 = 28 bits are required for 0.1 % data samples as compared to 12 bits for BCD and 10 for
straight binary. Note that k increases from j - 1 to j at the number 2j
and remains constant until the number 2 j +1 is reached. An elegant description of the single error correcting code is given in Ref. 18.
TABLE 6.

HAMMING'S SINGLE ERROR CORRECTING CODES
n,
k,
Message Bits
Redundancy Bit
Total No. Bits
m,
1
2

o
o

3

1
1

4
5
6
7
8
9
10
11

2
3

4
4

5
6

7

12

8
9
10
11
11
Etc.

13

14

15
16

m= n

+ k = total bits per symbol

1
2
2
3
3

3
3

4
4
4
4
4
4
4
4
5

\
TRANSMISSION SYSTEMS

15-27

Power Efficiency of Redundant Codes. Voelcker (Ref. 19) has evaluated the efficiency of error-correcting codes on the basis of power gain.
The conventional 5-bit (32 character) Baudot code used in Teletype communications was used as a standard of comparison. Two distinct approaches were considered: (1) systems in which one way transmission is
used and coding is used for error detection and correction, and (2) systems
in which coding is used only for error detecting and retransmission is used
for error correction.
In the latter system, called "Decision Feedback Systems," each character or symbol is checked for errors. If no error is detected, the character is accepted. If an error is detected, the error detector in the
receiver automatically signals the transmitter to repeat the character.
Two types of error-detecting codes were considered for the "Decision
Feedback Systems": (a) a 6-bit parity check code (5 message bits,
1 check bit), and (b) a 7-bit constant ratio code. This code, the Moore
code, is termed constant ratio because 3 of the 7 bits are constrained to be
a 1 (the remaining 4 bits are zeros). This 7-bit code contains 35 useful
characters and will detect one, three, or five errors but not two or four
errors.
For the one-way transmission systems, a 9-bit Hamming code was selected in which 5 bits were used for the message and 4 bits for checking
and error correcting.
The results for the various systems are shown in Fig. 8 and include the
evaluation of each of the systems for fading signal with additive noise.
The fading signals were assumed to exhibit Rayleigh characteristics.
Two limiting fading rates are considered: fast fading such that independent signal levels are obtained for adjacent binary bits, and slow
fading in which the fading is slow enough to result in essentially constant signal level during the duration of a single character (7 bits). Experience indicates that slow fading is a more realistic assumption. It is
further assumed that linear synchronous detection is used and the transmitter and receiver are synchronized.
The results of Fig. 8 confirm the conclusions set forth by Laemmel
(Refs. 13 and 14) that error-correcting codes are uneconomical in view
of the small increase in power required to obtain the same improvement.
This is particularly true when the cost of the elaborate equipment required
to detect and correct errors is considered.
4. FM DEMODULATION AND SYSTEM ERRORS

The equipment required for demodulation of FM signals typically consists of a bandpass filter, limiter, discriminator, and a low-pass filter as
indicated in Fig. 9. In telemetry or carrier frequency application, the

10,0

3

l11
Ul

Q)

2

Ul

Q)

.a

'u
CU

Oro

C

-c

"c'

Oro

0

co

Qj

0

a.

L

10- 5

10- 4

10 -3

10- 2

Probability of output character errors

(a)

(c)

10- 1

0

c

:::a

>

r-

50
Hamming code

20

I

"f.I)

Q)

'0

15

"c'

10

ona

n

a

Ul-o

40

z-I

~o
cc

30

ar-

20

U'l

Ul.!::

Parity check code

CUro
u
_

with feedback

'-..c
c:~
'00 ;:
~-g

CU

na

:::a

-<

U'l
-I

E.=

5

c:::l
._ 0-

D

..........
CUCU
;:;:

rocu

10

m

~

tl.O .....

0

.a..

-5

Z
U'l
-I

60

25

;:

0

Probability of output character errors

30

Qj

2,5

10- 1

10- 5

Oro

5,0

Qj

;:

~ -1
.a..

..c

(X)

..c

'u
CU

co

tv

7.5

U'l

0

00
a.C-

L

10- 5

-10
10- 4

10- 2

10- 1

10- 5

10-'

10- 4

Probability of output character errors

Probability of output character errors

(b)

(d)

FIG. 8. Power efficiency of redundant codes and decision feedback transmission systems: (a) nonfading signal; (b) fast-

fading signal; (c) slow-fading signal; (d) standard Teletype system.

t)

TRANSMISSION SYSTEMS

15-29

Clear signal

Input~
filter of

tone~

"AMA
Noisy signal
FIG. 9. FM demodulation.

bandpass filter is used to separate the desired channel from adjacent channels in a frequency-multiplexed carrier. In radio reception, the bandpass
filter is the IF amplifier which provides the selectivity for separating adjacent channels. The signal from the output of the bandpass filter is clipped
or squared off to remove amplitude modulation, and the resulting signal
is sent to the discriminator which performs the function of FM-to-AM
conversion. The ideal discriminator provides an instantaneous output
voltage which is proportional to the deviation of the instantaneous frequency from the carrier or reference frequency. The output of the ideal
discriminator is then a perfect reproduction of the signal modulating the
transmitter or FM oscillator.
FM Discrimination Based on Zero Axis Crossing. In the system of
Fig. 9 the discriminator sends out equal strength impulses for every crossing of the zero axis. The low-pass output filter smooths these impulses
into a relatively slowly varying voltage, the reconstructed signal. For this
example, frequency is measured as the average rate of zero axis crossings,
and the averaging is accomplished by the low-pass filter having a time
constant To = 1/2·l1B o. If the axis crossings of the limiter output were
counted by a counter for a period of time T e, the output of the counter
could be the average rate of zero axis crossings during the interval Te.
Note that these two averages are not the same; the counter perfectly retains the information for the period Te and discards it entirely and instantaneously before starting a new count. The low-pass filter, on the
other hand, provides a weighted average. Physically this means that
at any time t the output of the filter is equal to the sum of the contributions from the input at all past times. Each input pulse appears
in the output multiplied by the weighting function Ke- tiT where t is
the time interval between the present time t and the time of occurrence of
the particular input pulse; T is the time constant of the filter. Ke - tiT
thus specifies the weight with which any input at any past moment contributes to the present output.

INDUSTRIAL CONTROL SYSTEMS

15-30

Discriminator with Dual Resonant Circuits. Another common form
of discriminator, Fig. 10, measures frequency by impressing the FM signal
on two resonant circuits which are tuned to different frequencies. The
voltage developed across the two tuned circuits is rectified and the difference of the rectified voltages is a measure of the frequency (Refs. 24 and
25) .

r-------------------------l
Bandpass filter

B

1

.

I

"

1

Center freq. f1

+1

FM input

_I
I

Bandpass filter
B2
Center freq. f2

Low-pass
filter

Output
I-----'-~

Bo

1
1

- - - - _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ JI

Discriminator

Amplitude
response

Input to low-pass
filter proportional to
difference between
two response curves

Overall discriminator characteristic

FIG. 10. Conventional FM discriminator.

FM-Threshold Phenomena. In the example of Fig. 9, when the
carrier amplitude is of the same order of magnitude as the noise. voltage
in the circuit, some of the axis crossings do not occur and, in addition,
new axis crossings appear which are independent of the signal. The discriminator output now contains appreciable noise components, some of
which will appear in the output of the low-pass filter. It is intuitively obvious that the transition from normal operation tb noisy operation occurs

15-31

TRANSMISSION SYSTEMS

when the carrier SIN is small and limiting action fails. This is the familiar
threshold phenomena of FM systems and for the type of demodulators
described above is a function of both SIN and the limiter characteristics.
Middleton (Refs. 26, 27, 28, and 29) has developed the relations for
signal-to-noise ratios at the output of an FM system as a function of the
input signal-to-noise ratio, clipping level, and bandpass and audio filter
characteristics. The problem is solved on a general basis for both narrow
band and wide band FM where:
N arrow band FM: Maximum carrier frequency deviation is of same
order of magnitude as highest modulating frequency.
Wide band FM: Maximum carrier frequency deviation is considerably
greater than highest modulating frequency.

Narrow Band FM
For the narrow band FM case (Fig. 11) consider the system consisting
of a band pass or IF filter having a half-power bandwidth B%, a limiter,
and a discriminator. For carrier-to-noise power ratios in excess of 10,
Output

~

In

=

(NS)

C~)

Gaussian
IF or bandpass filter
Center frequency
Bandwidth Be

Limiter

=to

Ro

Discriminator

~

Ao

y 2bO

input = aO =

Ao = carrier peak amplitude
bo = mean noise power in
bandwidth = Be

Limiter

Discriminator

Wide band frequency
response-no distortion
of clipped wave
Ro = saturation level

Linear response vs. frequency for all frequencies
appearing at output of
limiter

Ro

ro=~

FIG. 11. Narrow-band FM demodulation system.

Middleton derives the expressions for output (SIN) I for the two extremes
of no limiting and heavy limiting.
No Limiting. Narrow Band FM.
where ao 2

> 10,

r 2 -<

.1
2,

ao =

V2b0'

Ao

Ao = peak carrier amplitude,
bo = mean noise power.

15-32

INDUSTRIAL CONTROL SYSTEMS

Heavy Limiting. Narrow Band FM.

The quantity ao is the ratio of rms carrier to rms noise and r is a ratio of
the rms modulation to a bandwidth factor that is a function of the spectral
distribution of the noise. The definition of (S / N)I is

where P s = measure of signal power associated with the modulation,
P de = d-c power component appearing in the output,
Ne = mean power associated with noise alone and including modulation cross product components generated by the nonlinear
discriminator-limiter operating on signal and noise but excluding dc.
The noise at the output of the IF or bandpass filter has a mean noise
power bo and a spectral distribution W(f). A bandwidth factor p is used to
characterize the noise:
b2

2

p

=-

bo

where bn =

--

Mean squared value of noise power spectrum about

Wo

Mean noise power

i~ (w -

wo)nW(f)

dl,

W (f) = spectral noise power distribution at 'output of bandpass or
IF filter.

The b'sare called the moments of the distribution about the frequency woo
The zeroth moment bo is equal to the mean noise power of the noise signal
described by W(f), and b1 equals the mean value of noise power spectrum
about the frequency woo If the distribution is symmetrical about wo, the
mean b1 will be zero. The second moment b2 is equivalent to the radius of
gyration of the noise power spectrum about the frequency woo If the distribution is symmetrical about Wo, the mean is zero and b2 is simply the
variance or square of the standard deviation of the noise power spectrum
referred to the frequency woo This follows since the variance (7"2 is defined
as the mean-squared value about the mean (Ref. 59):
(7"2

= b2

-

(b 1 )2 = Variance of power spectrum about mean.

TRANSMISSION SYSTEMS

15-33

The quantity r in the expressions for the signal-to-noise ratio is the ratio
of the rms modulation to the noise factor p defined above:

r

Rms modulation

= ------------p

Thus r is a ratio of the rms modulation to a bandwidth factor that is a
function of the spectral distribution of the noise.
Although the above expressions apply only for ao greater than 10, the
original work (Ref. 26) covers the case of ao ~ 1 where the noise power
equals or exceeds the cp,rrier power. Figure 12 is reproduced from the
original work and indicates the signal-to-noise ratio for narrow band FM
when the modulation is sinusoidal and the system is as indicated in Fig. 11.
For the example given in the figures, the signal is given by Refs. 6 and 26:

Vet) = Ao cos CWet
=

[Ve

+ 1/;) + VnCt),

+ Ao cos CWdt + 1/;)] cos wot -

[Vs

+ AoCwdt + 1/;)] sin wet,

20~--~--------~--------~------~

Modulation sinusoidal
Max. frequency deviation= 0.424 B~

15 Bx = 2"1 Power bandwidth
Li~iting level = ro = ... ~
10

r 2 =!

v 2bo

2

5~---4--------~----~~+-------~

.VI

Q)

o~--~--------~~~~--+-------~

.c

·u
Q)
~~

-5~--~------~~~~~--+-------~

.-::::
Cl)1:z;
~ -10~--~----~~~~~----+-------~

-15~--~--~~~-W--------~------~

-25~~~~--~--~--------+-------~

o
S
( -N).

Input

10

20

= _ ~ , decibels
,, 2b o

FIG. 12. Narrow-band FM output signal-to-noise ratio.

15-34

INDUSTRIAL CONTROL SYSTEMS

where Ao = peak carrier amplitude,
Wd = detuning in cycles per second = fo - fe,
27r
fo = center frequency of bandpass filter,
fe = carrier frequency,

1
t

",(t)

=

Do(t) dt

= time integral of modulation,

Do(t) = angular modulation,
V net) is a Gaussian noise source limited in bandwidth to the IF or
bandpass filter bandwidth.
The total modulation cp is the sum of the detuning effect
signal modulation:

cp =
;p =
The quantity

t + 1/;,
Wd + tf =

Wd

and the

Wd

Wd

+ Do(t).

r is defined in terms of ;p:

r=

p2

where [;P(t)2]av represents the average mean square value of the total modulation.
For the specific case illustrated in Fig. 12, the modulation is sinusoidal
and it is assumed thatwd = o. The frequency modulation consists of a
single sine wave of maximum amplitude Do:

tf = Do cos wst.
Further, a Gaussian filter of bandwidth Bg (in cycles per second) is assumed
for the bandpass filter. For a Gaussian filter W(f) the power spectrum is

W(f)
The half-power bandwidth

=

B~

Wo

exp

(-l /B g2 ).

for a Gaussian filter is related to the Bg by

B~ = 2 (In 2)Y2Bg.

For the Gaussian filter
27rBg
p

7r(B Y2 )

= V2 = V (In 4) .

Hence, substituting an expression for

r=
Do =

Do/V2
p
_C

,
7r(BY2) _ C
2
vln4

pry 2 = _ r,-----; V

r.

TRANSMISSION SYSTEMS

The curves in Fig. 12 are drawn for

Do

15-35

r = ~. Thus
7r(B~)

=-_.
In (4)

Note that Do is the maximum angular deviation. For the case of sine wave
modulation, the maximum frequency deviation is Do/27r. Thus
Maximum frequency deviation =

~: =

0.424B 72 •

Wide Band FM
For wide band FM, the system of Fig. 11 includes, in addition, a low-pass
output filter having a bandwidth Bo. Two new variables are introduced to
characterize the system; these are
1lA
IJ.

= Bo/Bg,

= Do/w

ll •

where Ws = frequency of sine wave modulation (ws = 27rfs),
IJ. = deviation rate.
Note that the definition of IJ. is equivalent for sine wave modulation to
the frequency deviation ratio, since for sine wave modulation the frequency
deviation is Do/27r:
IJ. =

Do/27rfB = Frequency deviation/fB'

For the case when the carrier-to-noise ratio is large and r is again less
than or equal to one-half the signal-to-noise ratio (S/N)n is given by
Ref. 26:

where ao 2 » 1,

r2

~

t.

The modulation is sine wave and the limiting is heavy (Ro «A o),

Ro

=

limiter saturation level,

Ao

=

peak carrier amplitude,

Ao
ao=~'

15-36

INDUSTRIAL CONTROL SYSTEMS

- n- +
- .1 ·nA exp [- (n - 1) 2nA 2 ]
2

+ :M (n2nA2 + !){8[(n + l)nAl
and

an = {

- 8[(n - l)nA]}).

ao = 1,
an ~ 1 = 2,

J = Bessel functions,

E> = error function,

nA = -Bo [2(1n 2) Y22]
BY2

With the exception of OA, ft, and (SIN) II, all the quantities are defined as
in the narrow band case. The signal-to-noise ratio, (SIN) II in the case of
wide band FM, is referred to the output of the low-pass output filter.
Figure 13 illustrates the variation of output signal-to-noise ratio (SIN)u
as a function of carrier input level. It is assumed that the IF bandwidth
remains constant, that the modulation is sinusoidal, that r2 = Y2, and that
the deviation ratio ft is varied so that the frequency deviation remains
constant.
The curves of Fig. 13 indicate the FM threshold effect which occurs at
about a 10-db input signal-to-noise power ratio; below this point the output signal-to-noise falls at a rate proportional to the square of the deviation ratlo .. At some value of the input signal-to-noise less than 0 db, the
individual curves become tangent to lines having a slope of 2 [output
SIN varies as input (SIN) 2].
From the viewpoint of signal-to-noise degradation, a comparison of
Figs. 12 and 13 indicates that (a) narrow band FM is inferior to hroad
band FM for all input carrier levels; (b) limiting is detrimental in narrow band FM; (c) broad band FM with heavy limiting provides the best
performance, (Ref. 26 ) .
These remarks apply for ideal discriminators and wide band limiting
action. Departure from these conditions will typically increase the interference effects of noise versus signal, since filter characteristics that are
narrow compared to the spectrum of the amplitude-limited noise at output
of limiter will tend to restore randomness to the clipped wave and destroy
the limiter's action.

15-37

TRANSMISSION SYSTEMS
30.----.---------r--~--r_~·--~--~

20r---~--------~++~~~+_--~~~

10

VI

a;

.0

'0
Q)

'0

,-:::::
tfJl~
'-'"

0
OA

fJ.

2.0
1.0'

0.35
0.71

0.4
0.2
0.1
0.05

3.53
7.07
14.1

. 20 Jog

1.77

ao

lO
-20~~~~~~--~--~~~------~

-16

-10

0

10

2

db

Ao

ao =

v'2bO =

Rms carrier
Rms noise

An = peak carrier amplitude
bo

(N8)

IT

= mean noise power

l'

.

= signa -to-nOIse power ratIO
at output of low-pass filter

r2 =

!

(freq. deviation = 0.424 B!)

BH = half-power bandwidth of IF or bandpass filter
OA

(Boh
= --(ln2)7:':
1.!.

BH

Bo

=-

Bg

Bb = low-pass output filter bandwidth
Bg = Gaussian IF or bandpass filter bandwidth

J.L

Frequency deviation

Frequency deviation

= Modulating frequency =

is

.fs = sine wave modulating frequency

FIG. 13. Wide-band FM output S/ N vs. input S/ N for sine wave modulation.

15·38

INDUSTRIAL CONTROL SYSTEMS

Since the superiority of wide band FM depends heavily on limiting,
care should be exercised to provide limiter and discriminator characteristics that are wide compared to the IF bandwidth. The IF or bandpass
filter characteristics should have negligible delay or amplitude distortion
over the range of signals. If this condition is not realized, the bandpass
filter will act like a nonlinear discriminator, causing serious mixing of
signal and noise. For a discussion of errors introduced by the frequency
characteristics of discriminators, see Baghday (Ref. 38).
Threshold Effects for Systems Exchanging Power for Bandwidth.
The threshold effect observed for wide band FM is typical for transmission
systems that exchange power for bandwidth. For this general type of system, the output signal-to-noise ratio will vary with the input signal-tonoise ratio as indicated in Fig. 14. The SIN characteristic for these systems has three distinct regions:
Region 1: Output SIN varies directly as input SIN.
Region 2: Rapid loss of improvement gained by exchanging bandwidth
for power.
Region 3: Output SIN varies as the square of input SIN.
The square law characteristic of Region 3 is not peculiar to FM systems
but is also found for AM and other forms of modulation. The boundary
between Regions 1 and 2 is the threshold point of operation. For broad
band FM systems, the threshold occurs at an input SIN of approximately
10 db.
Phase Lock Discriminator-Synchronous FM Detection

The threshold value of 10 db is not unique to broad band FM and does
not represent an inherent lower bound for acceptable performance.
Rather, it is the result of the methods used to demodulate the FM wave.
For purposes of illustration, assume that a bandpass filter has a bandwidth of 1000 cps and that data or message bandwidth is 10 cps. For
the normal discriminator, the threshold occurs when the signal-to-noise
ratio of the carrier is 10 db. The limitation is the noise power of the carrier bandwidth and not the message bandwidth. It is obvious that a substantial improvement could be realized if the threshold were limited by the
noise power in the message bandwidth rather than in the carrier bandwidth. The phase lock or correlation discriminator approaches this end
result (Ref. 30).
Figure 15 illustrates the basic principle of the phase lock discriminator.
In this discriminator the output of the bandpass filter is applied to a phase

15-39

TRANSMISSION SYSTEMS

Improvement factor
due to
power-bandwidth
exchange

Systems which exchange
bandwidth for power ~

'- Ideal system with. no
"'- power-bandwidth
exchange

(~ )output

Threshold

t

Region 3

Region 2

Region 1

(

)

Rapid loss of
improvement
gained by
exchanging
bandwidth
for power

( N~)outputoc(~)
N input

FIG. 14. Signal-to-noise variations in vicinity of threshold region.

~

Bandpass
Phase detector
filter
~
(multiplier)
bandwidth Be

~

Phase lock
loop filter

f-~

i
Voltage controlled
oscillator covering
bandwidth Be
FIG. 15. Phase lock discriminator.

Output
filter

Bo'::5.Bs

~

INDUSTRIAL CONTROL SYSTEMS

15-40

detector where it is literally multiplied by the signal from the voltagecontrolled oscillator (VeO) whose output is a linear function of its input.
The output of the phase detector is filtered by a loop filter, the output of
which is applied to the veo to close the loop. The effect of the feedback
loop is to lock the oscillator at the frequency of the incoming signal and
90° out of phase with it. The design of the loop filter is critical and is
optimized to minimize the phase error between the signal and veo output
over the range of specified input signals. The response of the phase lock
servo loop is typically limited to the information or message bandwidth
Bo (where Bo ::::::: Bs). The voltage input to the veo is a measure of the
frequency of the input signal.
The threshold for this system occurs when the servo loop loses synchronization. This normally occurs when the rms phase jitter between the
input signal and the veo signal has a magnitude of approximately 60°.
For a carefully designed servo loop, a rms phase error of 60° will occur
when
RmS carrier)2
(

Rms noise

A02

threshold phase lock =

3Bp

2b o = 4 V 2 (B 72)

V12imax
where Bp = the largest of the quantities, { _ ;4 v f,
f = frequency of signal being tracked by phase lock loop,
j max. = maximum rate of change of frequency f in cycles per second 2.
For sine wave modulation, the frequency modulation consists of a single
sine wave of amplitude Do:

DoCt) = Do cos wst radians/sec

= (Do/27r) Ccos wst) cycles/sec 2.

or

The frequency deviation is Do/27r cps. The maximum rate of change of
frequency

f. = -d (Do(t))
-dt

27r

max

wsDo
cycles/sec2.
27r

= --

Hence
B =
P

o.
J12W,D
27r

TRANSMISSION SYSTEMS

15-41

Assuming r2 = 72, as in the case of the linear discriminator, the one-half
power bandwidth of the IF or bandpass filter is related to Do/27r', the maximum frequency deviation, by

Do/27r' = 0.424B 72'
By substituting the expressions for By?' and Bp in the threshold equation

RmS carrier)2
(

Rms noise

threshold phase lock

r-.J2

Modulation frequency
Frequency deviation

Thus, for sine wave modulation, the threshold signal-to-noise power ratio
varies inversely as the square root of the frequency deviation.
For a frequency deviation of 100: 1, the threshold will occur at -14 db
for the phase lock loop as compared to + 10 db for the linear discriminator. The phase lock discriminator thus provides a means to extend the exchange of bandwidth for power and permit a greater power reduction
factor or, conversely, for a given dynamic range, the phase lock discriminator will permit operation at thresholds 10 to 30 db below that possible
for conventional discriminators.
The rms phase jitter Un for the phase lock loop (Ref. 30) in radians
per second is
CT n

where

3b oBp

= peak carrier level at threshold,
2v 2 B72
bo = mean noise power in bandwidth B 72 ,
CT n = rms phase jitter in radians.

AOt

=

=

_ /-

For sine wave modulation, the maximum angular deviation in radians is

1/Imax

= Dolw s radians maximum,
=

Dol ( v'2 w s ) radians rms.

INDUSTRIAL CONTROL SYSTEMS

15-42

The effective output signal-to-noise ratio will be

=
( 8)
N eff

(Do/0 ws)2

phase lock loop at threshold ern

ern

Hence:

( 8)

Neff threshold

= (_

~o

-V

_)2 =

2 Ws

!

(frequency deviation ratio)2.

FM Transmission System Transient Errors

The analysis of the transmission of variable frequency signals through
filters and other circuit elements is difficult. In general, the principle of
superposition is not valid and the rise time, overshoot, and nature of the
transient response depend upon the size of transient and the position of
the signal with respect to the center frequency of the filter or element
(Refs. 31, 32, 33, and 34).
Two general methods are available for approaching this problem, the
spectral approach and the dynamic approach. In the spectral approach,
transmission of the signal is analyzed in terms of its individual components. The usefulness of this method is limited by the complexity of the
computations. Papers by Carson and Fry (Refs. 35, 36, 37, and 40) appear to be the earliest publications discussing the dynamic response of a
linear system with variable frequency signals.
The basic viewpoint in the dynamic method is that the dynamic responses can be broken up into two components-the quasi-stationary component and the distortion component. The quasi-stationary component
represents the part of the response that is obtained from conventional sinusoidal steady-state circuit theory by substituting the variable instantaneous frequency for the assumed constant frequency.
In practical systems, the sluggishness of a filter or element will set a
limit on the speed with which the output can faithfully follow the input
frequency excursions. Thus the instantaneous output frequency will deviate from the assumed steady-state or quasi-stationary value by an
amount equal to the distortion or error component.
Baghday (Ref. 38) has extended the work of Carson and Fry to arrive
at an explicit statement for the maximum magnitude of the transient
error as a function of the rate of change of input frequency and the
characteristics of the filter or system.

TRANSMISSION SYSTEMS

15-43

Consider a signal or excitation having an instantaneous frequency

W8:

+ dt/;/dt,

Ws(t)

=

We

We

=

Carrier frequency,

dt/;/dt = Do(t) = Angular frequency modulation,
t

t/; =

f Do(t) dt

=

Phase deviation,

Do(t)/27r = Frequency modulation in cycles per second.

The system or element is assumed to have a linear characteristic and
the input signal is assumed to have a finite spectrum or the error in assum-

Continuous
frequency o----~
modulated
signal

Linear transmission
system element with
characteristic function
Z(jw)

Output ideal
(Steady state)
I -_ _~ response plus
error terms

(j {Linear with no poles on jw
Z w) axis or in the right half-plane

FIG. 16. Transmission system errors.

ing a finite spectrum is negligible (Fig. 16). The output dynamic response
of the system should closely follow the steady-state response as predicted
by a-c steady-state circuit theory.
The maximum fractional instantaneous error, the difference between
the ideal or quasi-static response and the actual response, will be equal
to or less than
o(t))max· (Z"(jw))
--.«1,
Z(Jw) max

1,

Errormax~ 2(D

dDo(t)
where D' oCt) = - - - ,
dt
Do(t) = angular modulation,
Do(t)
- - = frequency modulation in cycles per second,
27r
d2 Ze )
Z"( 'w) =
JW ,
J
d(jw)2

Error max = (

Actual response - Ideal response)
Ideal response

max

.

15-44

INDUSTRIAL CONTROL SYSTEMS

The above bound for the error is the most restrictive and applies for
all types of modulation of the FM carrier. If the modulation, variation of
frequency, is sinusoidal, a less restrictive bound for the maximum error
can be used:
Error max periodic ~!
.

(

Z"(jw)
ID'oCt) I· --.-.
1

Z(Jw)

I)

max

«

L

The restrictive form of the error limits in which the individual maximums
are multiplied specifies the magnitude of the error that will not be exceeded, regardless of which part of the filter or element response characteristic is being swept by the variable instantaneous frequency.
It is thus applicable to the general problem of spectrum analysis in
which the element is scanned with a variable frequency source. As a
simple example assume

dy;
-

dt

Do(t)

=

=

Do cos wst,

D

~ = Frequency deviation ratio,
Ws

Do

Maximum angular frequency deviation.

=

~hus

If the filter consists of a single-tuned parallel high-Q circuit, then
Z(jw) =

v (. )

~
Vi (jw)

1
= -------

1

+ jew -

wo)/rrB

Wo = Center frequency,

7rB = One-half the overall bandwidth
half-power points,
27rB

27rBYl

2

2

=--=--.

III

radians per second between

TRANSMISSION SYSTEMS

15-45

The maximum value of Z"(jW)jZ(jw) occurs at w - w~ = 0 and has a magnitude of 1j(7rB)2. Hence
Ws
Do
Error max ~ - • - « 1,
7rB 7rB
is

ideviation

<--.
,
= By)2
By)2

where ideviation is the frequency deviation in cycles per second.
This condition states that the product of the modulation frequency and
the maximum frequency deviation, when each is measured in units of onehalf the filter bandwidth, is equal to the maximum transient error provided this error is small «10%). The same result has been obtained by
Clavier (Ref. 34).
The appearance of the Z"(jw) term in the expression for the errors emphasizes the importance of considering the phase characteristics of filters
in addition to the amplitude characteristics. The specification, of a maximum error, is in effect a restriction on the variation of the time delay
characteristics of the filter over the swept frequency range.
Filter Characteristics. ' For common types of filters, the quantity
Z" (jw) jZ (jw) is always expressible in the form
Z"(jw) I
-----

I Z(jw)

max

Kmax

= -----,
2
(27rB)

where Kmax = maximum sluggishness index,
27rB = bandwidth in radians per second between half-power points.
The sluggishness index K is a single parameter which relates the time
delay characteristics of filters of widely varying form. For a given bandwidth, it is directly proportional to the quantity Z" (jw) jZ(jw) . Kmax
refers to the maximum value of the quantity Z" jZ. In practice it is often
convenient to operate over a fraction of the filter bandwidth. In this
instance the effective sluggishness index Keff should be used, where Keff
is the.,maximum value of K over the range of swept frequencies.
Baghday (Ref. 38) has plotted the characteristics of conventional filters
as a function of the deviation from center frequency (Figs. 17 and 18).
The results are normalized, and for the high-Q parallel resonant circuit and
the nth-order Butterworth filters the ordinate is the effective sluggishness
index K eff • vVith ~he exception of the high-Q parallel resonant circuit, the

INDUSTRIAL CONTROL SYSTEMS

15-46

effective sluggishness index is the quantity that applies for a particular
filter providing the signal frequency does not sweep beyond the frequency
at which Keff is determined. By using only a fraction (0.4 to 0.7) of the
half-power bandwidth, the advantage of the high attenuation character-

1i 24 -

27rBls

~

x~
.!::

~

6.0
5.6
~ 5.2
] 4.8
~ 4.4
~ 4.0

=Y, power bandwidth(radians/sec)

=

max. deviation from center freq.

20

~ 16 -

.c

'So 3.6

c:

~ 3.2 -

~

'[8 12

~C1J 2.8

:::l

Vi

~

~

8

2.4

-

E 2.0

~

ffi

,....---r--.-----.----,----r---,-,.--,...--,----,

~ 1.6

4-

o

1.2
0.2

0.4
x

0.6
~

0.8

1.0

1.2

1.4

1.6

o

1.0

(units of 7rBy,)

.
Z(Jw) =

4.0

5.0

(b)

(a)

N ormarlze d sIUgglS
. h ness m
. d ex
tuned amplifier

3.0

2.0

y --- (units of (j)

=

4[n(n

Keff
+ 1)(21/n

_ 1)] each st age a high-Q'
smgIe-

1

(1 + f - fo)n
Bd2
27rBn

{3 = -2-

Bl

.
radians/sec

= bandwidth of a single section, cycles per second

Bn = overall bandwidth, cycles per second
y

= max. deviation from center frequency wo

FIG. 17. n identical cascaded single-tuned amplifiers: (a) sluggishness index as a
function of filter bandwidth utilization, (b) normalized sluggishness index as a function of overall bandwidth utilization.

istic of a 6th-order Butterworth can be realized with a sluggishness index
of a 4th-order filter. In the case of the high-Q parallel resonant circuit,
the maximum value of K occurs at the .center frequency, and this value
should be used. Figure 18 presents the effective sluggishness index for n
identical cascaded amplifiers. Note that f3 is the effective half-power
bandwidth of the n stages. 2nB is still considered as the half-power band-

15-47

TRANSMISSION SYSTEMS

width of a single stage. In order to obtain the effective sluggishness index,
it is necessary to multiply the ordinate by the bracketed term which is a
function of n, the number of stages.

211B

:::: 280

radians/sec
max. deviation from
center freq uency

240

~ 3.0
.~ 2.8

Q)

-c

.=:!l

III

200

~ 2.6

~ 2.4

Q)

c:
.r::
III

160

'gjj
::J

'iii

r--..---r---r---.,.----r----.----.--,---,--,---r-~

3.2

"=

~'"
x~

3.4

= ~ power bandwidth,

~ 2.2

120

-c

~
u

80

.~
"iii

Li:j

40

~ 1.6

Q)

2.0

E 1.8

~

2

3 456

1.4

o

0.2

0.4 0.6
x

0.8 1.0

~ (units

1.2

1.4

o 0.2

1.6

0.6

1.0

(a)
Keff

+ 1) v_ / 2 lin

2.2

2.6

- 11

each stage a second order

1

(f Bd2
- fO) _jy2 (f Bd2
- fO)J
2'

[

(3

1.8
of (3)

(b)

..
.
Norma1Ized sluggIshness mdex =
4[2n(2n
Butterworth
.
Z(Jw) =

1.4

y~(units

of a)

1 _

21l"Bn

n

.

= -2- radIans/sec
BI = bandwidth of a single section, cylces per second

Bn = overall bandwidth, cycles per second
y

= max. deviation from center frequency wo

FIG. 18. n identical cascaded Butterworth tuned amplifiers: (a) nth-order Butterworth filter sluggishness index as a function of filter bandwidth utilization, (b) normalized sluggishness index as a function of overall bandwidth utilization.

Table 7 lists the pertinent characteristics of the filters. The ButterVlorth filter is usually characterized by a pole pattern in which the poles
fall on a semicircle whose center lies on the jw axis and whose radius equals
one-half the overall bandwidth of the filter between half-power points.
The exact position of the poles of an nth-order Butterworth filter are at
the locations of the 2nth roots of (-1) n+l that lie in the left half-plane.

INDUSTRIAL CONTROL SYSTEMS

15-48

TABLE

7.

FILTER CHARACTERISTICS

Butterworth Bandpass Filters

n=/
a

- /0 = frequency deviation from center frequency of the filter
= B /2 = t overall bandwidth (in cycles per second) between half-power points
Filter
High-Q parallel resonant circuit

Z(jw)
1

1

+ f (~)

Second order Butterworth
(critically coupled, or flatstaggered high-Q pair)

1

Third order Butterworth

Cascaded tuned amplifiers
n identical stages, a

=

half-bandwidth of each stage

Single Stage Filter

Overall Z (jw )

Single-tuned,
high-Q, parallel
resonant circuit

1

Second order
Butterworth

1

{3 = half overall
bandwidth

Specification of Filter Bandwidths. The dynamic and static responses
of transmission filters approach each other as the error becomes small.
Instead of expressing the error as a function of the rate of change of frequency and the filter sluggishness, it is convenient to express the bandwidth required for a given error and input signal:

2nB = KV I D" oCt) I max
where B = half-power bandwidth in cycles per second,

.K =
Keff

/K eff ,

~ 2e

= maximum value of sluggishness index over range of frequencies
swept by input signal DoCt),

E

= maximum fractional error.

TRANSMISSION SYSTEMS

15-49

5. AM DETECTION AND SYSTEM ERRORS

Amplitude modulation describes a class of systems in which the basic
principle is the. multiplication of the signal by a periodic function of time.
The frequency of 'the periodic function is called the carrier frequency ie.
For each frequency is present in the signal, the amplitude modulation or
multiplying process gives rise to a pair of frequencies displaced from the
carrier frequency by is as indicated in Fig. 19.
The effect of the modulation is thus to shift the signal spectrum into two
sidebands symmetrically displaced about the carrier frequency. These
sidebands contain all the information in the original signal. The amplitude of each sideband component is equal to one-half the corresponding
amplitude in the original signal.
If the periodic multiplying function is a sine wave, all the sideband
components are centered about the carrier fundamental frequency. For
M(t)
where M(t)
V (t)

= Vg (t) cos We t
= amplitude modulated waveform
= signal waveform
Amplitude
modulated
signal

Signal-r--~

I

I

Lower
sideband

I

i

\
Upper
sideband

I

A

I
I
I

A

"2
Frequency

~

(a)

Amplitude
modulated
signal

\

I

Upper
sideband

Lower
sideband
Signal
amplitude
spectrum

Frequency - -

(b)

FIG. 19. Frequency spectrum of an amplitude-modulated signal modulated by a sine

wave carrier: (a) single frequency signal; (b) signal complex with bandwidth Bs'

15-50

INDUSTRIAL CONTROL SYSTEMS

the general case of multiplication by an arbitrary periodic function, sideband components are produced at harmonic multiples of the carrier frequency in addition to the pair of sidebands centered on the fundamental.
If the complex modulated wave containing harmonic sidebands is passed
through a filter to eliminate the harmonic sidebands, the result is equivalent to modulation by sine wave carrier.
Other common forms of periodic multiplying functions are the square
wave and the impulse or sampling modulator. Full wave mechanical
choppers and solid state switching modulators are examples of modulators
using a square wave multiplying function. For this type of modulator,
the modulated signal includes the dominant sidebands centered at the carrier frequency Ie and, in addition, sideband pairs centered at all odd harmonics, nle (n odd), of the carrier frequency. The amplitude of the sidebands centered on the nth harmonic varies inversely as the order of the
harmonic, lin.
Classification of AM Systems. Amplitude modulated systems can be
grouped into three classifications depending on whether a carrier is added
to the sideband information. These are:
1. DSB-EC-AM: Double sideband-emitted carrier-amplitude modulation.
2. DSB-SC-AM: Double sideband-suppressed carrier-amplitude modulation.
3. SSB-SC-AM: Single sideband-suppressed carrier-amplitude modulation.

In DSB-EC-AM the carrier carries no information except the phase and
amplitude of the unmodulated wave. It is added to permit demodulation
of the modulated signal by means of nonlinear circuits that do not require
explicit use of the carrier signal. Because the addition of the carrier is
equivalent to the addition of a constant to the message signal, emitted
carrier systems are not useful for the accurate transmission of instrumentation or wide dynamic range data.
When a carrier is not added to the signal, suppressed carried modulation
results. Two types of systems are in common use: double sideband, in
which both sidebands are transmitted, and single sideband, in which only
one sideband is transmitted to conserve bandwidth. For both SSB and
DSB systems, the demodulation of the modulated signal requires the synchronization of the demodulator with the carrier.
DSB·EC Demodulation

Detectors or demodulators in common use in emitted carrier amplitudemodulated systems give an output which depends on the amplitude, but

TRANSMISSION SYSTEMS

15-51

not on the phase, of the input carrier. The "square law" and "linear" detector are examples of this nonsynchronous method of demodulation. For
the square law detector, the output signal is proportional to the square of
the amplitude of the input signal, whereas a linear relationship exists between input and output amplitudes for the "linear detector." The chief
advantage of these nonsynchronous detectors is the simplicity of circuits
required to effect demodulation. This advantage, however, is offset by the
requirement that a steady carrier signal be transmitted with the message
signal. In comparison with other types of demodulators, these nonsynchronous methods characteristically have poor noise rejection and increased distortion.
The calculation of the transmission of signal and noise voltage in amplitude-modulated systems is a familiar and simple process for linear elements in the system. In these linear elements, superposition holds and
the output of an element supplied with signal and noise is the sum of the
outputs that would be obtained if each were applied separately. However,
this principle of superposition cannot be applied when the signal and
noise pass through a nonlinear device such as a rectifier or limiter.
Rectification of Signal and Noise. Signal Suppression. Understanding the rectification of noise and of a mixture of noise and signal is important in relation to (1) its effect on the signal-to-noise ratio following
demodulation, (2) the measurement of a continuous signal in the presence
of noise, and (3) the detection of pulsed signal superimposed on noise.
A characteristic of nonsynchronous demodulators is the existence of a
threshold below which output SjN decreases faster than input SjN. This
effect is often referred to as suppression of the carrier or signal by noise
and is the result of the noise interacting with the weak carrier signal to
form additional noise components.
The interaction of noise and a weak carrier is due to the generation of
beat frequency components produced by noise frequencies beating with
the carrier. These beat frequencies will have an amplitude proportional
to the carrier amplitude Ao. Since these new terms are random with
respect to each other, the total noise power in the output will be the
sum of the noise plus a term proportional to the square of the carrier
amplitude:

N = No

+ kAo2

= Total noise power in demodulator output

where No = noise power in output in absence of carrier,
k = constant of proportionality,
N = noise power in output of demodulator,
kAo2« No.

i5-52

INDUSTRIAL CONTROL SYSTEMS

This expression is valid only for very small input signal-to-noise ratios.
For large values of signal-to-noise ratio, Middleton has shown that the
increase in nOIse power due to intermodulation of carrier and noise components tends to a limit which is primarily a function of the spectral distribution of the noise (Refs. 41 and 42). The results are given in Fig. 20
for a rectangular or uniform spectral distribution and for an optical
spectral distributIon. The optical spectrum is a term used to represent a
spectral distribution equal to the selectivity curve of a single-tuned circuit. The results apply to systems in which the carrier bandwidth is equal
to or greater than three times the output bandwidth.
- From Fig. 20 it is evident that the output noise increases by 4 to 7 db
when a carrier is present. This characteristic is important in applications
in which the detection of weak-pulsed signals is required. Note that in
Fig. 20, the ordinate is the ratio of output noise power with carrier to
output noise power without carrier. An alternate representation is to plot
the ratio of rms output noise to rms input noise for the demodulator. This
is given in Fig. 21 which was taken from a paper by Burgess (Ref. 43).
Characteristics of Nonsynchronous Demodulators. For small input
signal-to-noise ratios, it can be assumed that the output signal amplitude
is proportional to the difference between noise voltages when the carrier
is present and those when the carrier is not present:

where hand k are constants of proportionality. The output signal-to-noise
ratio is

(S/N)output

=

C(S/N)tnput.

NOTE: N is the output noise power but N "-' No since kAo2 «No.
Thus, when the signal is small, the output signal-to-noise ratio varies as
the square of the input signal-to-noise ratio, and signal suppression by
the demodulator exceeds the noise suppression indicated in Fig. 21.

TRANSMISSION SYSTEMS
7
I-

I
I
I
I
Single-tuned circuit
type of spectral shape
-...........
(optical spectru"m)

y

/

//V

V

15-53

...-

Uniform (square~ /'
spectral shape_

-

!/

~
-20

/'

~

o

-'10

10

20

Carrier-to-noise ratio, decibels

FIG. 20.

Increase of noise power at output of linear detector; N = output noise
power with carrier, No = output noise power without carrier.

For large signals the noise output remains constant as the inpu"t signalto-noise ratio is varied (Fig. 21). This means that the outputS/N must
vary linearly with input SJN. Therefore, if input SIN in decibels is
plotted versus output SIN in decibels, a curve should be obtained which
is asymptotic to a line with unity slope for large input SIN, a,nd to a line
with a slope of 2 for small signals. The work of Middleton and associates
confirms this characteristic for sine wave modulation and f01:'.aU types
of nonsynchronous demodulators and noise characteristics.
1.0

~
./

0.9

e: 0.8
'g g
Ql
VI

:>

~
0

:>

.S

E E 0.7
a::: a:::

/

/

/

/

/

---

~

0.6

0.5

o

0.5

1.0

1.5

2.0

2.5

3.0

Input Rms signal
, Rms nOise

FIG. 21. Linear detector input-output noise characteristic.

INDUSTRIAL CONTROL SYSTEMS

15-54

Universal Input-Output SIN Curve for Nonsynchronous AM Demodulator. The universal relationship between input and output SIN

ratios is given in Fig. 22. The results apply for carrier bandwidth in excess of three times demodulator output filter bandwidth, for sine wave
modulation, and for an optical noise spectrum. The curve of Fig. 22 is a
16

I

12

8

f

VI

Q)

.c
'(3

4

Q)

Asymptotic line
for large signals ~

"C

eli
VI
'0

0

-§.
ro

c:
tlO
.iii

......

//

-4

~

.9-

/J

~

0
"C

-8

Q)

.!:::!

ro

E
-12
0

z

-16
-20

I

[;
hII

V

/

~

~

~OO% modulation (m = 1)
I

I

I

V

. I

___ Asymptotic line
for small signals

II

-24
-14

I

-10

-6

-2

0

2

Carrier-to-noise-power ratio, (

6

10

14

~~:), decibels

1. To obtain ordinate scale for a given

Carrier bandwidth.
I
Carrier bandwidth
.
.
b d··d h ratIO, add 10 og
0
d to ordmate scale.
2 X utput bandwi th
O utput an WI t
2. This method is valid only for sinusoidal modulation with carrier bandwidth
times output bandwidth.

~

3

3. For m =;e 1.0 decrease ordinate scale by 20 log ~ .
m
m = modulation index
Ao = carrier peak amplitude
bo = rms noise power in carrier bandwidth

FIG. 22.

Universal curve for output signal-to-noise ratio for nonsynchronous demodulators.

TRANSMISSION SYSTEMS

15-55

universal curve that is valid for any carrier bandwidth and any output
filter bandwidth as long as the ratio is in excess of three as just indicated.
The curve is normalized to take into account variations in bandwidth
ratio and modulation index 11L The actual output SIN is obtained by
adding a correction term to the normalized value obtained from the curves:

(-NS)

(S)

+ 10 log

= output

N

norm

Carrier bandwidth
.
2 X Output filter bandwidth

For example, if the input SIN ratio is -2 db, the carrier bandwidth is
1 kc and the output filter bandwidth 50 cps. Then
8)
1000
= -4 db + 10 10glO - = +6 db.
(N output
2 X 50

DSB·SC·AM and SSB·AM Demodulation
Amplitude modulation is descriptive of a general class of systems in
which the amplitude of a carrier wave is a function of the message or
modulating signal. To gain a physical insight into the difference between
the various forms of amplitude-modulated systems, consider a signal
waveform V (t) which modulates a carrier having a radian frequency We.
Then
ll;f(t) = Ae[l + leV(t)] cos wet,
where Ie V(t) :s; 1 = modulation index,
[1 + Ie V(t)] = modulating function,
We = carrier frequency.
The modulated wave M(t) is the product of the modulation function,
[1 + Ie V(t)], and the sinusoidal carrier, cos wet. Instead of a cosine multiplying function of the carrier frequency, a square wave or sampling or
impulse type function of the carrier frequency could be used.
The modulated signal M(t) is the sum of a fixed carrier component, Ae
cos wet, and a varying amplitude component, AJ\; V(t) cos wet. For suppressed carrier systems the unity term in the modulation function is omitted
and the modulated wave becomes
M(t) = A ole V(t) cos wet, double sideband suppressed carrier modulation.

Since the amplitude of the message-bearing signal is twice as large for the
suppressed carrier waveform as compared to the general case in" which a
steady carrier is added, the signal or message power is four times greater
(amplitude doubled). Hence, a 6-db improvement in SIN results for a
given peak power limitation.

INDUSTRIAL CONTROL SYSTEMS

15-56

If Vet) is assumed to be a cosine wave,

Vet) = As cos wst,
then M(t) can be written in terms of the sum and difference frequencies:'

M(t) = Ao cos C + !kAoAs[cos (C

+ V) + cos (C -

V)],

where C = wet,
V = wstj
or, letting

kAoAs
A = - - = Upper and lower sideband amplitudes,
2

M(t)

=

Ao cos C + A cos (C

+ V) + A cos (C -

V).

The general modulated wave consists of a fixed carrier term Ao and two
sideband terms of equal amplitude at the sum and difference frequencies.
For ideal SSB transmission, only one of the two sidebands is transmitted:
AssB cos (C + V)
M(t) =
or
IAssB cos (C - V).
For DSB-SC, both sidebands are transmitted:

M(t) = ADsB-sdcos (C

+

V)

+ cos (C

- V)].

For the general amplitude-modulated case, DSB-EC-AM, both sidebands and the carrier are transmitted. Figure 23 indicates the type of
waveforms typical for each of the systems.
NOTE: For both DSB-SC and SSB, the amplitude of the modulated wave
does not have a close resemblance to the original modulating signal. . In
both of these systems it is necessary to utilize both the carrier phase and
amplitude in the demodulator to reconstruct the original signal.

If the peak power for both SSB and DSB-SC are the same, then SSB
will ideally have a 3-db (factor of 2) power advantage over DSB-SC since
the latter requires twice the bandwidth. If SSB and DSB-SC are compared with conventional DSB-EC-AM, then SSB transmission has a 9-db
power advantage and DSB-SC has a 6-db power advantage.
Quadrature Component Generation in DSB-SC Systems. To appreciate the practical problems involved in the transmission of AM signals,
it is convenient to identify the message signal components in terms of real

TRANSMISSION SYSTEMS

~f6

A

15-57

~ t1IIIIhllllllili

~

S:V~)t

)' W

Modulating signal

Amplitude- modulated signal
::;

"f

J-."

Ilf-I

.~
~

i

~

~)

JJJIIILlllllIlIllWIIIIILllllIIII--,--,..illJIIIILlllllllIllWlIlIl.w...1I1

we

W

Double sideband suppressed carrier signal

en

~

t

Time domain

If--I_ _

I

I!

~)

1lJ.W11111lJ.W1
II 1Iw.J..1I

L..UI

we

w

Frequency domain (spectra)

Single sideband signal

FIG. 23. Amplitude-modulated waveforms.

frequencies and to evaluate the effects of amplitude and phase distortion
by the transmission system. For a message consisting of a single sine
wave, the modulated wave consists of two sinusoidal sideband frequencies.
These sidebands can be represented as a sum of an in-phase and quadrature carrier frequency waveform. 'Vhere the in-phase component will be
a cos wet time function, since a cos wet modulating function is assumed, the
quadrature component will be a sin wet time function. As before, let the
suppressed carrier modulated signal be represented as
~l(t)

= A cos (C + V)

+ A cos (C -

V).

After transmission and amplification, the received modulated waveform

RCt) will be distorted owing to the amplitude and phase characteristics of
the transmission system:

INDUSTRIAL CONTROL SYSTEMS

15-58

where AI, A2 = amplitude of upper and lower sidebands after transmission,
01, (J2 = phase shift of upper and lower sidebands after transmission,

C = wet,
V = wst.
(1)

R(t)

= [Al cos (V

+ (Jl) + A2 cos (V -

(J2)] cos C

+ [-Al sin (V + (Jl) + A2 sin (V -

(J2)] sin C.

The cos C term is the in-phase, A p , carrier component and the sin C term
the quadrature component, Aq. Note that if the amplitude and phase
distortion is negligible, the amplitude of the quadrature component is
zero.
DSB-SC Demodulator. For DSB-SC systems, both the quadrature
and in-phase components are received. The intelligence, however, is
ideally contained only in the in-phase component. As a result, a simple
method for obtaining an in-phase carrier at the receiver consists of varying the phase of a locally generated carrier so that the output of a quadrature demodulator is zero. The output of an in-phase demodulator will
then contain all the message information. This type of DSB-SC demodulator is illustrated in Fig. 24 (Ref. 44). In the demodulator of Fig. 24
the outputs of both the in-phase and quadrature demodulators are combined to effect cancellation of correlated noise or disturbances present
in their carriers. The synchronous demodulators in Fig. 24 are typically
phase sensitive rectifiers.
The block diagram of Fig. 24 is typical for DSB-SC systems used in wire
or RF transmission. For RF transmission the RF signal is the input, and

Carrier
input

Low-pass
amplifier

FIG. 24. Synchronous demodulator for DSB-SC-AM.

TRANSMISSION SYSTEMS

15-59

no IF amplifiers are used. As a result no problem exists with image responses, and the selectivity of the system is determined by the output lowpass filter characteristics.
SSB-SC Demodulation. In the case of SSB transmission, one of the
carriers is not transmitted, and either Al or A2 equals zero in Eq. (1). By
letting A2 equal zero, then for SSB
R(t) = [AI cos (V

+0

1 )]

cos C

+ [-AI sin (V + 0

1 )]

sin C.

Thus, for SSB the message information is transmitted on both the in-phase
and quadrature components of the carrier. As a result no simple method
exists for obtaining a local carrier which is locked in phase with the transmitted carrier (45). To circumvent this problem, a small carrier frequency signal is transmitted continuously or in bursts along with the modulated waveform. The veo in the receiver must be synchronized to this
pilot carrier signal in order to effect demodulation. To provide reliable
operation, the amplitude of the pilot carrier is typically 10 to 30 db below
that of the normal operating level of the system.
Synchronous Demodulators

In the previous section an amplitude-modulated wave was represented
in terms of an in-phase carrier component and a quadrature carrier component. For DSB-Se transmission the information was ideally contained
in the in-phase component only.
Synchronous demodulation is the recovery of the message signal by
means of a time-varying circuit~ the parameters of which are varied
periodically at the carrier frequency.
Most practical synchronous demodulators can be represented as two
cascaded operations: (a) multiplication of the received signal by a periodic
function of the carrier frequency and (b) filtering. The multiplication
operation shifts the signal spectrum to its original location prior to modulation and, in addition, creates new frequency components at multiples of
the carrier frequency. The resulting signal must then be filtered in order
to recover the original messages.
The design of a practical demodulator involves the selection of the
multiplying function and the design of a suitable filter based on the relative amounts of in-phase and quadrature signals present in the input.
Demodulator Multiplying Functions. Three multiplying functions
are sufficient to describe most practical synchronous' demodulators: the
square wave,. the periodic impulse train, and the sinusoid.
If it is assllmed that the signal to be demodulated is the product of a
sinusoidal carrier and the message, the ideal demodulator, if no disturbances are present, will be a division of the demodulator input by a

INDUSTRIAL CONTROL SYSTEMS

15-60

sinusoid. Even if the practical difficulties of such a division are neglected,
the periodically infinite values of the multiplying function lead to a great
sensitivity to quadrature signals.
The multiplying function used in most synchronous demodulators is
the square wave. Bridge, ring, shunt series, and switching demodulators
in which tubes, rectifiers, transistors, choppers, or relays are synchronously
switched with the carrier are examples of square wave demodulation (Refs.
46 and 47).
A demodulator which periodically samples the input waveform and
performs a holding operation (sample and hold) between samples has a
periodic impulse train for its multiplying function. In this instance, the
filter and the demodulator are not physically separated since the holding
operation is a pseudo equivalent of a filter.
DSB·SC Synchronous Demodulators. Figure 25 is a block diagram
of DSB-SC synchronous transmission system. It is assumed that no
quadrature signal exists at the modulator output and that the quadrature
signal is the result of transmission circuit distortion. Any quadrature component generated by the modulator should be added to that resulting from
the transmiSSIon process.
Modulator

Transmission
circuits

Demodulator

~
V(t)

=As cos V

.---------,

>---+-----l

Vet) = As cos V
R(t) = received modulated signal = V p cos C
M(t) = modulated signal = 2A cos v cos C

A

Low-pass
output

+ V q sin C + N(t)

= KAoAs
2

K = modulation index
C

=

wet

V = wst
Vp = received in-phase carrier component = [AI cos (V
01) + A2 cos (V - 02)]
V q = received quadrature carrier component = [-AI sin (V + 01) + A2 sin

+

(V - 02)]

transmission circuit phase shift upper and lower sideband frequencies
AI, A2 = received upper and lower sideband amplitudes
01. (J2 =

FIG. 25. Synchronous transmission system.

15-61

TRANSMISSION SYSTEMS

Demodulator Output Amplitude Spectrum. The demodulation
process, in addition to shifting the message spectrum to its original location, introduces harmonic spectrums centered about multiples of the carrier frequency. These harmonics are error signals in the sense that they
did not exist in the original message. The amplitude spectrum resulting
from the demodulation of a modulated carrier are indicated in Fig. 26
for the square wave, sinusoidal, and impulse train multiplying functions.
The components of the demodulated signal spectrum around even multiples

Message spectral
density

a
Spectrum of input
to demodulator

a

We

Demodulator output
spectrum for
square wave
multiplying function

a

2we

4we

Demodulator output
spectrum for
sinusoidal
multiplying function

a

2we

Demodulator output
spectrum for
impulse multiplying
train

a

2we

4we
Frequency, W ~

FIG. 26.

Demodulator output amplitude spectrum for various demodulators

15-62

INDUSTRIAL CONTROL SYSTEMS

of the carrier frequency are shifted replicas of the message or signal
spectrum with amplitudes determined by the Fourier coefficients of the
multiplying function.
Output Filtering. The output filter must pass the message spectrum
without distortion and must reject all other components. The other components have spectra centered around the various harmonics of the carrier
and are called harmonic error. It is obvious that the design of a satisfactory filter becomes progressively more difficult as the highest significant
message frequency approaches the carrier frequency. When the highest
significant frequency exceeds the carrier frequency, the message spectrum
and the second harmonic error spectrum overlap and cannot be separated
by a filter. This limitation is related to the Shannon Sampling Theorem
and is called frequency folding error.
Synchronous Demodulator Input-Output SIN. The performance
of synchronous demodulators has been described in the literature (Refs.
48, 49, 50, and 51). As is true of the phase lock or synchronous FM discriminator, the output SIN of the synchronous demodulator does not have
the threshold phenomena characteristic of nonsynchronous demodulators.
For the linear envelope demodulator signal suppression below a zero-db
input SIN limited the usefulness of this device for low SIN. The synchronous demodulator operates effectively for high and low signal-to-noise
ratios. The relationship between input SIN and output SIN is given in
Fig. 27 for synchronous demodulators used in DSB-SC-AlVI systems. The
results apply for carrier frequencies much larger than message bandwidth
and for negligible phase error between the demodulator and modulator
carriers.
In conclusion, for large signal-to-noise ratio, the synchronous demodulator is no better than a linear rectifier demodulator. However, for small
signal-to-noise ratios, the synchronous demodulator is superior, being free
from the additional overmodulation noise or carrier suppression effect.
DSB·SC·AM System Errors

For an ideal DSB-SC system, the information is all contained in the
in-phase carrier component and the quadrature component is absent. If
the transmission system does not have an even amplitude symmetry and
odd phase symmetry about the carrier frequency, the received signal R (t),
eq. 1, will contain a quadrature component.
The received signal will, in addition to the in-phase and quadrature
components, contain a noise component (see Fig. 25). This noise component will hav6 a bandpass spectrum equal to the carrier signal bandpass
and can be represented as a sum of in-phase and quadrature carrier com-

TRANSMISSION SYSTEMS

15-63

16

en

12

Q)

.c

'u
QJ

"'C

eli
If)
'0
~

8

4

roc:

b.O

'iii

.....
:J

0

.&
:J

0
"'C

-4

QJ

.!::!

ro -8
E
(;

z

-12

/

L

/

-16
-14 -10

/

V

/

-6

/

/

-2 0

/

2

/

/

6

(Ao2)

. t
'
. 2bc;
Camero-nOise-power
ratio,

/

10

.

14

decibels

1. To obtain ordinate scale for a given

Carrier bandwidth
I
Carrier bandwidth
d'
I
- - - - - - - ratio, add 10 og
to or mate sca e.
Output bandwidth
2 X Output bandwidth
2. This method is valid only for sinusoidal modulation with carrier bandwidth ;::: 3
times output bandwidth.
Ao = carrier peak amplitude
bo = mean noise power in carrier bandwidth
FIG. 27. Universal curve for output signal-to-noise ratio for synchronous demodulators in DSB-SC-AM.

ponents. Then the signal at the demodulator input can be completely represented in terms of the in-phase and quadrature carriers.
The objective of the demodulation process is the recovery of the signal
that modulates the in-phase carrier and the rejection of the quadrature
carrier. The final separation of the message from the noise after demodulation of the in-phase carrier is not a part of the demodulation process
but rather a separate filtering problem. The discussion of DSB-SC system
errors is thus the evaluation of the effects of quadrature carrier signals on
the information contained in the in-phase carrier demudulator output.
The total quadrature signal at the demodulator input is, in the general
case, the sum of three components: (1) quadrature signals representing
one component of the input noise, (2) quadrature signals resulting from
amplitude and phase errors in the transmission system, and (3) in twochannel suppressed carrier systems using carriers in quadrature, each channel representing a quadrature signal to the other channel.

15-64

INDUSTRIAL CONTROL SYSTEMS

Error Criterion. In order to evaluate demodulator performance, an
error criterion or a measure of performance is required. Mathematical
simplicity leads to the use of the mean square value of the total error, in
which the error is defined as the difference between the message and the
output of the demodulator filter. However, this criterion is restrictive in
that time delay introduced by the filter and system has a pronounced effect
on the error. For most applications time delay is not of importance, and
the fidelity of the output signal amplitude and phase is the prime concern.
For these applications the time average of the mean square error will provide a more realistic measure of system performance and will be assumed
in the following discussion.
DSB-SC Errors. Since the original message m (t) is assumed to contain information, it cannot be considered a known function of time. The
message, the future values of which are unknown and uncorrelated, is thus
a random function of time. In the error discussion that follows it is
assumed that the message has the characteristics of random noise with a
bandwidth Es. This method of representation is realistic for actual systems, providing the actual message bandwidth is considered rather than
the bandwidth of the transmission circuits used to transmit the message.
In instrumentation information transmission systems, the transmission
circuit bandwidth typically exceeds the actual message bandwidth by a
factor of 2 to several hundredfold, depending on the constants imposed by
transient performance or sampling specifications, etc.
Figure 28 is a representation of the synchronous demodulation process
under consideration. The signal at the 'demodulator input is represented
by an in-phase component and a quadrature component. It is assumed
that both components are modulated by a noise-like signal of bandwidth
E s , and that the original message signal is contained in the in-phase carrier
component. The ratio of quadrature to· in-phase carrier power will be
denoted by K:
K = Quadrature carrier power.

In-phase carrier power
The output filter has a bandwidth Eo and is assumed to be a single time
constant RC filter (6 db/octave). The output of the filter is the recovered
input signal and will differ from the original input, M (t), by the error,
jjj2, where E2 is the time averaged mean square error.
Neglecting noise in the output due to the noise component in the inphase carrier, the demodulator output will include three error components
in addition to the desired message signal: (a) harmonic error, (b) quadrature error, and (c) filter error.

15-65

TRANSMISSION SYSTEMS
Demodulator

Yq

Quadrature carrier signal

r-P;ric;di;-l
: multiplying I
function
I
I

I

I

I

I
I

l--....:....;....--t-~

I
In-phase carrier signal

Yp

I
I

I

I

Filter, low-pass,
single time
constant
bandwidth Bo
M(t)
Original
message

I

L ______ J

Bo ;:::: Bs
M(t) = noise-like message signal

Bs = message bandwidth
R(t)

= amplitude-modulated signal at demodulator input

Vo(t) = demodulator output

E2

=

J(

= Quadrature carrier power

time-averaged mean square error
In-phase carrier power

=

(Vq)2
Yp

FIG. 28. Synchronous demodulator.

The harmonic error is the result of the new spectral components created
by the multiplying operation in the demodulator. These error components
are centered at the harmonics of the carrier frequency. The amplitude
of these harmonic components is proportional to the magnitude of the
signal. Hence, in order to obtain a given dynamic range at the filter output, it is necessary to provide sufficient filtering to reduce the magnitude of
the harmonic components to less than l/dynamic range.
The quadrature error represents the shifted spectrum of the quadrature
carrier signal after the demodulation process. The amplitude of the
quadrature signals at the demodulator output is of the same order of magnitude as that existing at the input and hence will depend· on the ratio of
quadrature to in-phase components.
The filter error represents the loss of information in a system in which
the output filter bandwidth is less than the message bandwidth.
In Figs. 29a, b, and c the time average mean square error E2 is plotted as
a function of we/Bo and Bs/we, where Bs/we is the normalized message bandwidth. The curves are reproduced from a paper by Booton and Goldstein
(Ref. 52) and apply for the case of no quadrature component, Fig. 29a,
and for a quadrature-to-carrier ratio of 1 and 9, Figs. 29b and c. Note
that for a given value of normalized message bandwidth there exists an
optimum filter bandwidth which minimizes the error.

1.0.---,---,---,----,-----r-------.

12
We

Bo

FIG. 29a. Mean square error for square wave multiplying function.
1.4 .-----.------,.---..,.-------,---..-------,
K=1
Quadrature = in-phase

1.2

1.0

%
~

0.8

!-:I

]f2

Bs
We

0.6
~o

0.4
~o

0.2

o
12
We

Bo

FIG. 29b. Mean square error for square wave multiplying function.
15-66

TRANSMISSION SYSTEMS

15-67

4.0,.---,..----...,....------.-----r----,------.-------,
K=9
Quadrature = 9X in-phase
3.5

3.0

2.5

1.5

%

1.0

Vz
~

Bs
We

Ylo
%0

0.5

o

8

0
10

12

We

Bo

FIG. 29c. Mean· square error for square wave multiplying function.

Figure 30 is a plot of error as normalized message bandwidth for various
values of J( and for the optimum value of output filter bandwidth. Although the optimum filter bandwidth varies with J( and the message
bandwidth, it is of the same order of magnitude as the mes'sage bandwidth.
From the figures it is obvious that the quadrature carrier component has
a pronounced effect on the error existing at the filter output.
Since the amplitude of the quadrature carrier component is zero at the
time the in-phase carrier amplitude is maximum, a sampling demodulator
which samples the in-phase carrier at this instant will not be influenced by
the magnitude of quadrature component. In practice a substantial improvement in demodulator performance can be realized by using a
sampling demodulator in this manner.
At the extreme of no quadrature component, the square wave multiplying function is found to be optimum for DSB-SC synchronous demodula-

15-68

INDUSTRIAL CONTROL SYSTEMS
0.7....-----.------,..------...,..-------,
Square wave
multiplying function

K _ Quadrature carrier power
0.6t--_-_ln--'C-p_ha_s_e,-ca_rrl_"er-,-p_ow_e_r- - + - - - - - - : 7 ' ' ' ' - - - - - - ;

0.5

0.4

E2
" 0.3

0.2

0.1

0.05

0.10
Bs

0.15

0.20

We

FIG. 30.

Mean square error as a function of quadrature component and message
bandwidth.

tors. At the other extreme, when the quadrature component is appreciably
larger than the in-phase carrier, the sampling" demodulator (impulse train
multiplying function) is optimum. For intermediate values of K, a sinusoidal multiplying function will prove most effective.
DSB·SC·~M Interference Characteristics. Since the quadrature and
in-phase components are independent in an ideal system, it is possible to
use the quadrature carrier to transmit a second message and to add a
pilot carrier to obtain a phase-locked carrier at the receiver. Under these
circumstances the DSB system performance in terms of power and bandwidth utilization is equivalent to that obtained with SSB systems.
In many practical applications the system limitation is not the noise
associated with the circuits and their corresponding bandwidth but rather
adjacent channel interference. Under these circumstances it is found
that the two-phase demodulator scheme of Fig. 24 will give a two-to-one
advantage over demodulation systems in which only a single in-phase
demodulator is used. The improvement in interference rejection is indi-

TRANSMISSION SYSTEMS

15-69

0.5
0.4

'E2
0.3

Single phase detection

0.2
0.1

Average power desired signal
= 1
Average power undesired signal

--~-=-------"--

d

B8

= separation of interfering carrier and
= message bandwidth,

desired carrier, cycles per second
cycles per second

E2 = mean square error
FIG. 31. Adjacent channel interference DSB-SC-AM.

cated in Fig. 31 for the situation in which both signals have D8B-8C
modulation and both signals have the same power and spectral distribution. Note that for a given mean square error, single phase detection
requires about twice the center frequency separation A of two-phase detection. For example, if ]jj2 = 0.2, A = 1.6B s for two-phase detection,
where as a separation of A = 4Bs is required if only cosine detection is
used.
The advantage of two-phase detection stems from the fact that the
output of both demodulators is correlated, and thus it is possible, by combining the outputs of the two demodulators, to cancel some of the effects
of the interference. If D8B systems with two-phase demodulation are
compared with 88B systems, it is found (Ref. 53) that in almost every
case D8B operation is superior to 88B.
6. PULSE TRANSMISSION

-VVith the exception of direct wire facilities, transmission systems require the use of a carrier to effect transmission. In FM and AM systems,
a, parameter of the carrier waveform contains the information and the
transmission process is an analog operation in which the variation of the

15-70

INDUSTRIAL CONTROL SYSTEMS

carrier waveform parameter is continuous over the dynamic range. For
these systems, the transmission of nonsteady data at accuracies exceeding
1 WI,
y;(w) = WTd = Linear phase variation,
Td = Transmission delay (constant over bandwidth-B Ha = wd27r).
The impulse transmission characteristic for this system is given in Fig. 32.
I

I
I

A(w)

"!-i---"""
I

Tl

=

2\

=

minimum pulse

spacing for ideal system

I
I
I
I
I

FIG. 32. Impulse response of ideal low-pass system with sharp cutoff.

The impulse response is zero at times
Tl

nTl

where

= 112ft = minimum pulse spacing for an ideal system.

Impulses can thus be transmitted at intervals of TI seconds without mutual
interference between peaks of the received pulses. This is a basic theorem
relating the physical limitation on pulse transmission rate and bandwidth
for an ideal system.
Ideal Systems with Gradual Cutoff and Linear Phase Characteristic

The ideal sharp cutoff system is impractical in the sense that the characteristic is difficult to realize in practice, and further that the oscillatory
nature of the response would result in appreciable interference between
pulses in a practical system. The oscillations in the impulse characteristic
can be reduced with a gradual rather than a sharp cutoff characteristic as
illustrated in Figs. 33a and b. The example in Fig. 33a also assumes that

INDUSTRIAL CONTROL SYSTEMS

15-72

i
fj\

l.0
OJ

-0

~

c..
E
III

0.8
0.6

/
/
1/

II)

::J
0
OJ

c:

0.4

.sc:
.s

0.2

-=

0

II)

-

/

~

i \
i '\
i \

1

\

1"-/

:

-

o
7r'

7'1

1

= WI = 2fl

Impulse characteristic

T
I

l.0
OJ

'"

0.8

-0

::J

'K 0.6
E


:;:::

~

\

'\

c.
(,J

' \.

JAb:r
,'// ~ ~

0.8

c:

/'

//c \\

~

Ci

~ / ' ~.,~ F

//

1.2

Q)

'C

/\
/ \

/' ,

~

/'

-4:

0

/

-0.2

/

~" "'-

V~I

D.>r\

\\+1\ ~ "-

~1
/

\\ ~~\'\~ '"

VB-ill'

""

/

~ ::\~~:Z II

,<-

x

"

/

~/' /

-0.6
-4fT

-3fT

o
1fT
-1fT
Frequency, cycles per second

-2fT

A, rectangular
B, cosine squared

.......

\ 7'/

r\ L

-0.4

/

~\'' ~,
'...to,. Il:~
~~
1\ \ "~-I /~/.
./

2fT

C, half-cosine
D, triangular

3fT

4fT

E, Gaussian
F, trapezium

Fig. 36b. Pulse spectra.
1.0
0.9

I

0.8

I
r

0.7
Q)

'C

~

0.6

E

0.5

a.
III

Q)

>
:.::;
III

Filtered
0.4 _pulse-""'"

Qj

0:::

I

0.3

j/

0.2
0.1
0d

i

If' r\

I

Filtered pulse

1\
\\

~Th-

\\

f,

o

\\

fi

f'

= 1f'_1_
= 1.JLC 2r

\\,

\\
\\

/

Gaussian
I...k- pulse

\~

V

//

\
0.4

IT) A-

JL

0.8

1.2

1.6
tfT

2.0

-

"
.......

.......
2.4

/r-

----2.8

FIG. 37. Filtered rectangular pulse and Gaussian pulse.
15-77

3.2

15-78

INDUSTRIAL CONTROL SYSTEMS

Correlation between Bandwidth and Pulse Transmission Characteristic. Figure 38 gives the response of an ideal system having a sharp
cutoff characteristic with a bandwidth B Y2a to a pair of test pulses with

finite duration. From the figure, it is evident that a bandwidth
B Y2a

=!I = 1/2T l

is required to resolve the two pulses. Note that the pulse spacing is equal
to the pulse width. If the bandwidth is decreased below the above value,
- - -,-; :-,,.-- 1-- -

:t _\:
/1
?~i
'......

1 \
I

1\11
I

-,.-- ,..--!--

1\

~T~T~T~

~LD
" ....'

FIG. 38. Effect of bandwidth on the transmission of detail (low-pass filter with cutoff at 11).

the detail or individual pulses are "washed out." The effect of increasing
the bandwidth beyond this value is principally to sharpen the sides of the
edges. To illustrate details of the figures, assume that the pulse width is
1 J-tsec and that a separation of 1 f-tsec exists between pulses (pulse interval
= 2 J-tsec). Then, for a 250-kc bandwidth, no sign of two pulses exists;
for 500 kc two pulses are clearly evident, and for 2 Mc details of the individual pulses become discernible.
Performance Specification

The derivation of the pulse transmission characteristic for an actual
system in which the amplitude and phase variations deviate from the
previous examples is an involved procedure. In practice, a satisfactory
evaluation of performance can be obtained by assuming that the pulse
transmission characteristic is approximated by one of the previous examples, namely, (a) sharp cutoff linear phase shift, (b) gradual cutoff
linear phase by equalization, or (c) gradual cutoff natural linear phase

TRANSMISSION SYSTEMS

15-79

shift, and that deviations of the actual system from the ideal will result in
an rms intersymbol interference V, which is evaluated in terms of the
phase and amplitude deviations from the selected ideal system. The
intersymbol interference V is a measure of the amplitude of distortion
components resulting from nonideal phase and amplitude characteristics.
For the ideal system, the received pulse amplitude is uniquely determined by the transmitted pulse pattern. In a system with distortion,
echoes and pulse overlaps add to or subtract from the assumed ideal response, and in the limit the identity of pulses may be lost. The intersymbol interference V is a ratio of the distortion component amplitude to
the peak received pulse amplitude in the absence of distortion:
Amplitude of distortion component
V = ---------------------------------Peak pulse amplitude with no distortion
For V = 1, the distortion component is equal to the ideal received pulse
amplitude.
Since the transmitted pulse train will vary in a random manner, the
distortion component will also exhibit random variations. As a result, the
intersymbol interference V, will vary as a function of time and will have
an rms magnitude Q. Experience has indicated that for small values of
U a peak factor of 3 to 4 provides a realistic measure of the peak intersymbol interference. For example, if rms interference V is 1070, the
peak interference will usually be less than 30 to 4070.
The performance of an actual transmission system thus requires, in
addition to the specification of transmission bandwidth and pulse rate,
the specification of the rms intersymbol interference. Note that the intersymbol interference sets a limit to the transmission rate which is independent of the power level. If transmission power is limited, then it is
necessary to specify, in addition, the error rate as a function of SIN.
Nonideal Transmission Systems

A convenient method of representing nonideal systems is to specify the
amplitude and phase deviations from one of the ideal linear phase systems.
Let

Ao(w) = Ideal amplitude characteristic,
!J;o(w) =

WTd

= Linear phase characteristic of ideal system.

Then, most systems can be described by an amplitude characteristic:

+ al cos wT + a2 cos 2wT + ... ),
1 + a(w),

A(w) = Ao(w)(l
A(w)jAo(w) =

15-80

INDUSTRIAL CONTROL SYSTEMS

wherea(w) is the fractional deviation of the amplitude frequency characteristic ftom that of the ideal, Ao(w). By letting g equal the rms value of a(w)
over the transmission bandwidth 2WI = Wmax where wd27r = B ~a, then

rz =

1](7r/WIT)~g

where 1] = 1 sharp cutoff linear phase system,
1] = 0.866 gradual cutoff natural linear phase,
2f = l/T,
WI = ! amplitude low-pass bandwidth,
T = pulse separation.
If 27r!I = WI, the rms intersymbol interference II, owing to amplitude deviations from the ideal amplitude characteristic, is simply equal to the rms
value of the amplitude deviations over the transmission bandwidth 2WI =
47rB~a.

By applying the same procedure to phase deviations from the ideal
linear phase characteristic tf;o(w),

+ (3(w),
sin wT + b2 sin 2wT + ....

tf;(w) = tf;o(w)
(3(w) = bi

Letting Q = rms phase deviation over the transmission bandwidth 2WI,
Sunde (Ref. 54) obtains the result

II. =

1](l/WIT)~Q

where Qis the rms phase deviation in radians. The total rms intersymbol
interference due to both amplitude and delay distortion is

rz = 1](7r/WIT)~(g2 + Q2)~.

In the above expressions, note that T is not the delay Td of the transmission
medium. T in both the amplitude and phase characteristics is the period of the
Fourier approximation of the deviations. It is numerically equal to the separation of echoes produced by the nonideal transmission system (see Goldman,
Ref. 55, page 106).
Note further that the transmission phase and amplitude characteristic
must be controlled to Wmax, not just WI (WI = 27rh) , the ideal bandwidth
for a transmission rate of 2!I pulses per second. Wmax will be at least a factor
of 2 greater than WI for optimum transmission methods [values of 3 to 4 are
common in conservative system design (Ref. 57)].
Sinusoidal Phase Deviation. In many practical applications, phase
deviations from the ideal linear phase relation set the performance limit.
In many of these instances, the phase deviation can be approximated by
a single sine term which has odd symmetry about the center of the transmission bandwidth. The resulting amplitude characteristic will exhibit
a cosine deviation and is indicated in Fig. 39.

TRANSMISSION SYSTEMS

15-81

t

Phase deviation
characteristic

---

(jew)

"

....... ,

,
Envelope~"

Frequency

....... ,
d max

'-..

j

delay..................

lL

b
,,/'

.,;. . . ."-<.._--;rJ

-bT cos uTy ........ --- ------", -b sin uT/"
b = 4fmax d max
FIG. 39. Sinusoidal phase deviation; W max is the frequency limit for which amplitude and
phase characteristics are controlled to permit operating with an effective bandwidth

B

- f

Ua -

The rms phase deviation is simply

< V2
fmax

1 -

b/V2 (Ref. 54) where

f max = wmax/27r,
d max = Maximum variation of envelope delay over the
transmission bandwidth Wmax.

Hence

rl = 1] (7r/WI T) 31(4/V2)fmaxd max,
WI =
T

!

amplitude low-pass bandwidth = 27rB 72a ,

= Pulse separation,

1] ~

1.

Intersymhol Interference Resulting from Low-Frequency Cutoff

Owing to use of transformers or a-c coupled components in transmission
systems, the low-pass characteristic exhibits a low-frequency cutoff. The
effect of a low-frequency cutoff can be avoided by employing a symmetrical bandpass characteristic in conjunction \vith a DSB-SC transmission
system. In order to select the appropriate transmission method, direct or
modulated carrier, it is necessary to evaluate the pulse transmission rates
and accompanying intersymbol interference for each method.
For a DSB-SC system in which the pulse rate is appreciably less than
the carrier frequency, the intersymbol interference can be determined by

15-82

INDUSTRIAL CONTROL SYSTEMS

the methods of the previous section. As the pulse rate approaches the carrier frequency, increased distortion or intersymbol interference results
from the modulation-demodulation operations. This distortion component can be evaluated from the rms error curves given in the section
describing DSB-SC operation.
As the pulse rate approaches the carrier frequency, the rms error due to
the modulation-demodulation process becomes large, and it is necessary to
minimize intcrsymbol interference due to phase variations by careful
phase eq~alization (Ref. 57).
For systems with low-frequency cutoff in which direct transmission is
used, intersymbol interference results from the displacement of the zero
or base line as the transmission rate is increased. This effect is called
zero wander and is most pronounced for a long train of unipolar pulses.
The number of pulses of one polarity, or of nearly all the same polarity,
which can be transmitted before serious distortion occurs, depends on the
extent of the low-frequency cutoff. If the low-frequency cutoff is unappreciable, this number may be sufficiently large that the prob~bility of
encountering such a sequence in a random pulse train is small. Hence
the resultant error rate due to low-frequency cutoff may be disregarded.
If it is assumed that positive and negative impulses are applied at random to the transmission system at intervals of T = 1/2j, and that the
transmission system has a sharp cutoff at wo and W1, then the rms intersymbol interference is simply (Ref. 54) :

A(w) = 1
w ~ Wo

=0

l
W

~

WJ

phase shift linear.

In actual systems, the low-frequency cutoff will be gradual between
W = 0 and Wo, rather than abrupt as assumed above. With a linear variation in the amplitude characteristic between 0 and Wo, Ii becomes

U=

(7rWO/3W12T)~

= Rms intersymbol interference resulting from
low-frequency cutoff at wo,

T

= Pulse separation,

WI

= 27r!I = High-frequency cutoff,

Wo

=

27rfo = Low-frequency cutoff.

TRANSMISSION SYSTEMS

15-83

For transmission at a rate 2ft = 11Tl with an rms interference of Ii. =
0.25, the frequency ratio from the equation above, wolWI, would have to be
less than 0.188. Actually a substantially smaller ratio would be required
since the phase distortion introduced by the low-frequency cutoff was neglected in the above evaluation. Low-frequency cutoff in a system in which
direct transmission is attempted thus places severe restrictions on the
performance of the system.
From either of the expressions for rL, it is evident that the effect of lowfrequency cutoff can be reduced by transmitting narrow pulses at longer
intervals than Tl = 112ft,. the theoretical minimum. If acceptable performance requires increasing the interval by a factor of more than 2 to 4,
the modulated carrier transmission may offer a decided advantage.
Dipulse Transmission. The zero wander of a system with a lowfrequency cutoff characteristic can be minimized by transmitting a pair
of opposite polarity pulses for each pulse in the original pulse train.
This is called dipulse transmission and is accomplished by letting a positive pulse followed by a negative pulse indicate a true signal, and a negative followed by a positive indicate a false signal. For dipulse transmission, the d-c level taken over a pulse pair is zero, and improved performance can be obtained at the expense of doubling the bandwidth for a given
transmission rate or halving the transmission rate for a given bandwidth.
For dipulse transmission, the peak interference due to low-frequency cutoff is about equal to (Ref. 54)
{; ::: folfl = Peak interference.

Note that to compare this with previous rms interference values it is necessary to multiply the rms quantity by a peak factor of 3 to 4.
Intersymbol Interference Resulting from Band Edge Phase
Deviations

In pulse transmission systems in which phase equalization is employed,
it may be impractical or unnecessary to equalize over the entire transmission band. As a result, a residual phase distortion will exist near the
band edges. This type of distortion can give rise to pulse distortion extending over appreciable time intervals if the band edge phase deviations
are large. This results from the fact that frequency components outside
the linear phase range are transmitted with increasing delay.
Consider a low-pass system (or symmetrical bandpass) having a sharp
cutoff, no amplitude variations, and a parabolic deviation from a linear
phase characteristic between w' and W max = WI (see Fig. 40).
As a result of the assumption of a parabo)ic phase deviation, the delay
distortion varies linearly in the band between w' and WI. For this example,

INDUSTRIAL CONTROL SYSTEMS

15-84

Amplitude characteristic

t

Q)

Vl

ro

Phase distortion {3
/ } --- (parabolic deviation)

.c
a.
"'0

c

ro

I

Y

I

Q)

"'0

:ec..

I l}1

-----------t-_---

E

~

Delay distortion

I
W'

wI

=

wmax

WI

Frequency

W

FIG. 40. Constant amplitude characteristic with band edge phase distortion.

the phase deviation f3 is given by
(3
(31

= (31[(W - W')/(Wl - w')]2,
= Phase deviation from linear phase characteristic at frequency WI'

For this example, Sunde gives the following rms intersymbol interference
for impulse type signals:
!!. = (7I"/WIT)Y2[(WI - w')/wd Y2 F((31),
WI = Low-pass sharp cutoff bandwidth,
T

(31

= Pulse separation,
= Phase deviation at band edge

WI,

F((31) = the table below.

o
o

0.25

1

4

00

0.14

0.43

1.24

1.42

If, for example, phase distortion were confined to the upper 10% of the
transmission band WI, then [(WI - w')/wd = 0.1. For a maximum phase
deviation of 1 radian at the edge of the transmission band, F equals 0.43 and
!l. equals 0.135 if T = 1/2fl' By allowing a peak factor of 4, the peak intersymbol interference becomes 4 (0.135) = 0.540 or 54%.
The severe tolerances on band edge phase deviation for a sharp cutoff
low-pass system can be overcome by employing a gradual cutoff natural
linear phase shift characteristic as indicated in Fig. 41. Note that the
transmission bandwidth Wmax = 2Wl is doubled. If the phase characteristic
is linear between W = 0 and WI, and if the phase deviation is parabolic be-

TRANSMISSION SYSTEMS

15-85

Phase
distortion 13
(parabolic
deviation)

(1)
II)

It!

.s::.

Co
"C

c:

It!
(1)

"C

:eCi
E

«

a

WI

=

W max

Frequency,

2wI

W

FIG. 41. Typical transmission frequency characteristic with phase equalization over
50% of transmission band.

tween Wl and Wmax = 2wl, the phase deviation {3 becomes
{3

= {3d(w -

wl)/(2wl - Wl)]2

=

{31(1 -

W/Wl)2

where {31 is phase deviation from a linear phase characteristic at W = 2Wl
Wmax ·

Then

II =

('1I-jW1T)%A = Rms intersymbol interference

where
{3I

7r'

27r'

47r'

00

2

4
0.120

8
0.185

0.330

0.070

00

Note that if the pulse separation T is the maximum given by T = 1/2!1,
then II = A. For the assumed parabolic phase deviation, the delay distortion varies linearly and is a maximum d max at the band edge:
d max = 2{3liwl'

The product of this delay distortion with the maximum frequency f max is
dmaxfmax

The quantity

dmaxfmax

=

2{3li7r.

is also tabulated above.

Symmetrical Systems-Amplitude and Phase Tolerances
vs. Dynamic Range

In a symmetrical system, the amplitude characteristic has even symmetry and the phase characteristic odd symmetry with respect to a prop-

INDUSTRIAL CONTROL SYSTEMS

15-86

erly chosen frequency. A low-pass transmission system is thus symmetrical with respect to zero frequency, if negative frequencies are included.
A double sideband system is symmetrical if the amplitude characteristic
has even symmetry and the phase characteristic odd symmetry with respect to the midband frequency.
The previous discussion has been concerned with the transmission of
bipolar pulses having a fixed amplitude. Sunde has extended the evaluation of transmission systems to include the transmission of pulses of varying amplitude (Ref. 54).
If a continuous analog signal is considered to have q identifiable amplitudes and if a time resolution of T seconds is required to resolve the detail
in the signal, then the transmission of the analog signal is equivalent to
the transmission of impulse type signals having q amplitudes and a separation of T seconds (see Ref. 55), page 85, and Ref. 58, page 33). If the
amplitude increments are equal, the successful recovery of the signal will
require the ability to distinguish the smallest amplitude increment Amnx/q.
Further, the distortion or intersymbol interference introduced by the system must be less than or at most equal to Arnax/ q, the smallest increment.
Letting J( represent a peak factor relating the rms intersymbol interference, Sunde (Ref. 54) has derived the following expression relating dynamic range and permissible distortion or intersymbol interference:
l/(q - 1) =

LIl(4/ A max)

limiting relation between intersymbol

lll-

terference and message dynamic range,
q = Dynamic range,

= Number of identifiable amplitude increments,
L = Peak factor applicable to Q,

Q=

Rms intersymbol interference,

4/ A max = Ratio rms signal amplitude

to maximum or peak amplitude.

If all negative and positive amplitudes have equal probability, then there

are q/2 negative and q/2 positive amplitudes with equal steps 2A max beq- 1
tween pulse amplitudes. For the case of equal probability of amplitudes

4/ Amax =

[(q

+

1)/3(q - 1)]%.

For this case, the limiting relationship becomes
1 = LQ[(q - 1)/3]%.

TRANSMISSION SYSTEMS

15-87

For large dynamic range q » 1:
L

1

f"'V

1

f"'V

V3!!. q,
2Ilq,

L = 3.46 = Peak factor.

Thus, in order to transmit a bipolar message signal having a bandwidth
or a time resolution T = 1/2iI with an accuracy of 1% (q = 200), the
rms interference !l must be less than or equal to U% over the bandwidth
o - II. Tolerances of this nature are difficult to realize and in practice can
only be approached if transmission bandwidths 10 to 100 times greater
than message bandwidth are utilized. The above result is a basic consideration in choosing between an analog or digital transmission system
for non-steady-state data.
The rms interference can be evaluated from the expression for U in
terms of q and Q, the rms amplitude and phase variations:

11

!! =
q

(q2

+ ~2) 72

= Normalized rms interference,

= Normalized rms amplitude variation over the message bandwidth WI,

Q = Rms phase deviation (radians) over the message bandwidth.
Since the message is assumed to contain no frequencies above WI, then the
quantities q and Qneed only be evaluated over the message bandwidth WI'
If the message contains noise which includes spectral components beyond
WI, it is necessary to control the amplitude and phase characteristic for
frequencies beyond WI.
Limitation of Information Capacity by Distortion

For an ideal system with a bandwidth /1 and a sharp cutoff characteristic with linear phase, the transmission capacity in bits per second is
given by the Shannon-Hartley law:
C =

iI log2

(1

+ SIN).

This expression gives the limitation on channel capacity imposed by random noise. From the previous discussion, it is evident that a limitation
also exists if distortion is present in the absence of noise. In idealized communication theory, distortion is disregarded in determining channel
capacity on the premise that it is predictable and can therefore be corrected, at least in principle. In actual systems, however, complete elimination, although possible in principle, cannot be accomplished.
.
Consider a system in which Amax is the maximum amplitude and :in is
an rms noise amplitude. For convenience, let A refer to the amplitude of a

15-88

INDUSTRIAL CONTROL SYSTEMS

small rectangular pulse which has a width equal to the time resolution required (Ref. 58). Then the number of identifiable amplitudes q is related
to Amax and 4n by

A maxi (q - 1) = L:1n,
L = Peak factor,
1/(q - 1) = L(4nI4)(:1IA max ),
where:1 equals the rms amplitude of A. But from the previous section,
1/(q - 1) = LQ(4IAmax).
Hence
by letting D = Q2, then
!J..2 = D = Noise powerISignal power
This means that random characteristic distortion has the same effect as a
random noise power DS, where D is a distortion factor.
In view of the above equivalence, the channel capacity in the presence of
random distortion but without noise is
C =

II log2 (1

+ liD)

With random interference from both distortion and noise, the interfp,ring
powers add directly so that (Ref. 54)

= 11 log2 [1

+ SI(DS + N)].

Since

it. is necessary that D «N IS for faithful reproduction of a transmitted
signal as in a data transmission system. In the above, g2 is the normalized
mean square amplitude variations and g2 the mean square phase variations,
both taken over the message bandwidth.
Note that, unlike random noise, the transmission capacity of a system
with distortion cannot be increased by increasing signal power. For a
given system with D and the noise power N specified, the effective signalto-noise ratio SI(DS + N) is limited to a maximum of liD for large signal
power and varies as SIN for small signal power.

TRANSMISSION SYSTEMS

15-89

REFERENCES
1. D. A. Bell, Information Theory and Its Engineering Application, Pitman, London, 1956.
2. C. E. Shannon, Communication in the presence of noise, Proc. I.R.E., 37, No.1,
10-21 (1949).
3. R. A. Fisher, The Design of Experiments, 5th edition, Oliver Boyd, London, 1949.
4. R. Piloty, Uber Die Beurteilung der Modulations Systeme Mit Hilfe des
N achrichtentheoretischen Begriffes der Kanalkapazitat, Arch. elektr. Ubertr., 5, 493
(1951).
5. B. M. Oliver, J. R. Pierce, and C. E. Shannon, The philosophy of P.C.M., Proc.
I.R.E., 36, Pt. 11, 1324-1331 (1948).
6. H. S. Black, Modulation Theory, Van Nostrand, Princeton, N. J., 1953.
7. H. Nichols and L. Rauch, Radio Telemetry, Wiley, New York, 1956.
8. S. Goldman, Information Theory, Prentice-Hall, Englewood Cliffs, N. J.) 1953.
9. Z., Jelonek, A comparison of transmjssion systems, Proceedings of a Symposium
on Applications of Communication Theory, London, 1952, W. Jackson, Editor, Butterworth, London, 1953.
10. N. Blachman, Informational capacities of AM and PM system, Proc. I.R.E.,
41, No.6, 748-759 (1953).
11. R. M. Stewart, Statistical design and evaluation of filters for the restoration of
sampled data, Proc. I.R.E., 44, No.2, 253-257 (1956).
12. R. S. Berkowitz, Methods of sampling band limited functions, Proc. I.R.E.,
44, No.2, 231-235 (1956).
13. A. E. Laeminel, Characteristics of communications systems, Report R 233-50,
PIB-178, Microwave Research Institute, Polytechnic Institute of Brooklyn, 1951.
14. A. E. Laemmel, Efficiency of codes as a function of their message length,
Proceedings of a Symposium on Applications of Communication Theory, London,
1952, W. Jackson, Editor, Butterworth, London, 1953.
15. L. A. deRosa, Recent advances in information theory, I.R.E. Convention Record, Pt. 8, Information Theory, 35-38 (1953).
16. H. Glixon, Can you take advantage of the cyclic binary decimal code, Control
Eng., 4, No.3, 87-91 (1957).
17. R. W. Hamming, Error detecting and error correcting codes, Bell System Tech.
J., 26, 147-160 (1950).
18. W. Keister, A. E. Ritchie, S. H. Washburn, The Design of Switching Circuits,
Van Nostrand, Princeton, N. J., pp. 284-287, 1951.
19. H. B. Voelcker, Simple codes for fading circuits, I.R.E. Trans. on Commun.
Systems, CS-6, No.2, 237-244 (1958).
20. C. E. Shannon and W. Weaver, The Mathematical Theory of Communication,
University of Illinois Press, Urbana, Ill., 1949.
21. R. M. Page, Comparison of modulation methods, I.R.E. Convention Record,
Pt. 8, Information Theory, 15-25 (1953).
22. S. Goldman, Information Theory, Prentice-Hall, Englewood Cliffs, N. J., 1953.
23. T. Hayton, C. Hughes, and R. Saunders; Telegraph codes and code converters,
Proc. Inst. Elec. Engrs. (London), Pt. III, 101, No. 71, 137 (1954).
24. G. Arthur, The statistical properties of the output of a frequency selective device, J. Appl. Phys., 25, No.9, 1185 (1954).
25. P. M. Schultheiss, C. A. Wogrin, and F. Zweig, Short time frequency measure-

15-90

INDUSTRIAL CONTROL SYSTEMS

ment of narrow band random signals in the presence of wide band noise, J. Appl.
Phys., 25, No.8, 1025 (1954).
26. D. Middleton, On theoretical signal to noise ratios in FM receivers: A comparison with amplitude modulation, J. Appl. Phys., 20, 335-351 (1949).
27. D. Middleton, The spectrum of frequency modulated waves after reception in
random noise, II, Quart. Appl. Math., 8, No.1, 59-80 (1950).
28. D. Middleton, The spectrum of frequency modulated waves after reception in
random noise, I, Quart. Appl. Math., 7, No.2, 129-174 (1949).
29. N. BIachman, The demodulation of an FM carrier and random noise by a
limiter and discriminator, J. Appl. Phys., 20, 28 (1949).
30. R. Jaffee and E. Rechtin, Design and performance of phaselock loops capable of
near optimum performance over a wide range of input signal and noise levels, Jet
Propulsion Laboratory Publication 20-243, Dec. 1, 1954.
31. H. Salinger, Transients in frequency Modulation, Proc. I.R.E., 30, 378 (1942).
32. C. C. Eaglesfield, Carrier frequency amplifiers (transient conditions with frequency modulation), Wireless Eng., 23, 96-102 (1946).
33. G. Hok, Response of linear resonant systems to excitation of a frequency varying linearly with time, J. Appl. Phys., 19, 242-250 (1948).
34. A. C. Clavier, Application of Fourier transforms to variable frequency circuit
analysis, Proc. I.R.E., 37, No. 11, 1287-1290 (1949).
35. J. R. Carson and T. C. Fry, Variable frequency eleetric circuit theory, Bell
System Tech. J., 16, 513-540 (1937).
36. B. Van der Pol, The fundamental principles of frequency modulation, J. Inst.
Elec. Engrs. (London), 93, Pt. 3, 153-158 (1946).
37. F. Stumpers, Distortion of frequency modulated signals in electrical networks,
Commun. News, 9, 82-92 (1948).
38. E. J. Baghday, Theory of low distortion reproduction of FM signals in linear
systems, I.R.E. Trans. on Circuit Theory, CT-5, No.3, 202 (1958).
39. J. W. Halina, A double sideband suppressed carrier communication system for
telephone application, I.R.E. Wescon Convention Record, Pt. 8, 61-67, 1958.
40. J. J. Hubert, Normalized phase and gain derivatives as an aid in evaluation of
FM distortion, Proc. I.R.E., 42, 438 (1954).
41. E. G. Fubini and D. C. Johnson, Signal to noise ratio in AM receivers, Proc.
I.R.E., 36, No. 12, 1461-1466 (1948).
42. D. Middleton, Rectification of a sinusoidally modulated carrier in the presence
of noise, Proc. I.R.E., 36, No. 12, 1467-1477 (1948).
43. R. E. Burgess, Observation of signals in the presence of noise, Phil. Mag., Ser.
7, 42, 475 (1951).
44. J. P. Costas, Synchronous communications, Proc. I.R.E., 44, 1713 (1956).
45. J. F. Honey and D. K. Weaver, An introduction to single sideband communications, Proc. I.R.E., 44, 1667 (1956).
46. B. Chance et al., Waveforms, M.LT. Radiation Laboratory Series, Vol. 19, McGraw-Hill, N ew York, 1949.
47. 1. A. Greenwood, Jr., J. V. Holdam, and D. M. MacRae, Electronic Instruments,
M.LT. Radiation Laboratory Series, Vol. 21, McGraw-Hill, New York, 1949.
48. R. A. Smith, The relative advantages of coherent and incoherent detectors, a
study of their output noise spectra under various conditions, Inst. Elec. Engrs. (London), Monograph 6, Radio Section (1951).
49. R. M. Fano, Signal to noise ratio in correlation detectors, Tech. Report 186,
M.LT. Research Laboratory of Electronics, Feb. 1951.

TRANSMISSION SYSTEMS

15-91

50. C. A. Stutt, Low frequency spectrum of lock-in amplifiers, Tech. Report 105,
M.LT. Research Laboratory of Electronics, March 1949.
51. P. E. Green, The output signal to noise ratio of correlation detectors, I.R.E.
Trans. on Inform. Theory, IT-3, No.1, 10-17 (1957).
52. R. C. Booton and M. H. Goldstein, Jr., The design and optimization of synchronous demodulators, private communication.
53. J. P. Costas, Interference filtering, Tech. Report 185, M.LT. Research Laboratory of Electronics, 1951.
54. E. D. Sunde, Theoretical fundamentals of pulse transmission, Bell System
Tech. J., 33, No.3, 721-788; No.4, 987-1011 (1954).
55. S. Goldman, Frequency AlIalysil) Alodulation and Noise, McGraw-Hill, New
York, 1948.
56. E. C. Cherry, Pulse response: A new approach to A. C. electric network theory
and measurement, J. lust. Elec. Engrs., 92, Pt. 3, No. 19, 183-196 (1945).
57. E. Hopner, An experimental modulation-demodulation scheme for high speed
data transmission, I.B.M. J. Research, 3, No.1, 74-84 (1959).
58. H. M. James, N. B. Nichols, and R. S. Phillips, Theory of Servo Mechanisms,
M.LT. Radiation Laboratory Series, Vol. 25, McGraw-Hill, New York, 1947.
59. G. James and R. C. James, Mathematics Dictionary, Van Nostrand, Princeton,
N. J., 1949, see definition of "standard deviation."

E

INDUSTRIAL CONTROL SYSTEMS

Chapter

16

Nuclear Reactor Control
W. E. Shoupp and M. A. Schultz

1. Introduction

16-01

2. Reactor Control System Requirements

16-05

3. The Reactor as a Servomechc:znism Component

16-07

4. Po ..... er Level Automatic Control

16-21

5. Example of the Design of a Reactor Automatic Control Loop

16-24
16-29

References

1. INTRODUCTION

General Requirements-Nuclear Reactor Control. There are two
reasons why the requirements of a control system for a nuclear reactor
or power plant are different from those of any other system. First, safety
requirements of a nuclear power plant are to some extent actually stipulated by law. Second, a nuclear reactor is a device which, if its control
system fails, can create not only local damage but also damage on a statewide basis. This is a new concept in liability, and consequently, the
primary requirement of a reactor control system is one of extreme safety.
Secondary requirements of performance, efficiency, and economics are
completely overshadowed by the safety requirements in the design of
the control system.
Description of a Nuclear Reactor (Ref. 1). There are many types
of nuclear reactors and to examine the control problem, a heterogeneous
thermal power reactor may be used as an example. A heterogeneous reactor is one whose fuel is in discrete-sized pieces placed in definite relationship to other reactor components. Figure 1 indicates the elementary
16-01

INDUSTRIAL CONTROL SYSTEMS

16-02

Control rod
actuator
mechanism
'--"""""",r----'

1{""'~Corltrol

rod

Coolant out

Neutron
detector

Coolant in

FIG. 1.

Basic components of a power reactor (Ref. 3).

components of such a reactor. The fuel is located in the center section
of the reactor which is sometimes called the core. This fuel is in solid
form for a heterogeneous reactor and consists principally of uranium,
either U235 or U238, singly or in some combination. Other fuels, such as
plutonium or thorium, may also be used.
Homogeneous reactors ar~ ~hose containing fuels in liquid or slurry
form. In either case the fuel is generally intermingled with a moderator
which is some suitable light element such as hydrogen, beryllium, or
carbon. The moderating material is used to slow down neutrons created
in the fission process to provide the desired energy spectrum. Passing
through the core, or in close contact with it, is a heat transfer material
or coolant. Gases, water, or liquid metals may all be used as coolants.
Outside the core proper is some reflecting material which is used to conserve neutrons and reflect them bnck into th'e core.
Surrounding the reflector is a biological shield which attenuates the
nuclear radiations emanating from the core. Inside the core or reflector
is equipment for regulating the power level of the core by controlling the
number of neutrons in it. The principal devices used for regulation are
generally called control rods. Many other devices are available to change
the number of neutrons in a reactor, but these devices have the same
general effect as control rods.

NUCLEAR REACTOR CONTROL

16-03

Descriptive Terms and Definitions. These definitions are not completely accurate from an analytical point of view. The definitions have
been abstracted with permission from Ref. 3.
Fission Process. ,"Vhen a neutron at a given energy is absorbed by a
uranium nucleus, there is a finite probability this nucleus will split into
two· or more fragments. This process is called fission, and in addition to
releasing a large amount of heat, two or three more neutrons each having
an approximate energy of 2 lVlev are released from the fragments. These
neutrons are then available to split more uranium nuclei.
1lJultiplication Factor (k). The ratio of the number of neutrons in
anyone generation to the number of corresponding neutrons of the immediately preceding generation is known as the multiplication factor. If
k is equal to or greater than unity, a chain reaction can take place. If k
is less than unity the reaction will ultimately die down.
Reactivity (8k). Reactivity is proportional to the amount the multiplication factor differs from unity. 8k = (k - 1) jk.
Neutron Lifetime (l). The average time between successive neutron
generations in a reactor is defined as the neutron lifetime. l* is used for
the mean effective lifetime of a neutron in a finite reactor containing
U235 (l* = ljk).
Thermal Reactor. A reactor in which the bulk of the fissions are
caused by neutrons having kinetic energies close to thermal levels (approximately 0.025 to 0.1 ev) is called a thermal reactor. Thermal reactors have neutron lifetimes in the 10- 3 to 10- 5 sec range.
Fast Reactor. A reactor in which the fission produced neutrons are
not slowed down appreciably before fission again occurs is called a fast
reactor. These reactors have neutron lifetimes in the 10- 6 to 10- 8 sec
range.
Intermediate Reactor. A reactor using primarily neutrons in the re-:
gion between fission and thermal energies is called an intermediate reactor. Neutron lifetimes are correspondingly between 10- 5 to 10- 6 sec.
Neutron Level (n). The number of neutrons in the core is proportional
to the number of fissions occurring. For 3 X 1010 fissions per second
one watt of power is produced.
Reactor Period (P). The period of a reactor can arbitrarily be defined
as
1

P=1 dn

n dt

where n is the neutron level and dnjdt is the rate of change of neutron
level.

16-04

INDUSTRIAL CONTROL SYSTEMS

Delayed Neutrons (/3, /3i). Not all the neutrons that are created in
fission process are given off instantly. A small fraction of the neutrons
are given off at discrete times after the fission process occurs. For a
reactor fueled with U235 approximately 0.75% of the total neutrons procured are delayed neutrons. At least six distinct groups of neutrons are
given off at different times and in different quantities. The symbol /3
is used to denote the total fraction of the delayed neutrons, with /3i being
the fraction of the delayed neutrons in the ith group. The symbol Ai is
used to represent the decay constant of the ith group of delayed neutrons
and is an inverse time constant.
Reactor State. This is defined by the value of the multiplication factor.
Sub critical Reactor. k < 1.
Critical Reactor. k = 1.
Supercritical Reactor. k > 1.
.:,.Prompt Critical Reactor. When a reactor is capable of sustaining a
chain reaction without the use of the delayed neutrons, the reactor is
said to be prompt critical. This corresponds to a multiplication factor
k = 1.0075 for a thermal reactor containing U235 fuel.
Temperature Coefficient. The amount that the reactivity of a reactor
changes per unit change in temperature is defined as the temperature coefficient. If, as a reactor heats up, its reactivity increases as a function
of temperature, the.reactor has a positive temperature coefficient. If as
the ·reactor heats up its reactivity decreases, the reactor has a negative
cd·efficient. Most present-day reactors are designed to have negative
temperature coefficients.
Fission Product Poisoning. After a thermal reactor has been operated
for a while, certain unwanted fission products, called poisons, are formed
which have large probabilities of absorbing neutrons and removing them
from the chain reaction. Two of the most common are xenon135 and
samarium149. If these nuclear poisons are produced in appreciable
amounts, they can affect the overall multiplication factor of the reactor.
Safety Rods. Control rods made of neutron-absorbing material, whose
functions are primarily to shut down a reactor quickly, usually by rapid
insertion, are called safety or scramming rods.
Shim Rods. Control rods which change large amounts of reactivity
but which are moved slowly, are sometimes called sh1:m rods.
Regulator Rod. A control rod which is used in an automatic control
system to maintain a given power level or to change this power level is
called a regulator'Tod. Regulator rods can, if necessary, be moved
quickly but can change only small amounts of reactivity (usually limited
to less than the difference in reactivity between critical and prompt
critical) .
th~

16-05

NUCLEAR REACTOR CONTROL
2. REACTOR CONTROL SYSTEM REQUIREMENTS

Basic Functions of the Overall Reactor Control System

The basic functions are to start up, shut down, and to operate the reactor. These control functions are usually performed by three distinct
interconnected systems. Figure 2 illustrates an elementary block diagram of a reactor control system.
r-----------r----------l

I

Startup system

I

I
I
I
I
I
I
I
I

Manual
or
automatic

I

Control
rod
actuators

Safety shutdown system

I

I

I
I
Scramming
actuators

I
I
I

Period
circuits

I

Level
circuits

Control
rods

Safety
rods

I

Neutron

Reactor

~ _ _ _ _ ~t~r

I
I
I
Power
Idemand
I
I

I

I

Neutron
detector

-,

_ _ -.---J_

Neutron
detector

Regulator
rod

Regulator
rod
actuator

Comparator

Error
signal
amplifier

II

Scramming
circuits

Other plant parameter
detectors

~-----­

I
I

I
I

I
L ___ ~ower level contr~stem _ _ _ ~

FIG. 2. Elementary block diagram-reactor control system.

The startup system contains a neutron detector or detectors which
are capable of measuring neutron level over a wide range-up to ten
decades. The range from 0 power to full power in a reactor covers nuclear
fissions resulting in a few neutrons per second to many billions per second. Noone detecting element is capable of covering this range, so a
multiplicity of instrumentation is used. Neutron level, n, and period, P,

16-06

INDUSTRIAL CONTROL SYSTEMS

are both measured and indicated. If the rate of change of power level
as indicated by the period circuits is too high, a connection is made to
the scramming circuits of the safety shutdown system whereby the reactor is quickly shut off or scrammed. Startup periods between 10 and
60 seconds are presently employed. The level in a startup is usually
controlled by withdrawing control rods from the reactor. After the reactor is made critical, the control rods change the multiplication factor
to slightly above one creating an excess of neutrons, and the power level
is made to rise slowly. The neutron level may be observed by an operator
or automatically and a measure of the level is used to control an actuator
mechanism driving the control rod or rods. This type of startup system is
used to bring the reactor into its normal power operating range.
The power level control system which takes over at this point starts
from two inputs, first a neutron detector whose output is proportional to
the power level, and a power demand reference signal representing the
desired reactor output. These two signals are compared and any error
signal amplified to control the motion of the regulator rod through an
actuator mechanism. The regulator rod position then continuously
changes the multiplication factor 6f the reactor to keep the power output
at the demanded level.
The safety shutdown system is superimposed on the other controls
for supersafety. Here many detectors are used, including a neutron
detector and sometimes input signals from many other plant parameters.
Variables such as temperature, pressure, coolant flow, and interlocks can
be used to determine that the plant is not behaving properly and the
reactor can be shut down immediately via the scramming circuits,
scramming actuators, and safety rods.
Performance Requirements of the Control System
The startup requirements of the reactor control system are generally
specified in terms of time rates. Variables involved are the neutron
level, the startup level, the range of the startup operation, and the periods
that will be permitted. In addition, a drastic limitation on startup time
rates may be placed upon the reactor by thermal requirements of some
of the components or auxiliaries. For example, a pressure vessel made
of thick walls might have a limitation in temperature stress such that
the temperature of the material inside the vessel would be permitted to
change only by a degree or so per minute. Consequently, overall reactor
startup times ranging from 15 minutes to several hours may be involved.
Power operation requirements are given in terms of stability, accuracy of power level demanded, time needed to change power level, and
peak transient level permitted from either an internal or external cause.

NUCLEAR REACTOR CONTROL

16-07

The reactor shutdown requirements stipulate that no damage be
caused to the reactor and no ancillary problems be caused in the plant
or the neighborhood. A reasonable peak power level and energy limit
in a transient burst must be specified. In addition, a listing of auxiliary
failures which might cause reactor damage, such as loss of coolant flow,
must be completely specified by a peak reactor temperature limit and a
given amount of tolerable output energy. It is the function of the control system to see that all of these requirements are met.
3. THE REACTOR AS A SERVOMECHANISM COMPONENT

The Reactor as a Control Component without Temperature Coeffident. In the block diagram of Fig. 2, the reactor is a component in

each of the three functional control systems. Its performance as a control element is therefore needed and this performance is most readily
obtained by determining its transfer function.
The basic kinetic equations that determine the time behavior of an
elementary reactor not possessing a temperature coefficient are (Ref. 2) :
dn

at

(1)

r::

ok - {3
-l-*- n

6

+ i~AiCi

(Neutron level equation)

and
(2)

dC i

-

dt

where n = the
ok = the
{3 = the
(3i = the
l* = the
Ai = the
Ci = the

{3i

= - n - A·C· (Delayed neutron equation),
l*

t

t

neutron level,
reactivity,
fraction of the delayed neutrons,
fraction of the delayed neutrons in the ith group,
mean neutron lifetime,
decay constant of the ith group of delayed neutrons,
concentration of the ith group of delayed neutrons.

Transf.er Function. The solution of these equations for a sine wave
input change in reactivity 8k (s) involves a linearization process in which
the reactor is assumed to be operating at a steady state level no and has
a small perturbation 8n(s) superimposed upon it. The transfer function
has been derived in this manner by several authors (Refs. 3-6), and is
of the form:
(3)

on(s)
ok(s)

INDUSTRIAL CONTROL SYSTEMS

16-08

where K RGR(8) is the reactor transfer function and 8 = .iw is the Laplace
; transform operator. For a U 235 fueled reactor with a lifetime l* = 1.2.5 "
X 10-3 sec and five principal groups of delayed neutrons, the reactor transfer function has been given as (Ref. 5)
"
(4)

+

+

+

+

on(8)
no(8
14)(8
1.61)(8
0.456)(8
0.154)(8 + 0.0315)
=
.
Ok(8)
l*8(8 + 14.4)(8 + 5.41)(8 + 1.41)(8 + 0.32)(8 + 0.08)

Reference 3 indicates the transfer function for a similar reactor with an
l* ~ 10-4 sec and six groups of delayed neutrons as

ones)

(5)

--=

ok(s)

f no(8 + 14)(8 + 1.61)(8 + 0.456) X )
l (8 + 0.151)(8 + 0.0315)(8 + 0.0124)
f l*8(8 + 77) (8 + 13.38) (8 + 1.43) X )
l (8 + 0.336)(8 + 0.0805)(8 + 0.0147)

Bode Diagram. Figure 3 indicates the transfer function gain and
phase shift for reactors having different lifetimes but all possessing zero
temperature coefficients. In this figure the gain is normalized to equal
zero db at one cycle per second for l* = 10- 4 sec.
20
Q3

.0

,

C1)

~ r-.....

5

:e0..

0

 f5k(s)
+ ~-

~

~

I
I

KRGR(S)
Reactor
transfer
function

ones)

f----------Kn;G1'c (s)

L-

I

Moderator
to reactivity
transfer
function

~

Fuel to
moderator
transfer
function

-

'I

MW ~IT~ITW

I
I
I

L _________ ~

(b)

(a)

(c)

Reactor transfer function with simple temperature coefficient feedback:
(a) transfer of heat from fuel to moderator and moderator temperature affecting
reactivity; (b) combined transfer function, reactor, and feedback; (c) temperature
coefficient feedback in terms of single time lag.

FIG. 4.

fer function with temperature coefficient is of course derived as
(6)

where KRGR(S) is the transfer function of the elementary reactor as
given in Fig. 3. A simple form of KTOG TO (s) can be analyzed with fair
accuracy by considering the two part process to consist of a lumped time
lag in transferring the heat from the reactor to the moderator, and a gain
term related to the power level and the value of the negative temperature
coefficient. This type of approximation is quite accurate for homogeneous
reactors of the type treated by Weinberg and Ergen (Ref. 9) and for
some heterogeneous reactors. It is assumed that one simple time lag
exists between the neutron power output and the ultimate reactivity
change caused by the temperature coefficient. The transfer function of
this lag is given by

(7)

KTC

KTCGTC(S)

= --,
TS

+1

where K TC = constant multiplied by the temperature coefficient,
T = the overall time constant of the thermal lag,
S = the Laplace transform operator.
The block diagram of this system is indicated in Fig. 4c.
Bode Diagram. An example of this combined reactor-temperature
coefficient transfer function is presented in the Bode diagram of Fig. 5
for several values of K TO , T = 0.159, and l* = 10- 4 sec.

NUCLEAR REACTOR CONTROL

16-11

55
VI

Q)

r-...

50

..c

'u 45
Q)

"0

40

KTC

~ L-

-

40

Q)

VI

=0.0095

0
20

l~

t

r0-

\

\ K TC

Q)

"0

~I\'""'

r-- I-t-

~a. 35
E

f--

t-- t-r-

"0

~ '--

"'0

~

~

0°

i'-....
i"'-I-

~

N

VI

(l)

~~

I""" .... i'.

VI

... ~

ro

i5: -45°

0.001

~,

0.01

0.1
1.0
Frequency, cycles per second

10

-I-- ..

100

FIG. 8. Example of reactor transfer function with two-path temperature coefficient
feedback (Ref. 3).

INDUSTRIAL CONTROL SYSTEMS

16-16

From Fig. 8 it can be seen that some of the dominant features of the
single-time lag feedback given in Fig. 5 are still retained, i.e., infinite
gain does not occur at zero frequency, and the high-frequency portions
of· the diagram are completely determined by the simple reactor neutron
lifetime. The phase shift portion of the diagram also indicates that this
configuration should be quite stable.
The Reactor as a Control Component with Multiple-Path Temperature Coefficient Feedback

The process indicated in Fig. 6 can be refined still further and multiple
temperature coefficient feedbacks defined. Figure 9 indicates the block
diagram of the temperature coefficient feedback paths for a testing reactor similar to the materials testing reactor (Ref. 14).

Reactor
transfer
function
n(s) or P(s)

Aluminum
absorption

a

l

Fuel
absorption

a2
Aluminum
absorption

aa
ok(s)

Water
absorption

a4
Fast neutron
leakage

a5

Water
function

Slow neutron
leakage

as
Aluminum
absorption

a7

Structure
function

FIG. 9. Block diagram multiple path temperature coefficient feedback for a testing
reactor.

NUCLEAR REACTOR CONTROL

16-17

Requirements

1. Here changes in the fuel temperature cause changes in the neutron
a bsorption cross sections of uranium and aluminum.
2. Changes in the water temperature cause water cross-section changes
and also affect the fast neutron and slow neutron leakage.
3. Finally, changes in the core structure can cause changes in neutron
absorption and dimensional changes in the reactor.
To each one of these changes can be assigned a local temperature coefficient a which may be positive or negative. The net reactivity feedback effect is obtained by summing up all the individual reactivity
changes as a function of frequency. The block diagram of Fig. 9 appears
to be quite complex, but an overall reactor transfer function may be
obtained graphically, or with the aid of an analog computer, providing the
various temperatures, coefficients, and time constants can be obtained.
The solution to this type of problem is usually a further refinement on
the two-path case previously treated in this Sect. 3.
The Reactor as a Control Component with Poisoning Feedback

In a thermal reactor, fission product poisons can build up which affect
reactivity. The isotopes causing the most reactivity change are Xe 135
and Sm149 • The behavior of these poisons can also be represented as a
feedback path around the reactor in a similar manner to the way that
the temperature coefficient was represented. The Sm149 isotope behaves
as a steadily increasing negative feedback depending upon the neutron
flux level in the reactor and the duration of the reactor operation. This
isotope is formed as the stable end product of the chain (Refs. 3, 15) :
(15)

149 ~ Sm 149
~\.
r Pm
-r
Nd 149 -

(t
bl )
sae.

This reaction occurs in approximately 1.5% of all fissions and Sm 149 has a
cross section for thermal neutron capture of approximately 5.3 X 104 barns.
Kinetically the fission product feedback from Sm 149 follows the equations
(16)

dP
-

dt

= 'YP¢ -

ApP

and
(17)

dS
-dt = ApP
. - as¢ ,

where P = number of Pm atoms present per cubic centimeter at any time t;
S = number of Sm atoms present per cubic centimeter at any time t;

16-18

INDUSTRIAL CONTROL SYSTEMS

'YP = fractional yield of Pm considering it to be the direct fission
product. The N d is ignored because the half-life of N d is
small compared with that of Pm; consequently, Pm may be
mathematically considered to be the direct fission product;
Ap = decay constant of Pm 149 ;
¢ = thermal neutron flux used interchangeably with previous definition of n;
(J's = microscopic thermal neutron cross section of 8m149.

The Xe 135 reaction has a much higher probability and a more complex
decay scheme (Refs. 15, 16).
(18)

Te

135

1 min
~

135

I

6.7 hr
~

Xe

135

9.2 hr
~

Cs

135

6

2.1 X 10 yr

) Ba

135

.

This reaction occurs in approximately 5% of the fission products and as
before, the Te 135 decay to 1135 can be ignored as occurring quickly compared with the other time constants involved. The buildup of the Xe 135
poison behaves kinetically as
dX

(19)

-

dt

=

All

+ ('Yx -

=

All

+ 'YI¢'

dI

(20)

-

dt

(J'xX )¢ - Ax X,

where X = number of atoms of Xe 135 present per cubic centimeter at any
time t,
I = number of atoms of 1135 present per cubic centimeter at any
time t,
'Yx = fractional yield of xenon as direct fission product,
135
(J' x = microscopic thermal-neutron absorption cross section of Xe
6
rv (3.5 X 10 barns),
¢ = thermal-neutron flux,
AI = decay constant of 1135 ,
Ax = decay constant of Xe 135 •
By using a linearization technique whereby the variables are split into a
steady-state term and an incremental variation about this steady state
such that
(21)

X = Xo

+ oX,

¢

= ¢o + o¢,

and

I = 10

+ 01,

a transfer function for small sinusoidal signals can be derived. This poisoning feedback transfer function has been found to be (Ref. 22)
(22)

oX

('Yx - (J'xXo){s

+

[AI'YI/('Yx - (J'xXo)]

+

AI}

--- = ---------------------------------o¢
(S
AI)(S
(J'x¢o
Ax)

+

+

+

NUCLEAR REACTOR CONTROL

16-19

Before this expression may be used, a generalized relationship between Xo
and CPo must be obtained as
(23)

Xo = ('Yx

+

'1(1) CPo

Ax

+

O"xCPo

•

Characteristics. This expression and the transfer function can be
examined numerically by using the following constants from Stephenson
(Ref. 16):
AI = 2.9 X 10-5

Ax = 2.1 X 10-5
'1'1 = 0.056

'Yx = 0.003
o"x

=

3.5 X 10-18

1. From eq. (23) the steady-state poisoning rises linearily with flux
until a flux level of approximately 1012 neutronsjcm2 -sec is reached.
2. At higher flux levels the Xe concentration rises more slowly until,
at flux levels of approximately 1014 and higher, there is no further increase
in poison concentration.
3. From a transfer function point of view, one flux level is of great
interest. From eq. (22), when (y.x - CT.xXO = 0) corresponding to a flux
level, with the above numerical values of cpo = 3 X 1011, the phase of the
transfer function shifts its ultimate end point with frequency. That is,
at high frequencies for cpo less than 3 X 1011 there is a total phase shift
in the Xe feedback path of _90°. 'Vhen cpo is greater than 3 X 1011,
there is an ultimate - 270° phase shift in the transfer function. The
transfer function gain at zero frequency when Y.x - CT.xXO = 0 is
yI/ (O".xcpo + A.x), and there is no discontinuity in gain as a function of CPo.
Figure 10 shows the Xe135 concentration for small
oscillations in flux normalized in gain about the cpo = 1014 case. The
absolute level for the cpo = 1014 curve is +19.1 db. The gain at zero
frequency is a constant for fluxes roughly below cpo = 1010 • At higher
levels the gain steadily decreases with flux.
To use this feedback transfer function in examining reactor stability
means that another loop must be tied back around the reactor (Ref. 17).
The poisoning loop to be considered can be around a simple reactor or one
containing complex negative temperature coefficient feedbacks. As all
reactors have a temperature coefficient of some sort, the representation
of the reactor transfer function as KRTCGRTC(S) rather than KRGR(S) is
reasonable. It will be recalled in the case of simple negative temperature
Bode Diagram.

16-20

INDUSTRIAL CONTROL SYSTEMS

70
60~-----4-------+------~------~------+-------r-----~

50~====$=====~~
40~-----+------~--~.-+------4--~---r------~----~

~ 30
.c
·u

~ 20~-----4-------+--~~~~~~~------+-------r-----~

c:

~ 10
0~-----4~~---+~----~----~~~~~+-------~~--~

-10
-20~-----4~L----+----~~--

___

-30

-25
-50~-----4--~~~~----~------~------+-------r-----~

-75
~ -100~--~·~--~~~~~-4--~--~~

__~~~=---~----~

Q)

~

~

-125

"C

~-150~-----4-------+----~~~--~-r~----~------T-----~

:c
~

5: -175
I'll

..c:::

~ -200~-----4-------+-------B~~--~~~

-225
-250~-----+------~------+---~~~~---+~~--~----~

-275

(b)

10- 5
Frequency; cycles per second

FIG. 10. Transfer function xenon poisoning feedback: (a) amplitude response, (b)
phase shift (Ref. 3).

coefficient feedback that the reactor transfer function depends only upon
the amount of feedback at zero frequency, and very low frequency responses could be approximated as KRTOGRTO(S) = l/K To . As the poisoning feedback occurs only at .extremely low frequencies, the use of this
relationship for the reactor transfer function in poisoning feedback prob-

16-21

NUCLEAR REACTOR CONTROL

lems is a good approximation. The feedback loops involved are shown
in Fig. 11. In this figure, before the complete poisoning loop is available,
oX (s) joe/> (s) must be multiplied by a gain term which depends upon the
fission cross section of the fuel used. The complete poison feedback
from neutrons to reactivity is indicated by IC:G:As).
For U235 fueled reactors (Ref. 22) indicates that thermal reactors
operating up to flux levels of 3 X 1011 are inherently stable without any
negative temperature coefficient in the reactor. At flux levels above
3 X 1011 a small negative temperature coefficient is required in order that

r-----------------,
I

(b)

I

I

I

I

I '--_ _---oJ

I

I

I

KxGx(s)

~----------------~

(a)

FIG. 11. Elementary block diagram of xenon poisoning feedback: (a) temperature

coefficient loop and poisoning loop, (b) combined reactor and temperature coefficient.

the combined loops be stable. Although this reference shows that instability is possible if insufficient negative temperature coefficient is present, this is not a serious situation. An unstable Xe135 feedback loop will
oscillate at frequencies of approximately 1 to 2 cycles per day. Normal
control rod motions for other purposes usually tend to mask out these
oscilla tions.
4. POWER LEVEL AUTOMATIC CONTROL

Description of Control Loop. Figure 2 indicates that the complete
control system for a reactor consists of three operational loops. The
startup loop is usually manual and open. The shutdown loop is either
in an on or off state. The power level loop is the only one which exhibits
regulatory action, and consequently it will be used as an example of
how automatic reactor control is accomplished.
Control Modes. An automatic control system in the power level
range consists of a control loop around a regulator rod or a shim rod
group and can be operated either as a proportional regulating system or

INDUSTRIAL CONTROL SYSTEMS

16-22

as a discontinuous regulating system. In this application, a proportional
regulating system is one in which the position of the control rod or rods
is changed in proportion to and in phase opposition with any error created
either by an external power demand change or an internal system transient. Similarly, a discontinuous regUlating system is one in which no
control is exercised until the error is some fixed percentage away from a
preset group of conditions set up in the control loop. When sufficient
deviation occurs from these demanded conditions, a control rod position
is changed usually at a fixed velocity. Discontinuous regulating systems
have been built to hold reactor power level to within 0.50/0 of the demanded level. Higher accuracy if needed can be obtained with the proportional type of control system. The discontinuous system is used
when there is a noise problem, in that it is less sensitive to random noises
which may originate anywhere in the loop. In high power reactors noise
is usually not a serious problem and either system may be used depending upon the accuracy requirements.
Figure 12 shows a block diagram of the control system in the power
Power
demand -----+--\
signal

FIG. 12. Power level control block diagram.

level range. The reactor multiplication is changed by direct movement
of the control rods. The output of the reactor is measured by a neutron
detector, generally an ionization chamber. Where slow response can be
tolerated, a neutron thermopile may be used. The reactor output is then
compared with the desired power demanded in the comparator and the
error between the output and the demanded output is amplified in the
error signal amplifier. The output of the amplifier is used to control an
actuator which moves the rods the proper amount and in the proper
direction to eliminate the error. The comparator, error signal amplifier,
and actuator may be of any suitable type. Pneumatic, hydraulic, electrical, and mechanical devices have all been used (Refs. 18-20). A brief
description of these major components in the loop, from a control system
point of view, follows.

16-23

NUCLEAR REACTOR CONTROL

The Reactor. The reactor transfer function for several reactor approximations has been given in Sect. 3. The principal feature to be
noted is the nonlinearity of the transfer function. The reactor gain is
proportional to the level at which the reactor is operating. This is usually
an intolerable situation as the control loop must operate in a stable manner over a wide range in gain. Some means to eliminate the gain dependence upon level is generally added to the control loop.
Comparator (Refs. 21, 22). The comparator in an automatic control
loop serves two purposes. First, it provides an error signal which is
essentially a subtraction between the neutron detector signal and the
power demand signal. Secondly, it is generally used to compensate also
for the reactor nonlinearity. The preferred form of the comparator output signal is error/level. In this manner, the reactor nonlinearity is
cancelled by the complementary nonlinearity of the comparator. Figure
13 shows two elementary forms of comparator circuits.

Feedback
E"b

Vn

KVn

Input 1
proportional
to n

1111,
Ye

(a)

Magnetic
amplifier

"C

ro

.s

Input 2
proportional
to no

(b)

FIG. 13. Elementary forms of comparator circuits: (a) battery circuit, (b) magnetic amplifier circuit (Ref. 3).

Battery-Operated Circuit. Figure 13a is the simplest form, whereby
the signal from the neutron detector is V n, which is proportional to the
neutron level of the reactor. If a reference voltage Vo is arbitrarily defined as Vo = Eb/K, then Ve = KV n - Eb = (Eb Vn/V o) - Eb
Eb(n - no)/no where Ve is the output error signal, n is the actual reactor
operating level, and no is the demanded steady-state level. This circuit
when connected to an output signal from the reactor does not quite cancel
out the reactor gain dependence upon level. Actually a signal inversely
I-'

16-24

. INDUSTRIAL CONTROL' SYSTEMS

proportional to n rather than no is desirable, but- the circuitry is usually
more complex. The difference between the actual level n and the demanded steady-state level no is usually quite small as the control system
acts to. make the two quantities the same. In a practical circuit, to
: ensure that no current is taken from V e , analog computing techniques
may be used and an operational amplifier input ·connected to Ve to prevent loading.
Magnetic Amplifier. The intense reliability r~quired of reactor control circuits sometimes precludes the use of vacuum tubes in the control
system, and consequently magnetic amplifiers have been used. Figure
13b indicates an elementary amplifier circuit which operates on the principle that, if sufficient negative feedback is used in an amplifier circuit,
the gain of the amplifier depends inversely upon the amount of feedback.
In the circuit of Fig. 13b, the load current IL = A (n - no) I (1 + AB)
where A is the gain of the amplifier and B is the feedback factor. If AB
is now made large compared with I,lL = (n - no) lB. It now only becomes necessary to make B proportional to either n or no in order that
the comparator output have the proper form. Again, in practical circuits, it is usually easier to obtain no than n.
The Error Signal Amplifier. The error signal amplifier may be a
. conventional vacuum tube, magnetic, or hydraulic amplifier. It amplifies
the error signal level from a few milliwatts to a few watts in order to
control the actuating device. Because of the flexibility and high state
of refinement of the control art, the frequency response of the amplifier
presents no problem in comparison with the response of the rest of the
system. The amplifier can be regarded and designed as pure gain in a
servo concept.
Actuators. The actuator mechanism is complicated because it may
be called upon to perform dual functions, i.e., in the case of shutting
down a nuclear reactor a rapid action may be required, whereas for
startup and power level control only a comparatively slow motion is
needed. In the control loop of Fig. 12, the frequency response of the
actuator may range from a few· cycles per minute to a few cycles per
second. The actuator mayor may not contain its own power amplifier,
and the output of the actuator is coupled directly to. a control rod. In
present-day reactors, the control rod may weigh between 25 and several
hundred pounds.
5. EXAMPLE OF THE DESIGN OF A REACTOR AUTOMATIC CONTROL LOOP

Specifications ,and Limits. All the previously described components
can now be put together in a loop:to illustrate a design problem. To keep
the example simple? the control rod speed will be assumed to be set by

16-25

NUCLEAR REACTOR CONTROL

some operational feature, such as the desire to override Xe135 within a
given time. Transient response of the loop will also be assumed to be
of no consequence, as the speed of rod motions and that of other pertinent
perimeters will be such that no large transients could occur. Consequently, the basic requirements for the design boil down into, "Given a
eeactor with a maximum rod speed, design a control loop for absolute
stability." An auxiliary question is, "To what variations in power level
is the resulting loop capable of maintaining the reactor."
Control Loop. For illustration, one can assume a discontinuous type
control system as indicated in Fig. 14. The reactor of this block diagram
Amplitude
function

I

I

I

n

Phase
I
icompensation
L ________ J

I

(a)

(b)

FIG. 14. Block diagrams of discontinuous type control loop: (a) compo.nent dia-

gram, (b) elementary servo representation.

could have anyone of the reactor transfer function representations' previously indicated, but for a specific example the reactor chosen will have
the transfer function given for the K po = 0.0047 case of Fig. 5. Additional phase compensation mayor may not be needed in the loop 6f Fig.
14, and this will be determined at the conclusion of the analysis'. The
contactor amplifier indicated in the block diagram may be considered as
a simple relay which closes a set of contacts when the error signal level
reaches a fixed amount and opens these contacts when the error signal
level drops below another fixed value. A corresponding set' of contacts is
used when the sign of the error signal reverses. This relay ca.uses a motor
to rotate in one direction or the other and to be stopped when the error
signal level is too small to keep either set of contacts closed. Figure 15
illustrates the terminology that will be used. The error signal into the
relays is proportional to (n - no) Ino. As the error signal increases, it
reaches the point b which closes the relay contacts that start the'drive
motor and creates a reactivity rate change signal V. Once the control
rods are started moving in the direction to reduce the error signal, the

16-26

INDUSTRIAL CONTROL SYSTEMS

Error signal
n;;ono

=x= Ixl sin wt

FIG. 15. Relay notation indicating start and stop points.

hysteresis of the relay causes the contacts in the relay system to remain
closed until the point a is reached and the drive motor is turned off. The
contactor amplifier is presumed to be symmetrical for negative signals.
The drive motor will be assumed as running at constant velocity after
an initial time lag T = 0.5 sec in getting started. This is a reasonable
value which many motors used in this service can exceed (Ref. 23). A
control rod is geared to the motor and the control rod motion is characterized by being able to change reactivity at a fixed rate in 8kjsec.
Analysis Procedure. The type of system indicated in Fig. 14 is a
nonlinear system, the principal nonlinearity being caused by the contactor. The reactor nonlinearity is presumed to be wiped out by the
action of the comparator. As is well known in control practice, the gain
of a closed loop consisting of only linear components is a function of
frequency. Any nonlinear component in a loop such as the on-off contactor in this reactor control loop causes the loop gain to be a function of
both frequency and amplitude. When the amplitude-dependent functions
in the system can be separated from those which depend upon frequency,
the loop gain can be expressed as the product BKAG, where A is a complex function of. amplitude, independent of frequency, G is a complex
function of frequency independent of amplitude, K is a constant gain
factor, and B is the feedback factor which equals -1 in this reactor
control loop. The overall transfer function of the closed loop is the

NUCLEAR REACTOR CONTROL

16-27

familiar expression (Refs. 24-26) :
(24)

Output

I(AG

Input

1 + KAG

KA
G-

1

+ I(A

Expressing the overall transfer function in this form indicates that the
stability of the system can be examined by comparing G-I and -KA.
This comparison can be made simply on a polar plot of G-I and -KA.
The value of G-l is plotted for all values of frequency, and -KA is
plotted for all values of amplitude. If the two loci intersect, that is, if
G-l = -KA, the system is capable of sustaining an oscillation.
Stability Plot. The loop components in the block diagram of Fig. 14
can be split up into the frequency function G and the amplitude function
A as just described. The function G is the product of the transfer functions of the reactor, the error signal amplifier, and the drive motor. The
function A comes from the contactor amplifier alone and describes the
effects of the relays. The method of determining the response of the
relays is usually based upon the development of Kochenburger (Ref. 27)
and depends upon the assumption that only the fundamental component
of the square wave signal of rod velocity coming out of the relay IS
significant. Higher harmonics are attenuated by the rest of the system,
particularly by the motor, and consequently may be ignored. From
Kochenburger, the terms which are of consequence in the analysis are
the ratios b/a, V /b, and x/b. Briefly, when b/a = 1, the output V is in
phase with the input x. vVhen b/a> 1, phase shift occurs between x
and V with the output phase lagging the input phase. The ratio V /b
appears directly as a gain factor in the contactor amplifier and the complete amplitude function equals (V /b)D where D is a complex function
of b/a and x/b. This complex amplitude function is plotted in Fig. 16
for the case where b/a = 2; V = 10- 3 ok/sec; and b = 0.1. This is a
reasonable set of numbers which can be attained easily by the relay and
by a typical control rod drive mechanism. Current practice in reactor
operations limits V to a range of between 10- 3 to 10- 6 ok/sec. The start
limit b depends upon the accuracy to which it is desired to hold the
power level, as b represents the dead zone.
Phase Compensation. The transfer function of the reactor now must
be modified in that the input of the reactor is not a change in reactivity,
but a change in rate of change of reactivity. Consequently, the output
will be a change in level as a function of the change in reactivity input
rate, that is, the transfer function is of the form on/n/sok. We can now
combine all the frequency-dependent portions of the transfer function
G (s), including the l/s term, invert this function, and plot it on the polar
diagram as shown in Fig. 16. In this particular example the reactor

.....i

0-

~

(X)

zo
c

(J)

-l

:::c

>

r-

()

o
Z

-l

:::c

o

r(J)

-<

(J)

-l

m
~

(J)

FIG. 16. Stability. plot for discontinuous control· system example.

NUCLEAR REACTOR CONTROL

16-29

control loop is stable in that the ,two curves do not intersect. The main
margin is approximately 17 db, 'and the phase margin is approximately
21°.
'
'
The same stability criteria hold here as would hold for other systems
and the phase margin appears to be somewhat low. Consequently, a
phase correction network would probably be inserted in the block diagram
of Fig. 14 to increase the phase margin to 35° or better. The above presented example for the design of a reactor control loop. for stability is
only one of the many types of control calculations that must be mad~
before the complete reactor control system is available.' However, the
above techniques suggest that reactor control problems' can be solved
with simple presently available methods.
REFERENCES
1. A. S. Thompson and O. E. Rodgers, Thermal P0tver from Nuclear Reactors,
Wiley, New York, 1956.
2. H. Soodak and E. C. Campbell, Elementary Pile Theory, WileYl New York,
1950.
'
3. M. A. Schultz, Control of Nuclear Reactors and Power Plants, McGraw-Hill,
New York, 1955, Chapter 3. "
"
4. Joseph P. Franz, Pile Transfer Functions, AECD-3260, October 26, 1951.
5. J. M. Harrer, R. E. Boyer and Darwin Krucoff, Transfer function of Argonne
CP-2 Reactor, Nucleonics, 10 (8), 30-36 (1952).
6. U. S. Atomic Energy Commission, The Reactor Handbook, Vol. 2, Engineering,
AECD-3646, U. S. Government Printing Office, Washington, D. C., 1955.
7. J. Chernick, The Dependence of Reactor Kinetics on Temperature, BNL-173,
Brookhaven National Laboratory, Upton, Long Island, New York, December 20,
1951.
8. L. B. Robinson, Concept of stability for nuclear reactors, J. Appl. Phys., 25,
516-518 (1954).
9. A. M. Weinberg and W. K. Ergen, Some aspects of non-linear i(inetics, Proc.
Kjeller Conference on Heavy Water Reactors, Jener, 1953.
10. H. J. Lipkin, A study of non-linear kinetics of the Chatillon reactor, Nuclear Energy, 1, 203-213 (1955).
11. J. M. Harrer and J. A. DeShong, Jr., Discontinuous servo for control of
power reactors, Nucleonics, 12, 44-51 (January 1954).
12. J. A. Fleck, Jr., Temperature dependent kinetics of circulating fuel reactors,
Convention of the Nuclear Engineering and Science Congress, December, 1955, Cleveland, Ohio.
13. D. 'Little and M. A. Schultz, Designing heterogeneous reactors for stability,
I.R.E. Trans:. Nuclear Sci., NS-4 (1),30-33 (March, 1957).
14. R. A. Charpie et al., Editors, Reactors, Progr. Nuclear Energy Series II,
McGraw-Hill, New York, 1956.
15. S. Glasstone and M. C. Edlund, The Elements of Nuclear Reactor Theory,
Van Nostrand, Princeton, N. J., 1952.
16. R. Stephenson, Introduction to Nuclear Engineering, McGraw-Hill, New
York, 1954.

16-30

INDUSTRIAL CONTROL SYSTEMS

17. J. N. Grace, M. A. Schultz, and T. E. Fairey, Inherent reactor stability,
Proceedings 1955 Conference on Nuclear Engineering, University of California, Los
Angeles, California, California Book Company, Berkeley, California, pp. Bl-21.
18. J. M. Harrer, Control rod mechanisms, Nucleonics, 13 (6), 48-51 (1955).
19. C. M. Rice, Hydraulic control-drive mechanisms, Nucleonics, 13 (11), 116-122
(1955) .
20. M. Silverberg, Hydraulic nuclear reactor controls, Nuclear Engineering and
Science Congress, Cleveland, Ohio, American Institute of Chemical Engineers, De·
cember, 1955.
21. The Reactor Handbook, Vol. 2, Engineering, AECD-3646, U. S. Government
Printing Office, Washington, D. C., May, 1955, Chapter 7.4.
22. M. A. Schultz, Control of Nuclear Reactors and Power Plants, McGraw-Hill,
New York, 1955, Chapter 4.
23. J. A. DeShong, Performance of Servo Motors for Reactor Regulating Rods,
AECD-3391, Argonne National Laboratory, Naval Reactor Division, Lemont, Ill.,
February 5, 1951.
24. G. S. Brown and D. P. Campbell, Principles of Servomechanisms, Wiley, New
York, 1951.
25. H. Chestnut and R. W. Mayer, Servomechanisms and Regulating System Design, Wiley, New York, 1951.
26. John B. Truxal, Automatic Feedback Control System Synthesis, McGrawHill, New York, 1955.
27. R. J. Kochenburger, A frequency response method for analyzing and synthe·
sizing contact or servomechanisms, Trans. Am. [nst. Elec. Engrs., 69, Pt. 1, 270-284
(1950).

E

INDUSTRIAL CONTROL SYSTEMS

Chapter

17

Control of Interconnected
Power Systems
Nathan Cohn

1. Introduction and Scope
2.
3.
4.
5.

Interconnected Power Systems
The Generation Control Problem
System Governing
Supplementary Regulation

6. Area Regulation
7. Regulation as a Function of Bias Setting
8. Economy Dispatch
9. Control Execution
References

17-01
17-03
17-08
17-17
17-24
17-29
17-50
17-64
17-103
17-124

1. INTRODUCTION AND SCOPE

Automatic Control in the Power Industry. The important contributions which instruments and automatic controls can make to improved
operating economy and reliability of electric power systems have long
been recognized. Modern power stations make extensive use of automatic
control equipment to regulate many of the parameters related to energy
conversion and utilization. A modern coal-burning steam plant would
typically be equipped for automatic control of combustion, feedwater
flow, superheat and reheat temperatures, air heater and mill temperatures,
feedwater pump recirculation, tank and heater levels, station voltage,
17·01

17-02

INDUSTRIAL CONTROL SYSTEMS

and many other related variables. The objective that justifies such extensive use of automatic controls is the safe, reliable operation of the
station at minimum cost. Such local station control loops, although of
vital importance to plant operation, are not included in the discussion of
this chapter.
The Area-Wide Concept. Another step forward in the use of automatic control in the power industry has been to relate automatically
the operation of individual stations with one another so that the objectives of continuity of service and high economy are achieved for a farflung network as a whole. There is the need and opportunity to coordinate the operation of the many generating stations of a network so that
prevailing customer demand is fulfilled, power interchanges with neighboring networks are established and maintained, and the outputs of available alternative sources are maintained at such levels as will provide
optimmn over~ll economy.
ThIS area-wide generation problem, which is more fully discussed in
Refs. 1 and 2, is considered in this chapter. Basic concepts related to the
control of generation and power flow on interconnected systems are outlined and analyzed, and steps leading to system optimization are defined
and appraised.
In practice, there are many variations in the control systems which
may be synthesized to solve the generation control problems of a given
utility or a group of utilities. Each operating group will define its own
objectives, which in turn will influence the control arrangements that are
to be. used. There are, however, common denomina:t.ors in the concepts
that define control objectives. It is these fundamental concepts and the
basic nature of solutions ,that are discussed in this chapter.
Terminology and Definitions. Terminology in this chapter adheres
generally to the prevailing day-to-day use by power systems engineering
and operating personnel. No effort is made to translate this practical
terminology into the language or symbology of feedback control specialists. There are in general no approved definitions or definitive terminology for many of the parameters, concepts, and philosophies encountered
and utilized in this field. Therefore, to avoid ambiguity and misunderstanding, pertinent terms are defined where first used and all later usage
adheres to these definitions.
Assumptions and Simplifications. Where· graphical representations
or performance equations are shown in the text, they generally apply to
steady-state conditions that follow illustrative step function changes.
This, and assumptions that are in each case stated, permits sin1plification
of the analyses without destroying the basic validity of the resulting

17-03

CONTROL OF INTERCONNECTED POWER SYSTEMS

conclusions which illustrate and define the nature of automatic control
responses on interconnected electric power systems.
2. INTERCONNECTED POWER SYSTEMS

Growth of Interconnections. Interconnections throughout the United
States continue to grow and expand. Six major interconnections embrace
most of the nation's central station facilities. The geographical extent
of each of them and its approximate load peak in millions of kilowatts
are shown in Fig. 1. Some of the adjacent interconnections shown in Fig.
Canadian - United States
Eastern interconnection
(30)

PA.-N.J.-MD.
interconnection .
(11)

Texas
interconnection
(7)

FIG. 1. Principal interconnections in the United States and eastern Canada. Figures
in parentheses are the approximate interconnection peak load in millions of kilowatts.

1 have at times operated in parallel with each other, and continuous
parallel operation in future years; reducing still further the total number
of interconnections in the country, is not unlikely.
Advantages of Interconnections. Interconnection contributes to the
two cardinal objectives of power systems operations: (1) continuity of
service and (2) economy of power production. During normal operating
periods, generation is shared. Interchanges between adj acent utilities are
scheduled to take advantage of load diversity or available lower cost
capacity, permitting lower overall operating costs and possible deferment
of capital investment for new stations. Scheduled outages for maintenance can be staggered.
During emergencies, spinning reserve capacity is shared, thereby contributing to continuity of service.
Systems and Areas. The terms system and area are not always
uniquely defined in power systems control discussions. Each is used at

17-04

INDUSTRIAL CONTROL SYSTEMS

times to identify a part, or all, of an interconnection. For purposes of
this chapter each will be given a specific meaning. This will permit ready
identification of an interconnection as being of the single area or multiple
area type, depending on its basic operating philosophy as related to absorption of customer load changes.
The term interconnected system identifies the complete interconnection.
It embraces all the utilities or groups of utilities (all the generating sources
and loads) which are linked together in the network. When the context
makes its use clear, the word system is used alone, without the qualifying
interconnected.
The term area identifies that part of an interconnected system which is
to absorb its own load changes. It may be a single company, responding
to its own load changes; it may be part of a company, operating to respond to load changes that occur in only a given part of the company's
network; it may be a whole group of companies pooled together to absorb
the load changes that occur anywhere within their collective boundaries.
A single area interconnected system is one in which load changes are
absorbed by the system as a whole, regardless of where on the system they
occur. Load changes that occur in any part of the system may be
absorbed elsewhere within the system, in accordance with the allocation
practices prevailing at that particular time. No one part of the system
is expected to adjust its own generation to absorb its own load changes.
Tie line power flows are, therefore, neither scheduled nor controlled.
Synonymous terms are single area system, and single area interconnection. The Pennsylvania-New Jersey-Maryland interconnection, shown
in Fig. 1, operates as a single area system.
A multiple area interconnected system is one that consists of a number
of operating areas, each of which is expected to adjust its own generation
to absorb its own load changes. Tie line power flows between areas are
scheduled and maintained. Synonymous terms are multiple area interconnection and multiple area system. Five of the six interconnections
shown in Fig. 1 are of the multiple area type.
Representation of an Interconnected System

Simplified representations of an interconnected system are shown in
Figs. 2 and 3. Figure 2 shows several operating companies linked together
in an interconnection. The intercompany ties are shown in simplified
form. There would usually be additional links between the companies,
but the simplified schematic will serve the purposes of this discussion.
Figure 3 is a further representation of the interconnection. Each company has its own load, labeled L with a corresponding subscript, representing the aggregate of all loads within the area. Each company has

CONTROL OF INTERCONNECTED POWER SYSTEMS

17-05

FIG. 2. Simplified diagram of several operating companies linked together to form

an interconnection.

FIG. 3. Schematic representation of the interconnected system. Each company has
its own load L, with a corresponding subscript, and its own alternative generating

sources G and G' , with corresponding subscripts. Each company has a tie line T
with each of its two neighbors.

INDUSTRIAL CONTROL SYSTEMS

17-06

its own alternative generating sources, labeled G and G' with corresponding subscripts, representing all the generating sources within the company
area. Each company has a tie line wjth each of its two neighbors, each
tie representing all its links with that neighbor.
Figure 4 shows all the companies (the complete interconnection) oper-

///-------:n:-~

/

/

/

/
/

/

operating"'/ ""'-.

a~'

~

\

\

\

/

/
I

\
\

I

\

\
\

\

\

\

/
~

"-"'-

t
fz:;:\

" -- V
---------~
............

/
---'

/'

/

/

\
I
I
/

/

///

FIG. 4. The complete interconnection operating as a single area system. See Fig. 3
for definition of symbols.

ating as a single area, as indicated by the dash line circle. Intercompany
tie line loadings are not of consequence, provided of course they are within
the capabilities of the ties. Load ch~nges that occur in the system are
assigned, regardless of where they oc_cur, in accordance with prevailing
system-wide allocation programs: On this basis, anyone of the companies is likely to absorb the load changes of another company. The five
interconnected companies are at once a system and an area.
Figure 5 illustrates multiple area operation with each' of the five companies of the interconnection operating independently as a separate area.

CONTROL OF INTERCONNECTED POWER SYSTEMS
/'

".---

......

;/

, "-

/

17-07

'\
~~~--

I
\

\

\

//

/

/

\.

,...-

/

I
\

\

\

\.

'-,

--_/

2AB

I
\

\

\.

'-

'--_/ /

FIG. 5. The interconnection arranged to operate as a multiple area system, with five
operating areas.

This is indicated by the five separate dash line circles. When a load
change occurs in a given area, it is the generation of that area. that is to
be varied to accommodate that load change. Interchanges over the five
interarea ties, labeled T with suitable subscripts, are now important and
are scheduled to specific levels.
Figure 6 shows another multiple area operating arrangement for the
interconnection. Companies A, B; 0, and E are joined in a pool to
operate as one area. Company D operates independently as another area.
The complete interconnection now has two operating areas, indicated by
the two closed dash lines. Power flow on the two interarea ties, T OD and
T DE, is now important and is sch~duled and regulated.
Responsibilities of Interconnections. vVhile sharing in the benefits
of interconnected operation, each participant is expected to share comparably in its responsibilites. This involves cooperative participation in
system regulation in concordance with the established philosophies of the
interconnection, so that smooth, neighborly, and mutually beneficial operation is achieved.

17-08

INDUSTRIAL CONTROL SYSTEMS

/...----"".
/

/

'" "-

//

----, "-

I

'\

/

/

\

\

,
\

/
/

I

I

I
/

I

/

/

-

I
I

"-

I
I

"-

'\

\
\

\

\

\
\
\

I

/
/

/

\

/

\
\

\
\

'\.

"'- "-

'" , -......

/

/

/

I

I

/

,/

-......

-

------

./

./

./

./

FIG. 6. The interconnection arranged to operate as a multiple area system with two
operating areas instead of five as in Fig. 5.
3. THE GENERATION CONTROL PROBLEM

The Basic Problem
Fundamental Operating Objectives. A first objective in the operation of an electric power system is 'continuity of service to customers.
This means that generation must be adjusted, in real time, to match prevailing demand. A second objective, to be achieved as long as it is consistent with continuity of service and dependable operation, is to generate the required total output at minimum overall cost.
WaU's Problem. The problem of matching output to demand is a
fundamental one in energy conversion systems. James Watt faced this
problem with his first steam engine. He solved it with his well-known
flyball speed governor, itself a pioneer achievement in automatic feedback
control, which automatically adjusted input until output satisfied demand.
Speed governors are still part of today's problem, and of its solution.
Watt, however, had only one energy source in his problem, and a single
governor matched output to demand. On modern interconnected systems
literally dozens or hundreds of alternative energy sources will be oper-

CONTROL OF INTERCONNECTED POWER SYSTEMS

17-09

ating in parallel, each carrying a part of the total load and each speedgoverned to change output in response to demand. Determining how to
allocate demand changes among them, and achieving such allocations,
adds a complex dimension to the generation control problem.
The Problem of Multiple Sources. The many generating sources of
an interconnected system will be spread out over a large area, hundreds or
thousands of square miles or more in extent. Important factors to be
considered are:
1. The generating units will differ in size, type and age, and will have
differing efficiencies, differing fuel and operating costs, varying loadcarrying capabilities, and varying response characteristics.
2. The generating units will be at varying distances from load centers,
and transmission losses will be influenced by the generation allocations
that are utilized.
3. There will be buy and sell power interchange agreements between
adjacent areas.
4. There will be limits to the power that can be carried over certain
transmission lines.
5. Spinning reserves must be appropriately maintained in various areas.
6. Where hydroelectric power is involved, there will be problems of
storage and stream flow.
All these factors, and related ones, will influence the allocation of generation to each of the sources. The dual objectives will be to secure the
correct total generation to match prevailing total demand and to allocate this total among alternative sources for optimum economy consistent
with continuity of service.
The Integrated Problem

For a given operating area of an interconnection, the control of total
generation and its allocation among alternative sources may be regarded,
despite its complexity and the number of variables encompassed, as a
single integrated control problem. The typical steps of perception, evaluation, and correction, inherent in the solution of any control problem,
may occur at widely separated points, and the information channels that
link together the component parts of the measurement and control
loops may be hundreds of miles in length. Telemetering problems, as
discussed in Ref. 3 should be considered. There will be multiple objectives to be achieved and many significant parameters to be considered.
Automatic computation will be utilized, and a number of controllers will
be required, operating either in parallel or in cascade. The design objective is to synthesize means for fulfilling all the regulating requirements
into a single coordinated solution.

17-10

INDUSTRIAL CONTROL SYSTEMS

General Steps in Planning a Solution. In considering the integrated
generation control problem of an operating area and in planning for its
solution, three general planning steps will be helpful. These are as follows:
1. Define Operating Criteria. Define the operating criteria which in
turn will define the interrelations and set points for significant parameters.
Some of the set points will be fixed; others will change with varying area
conditions.
2. Establish Set Points. Provide means for establishing the set points,
either by utilizing manually preset programs or by real time computation
or control.
3. Plan Control Execution. Provide means for executing the control
steps so that the set points established for the various parameters are
achieved.
Points to be Considered. In carrying out these general steps, consideration should be given to a number of points whose proper treatment
can contribute greatly to the overall effectiveness of the synthesized control system. These points are as follows:
1. Coordination with Governors. Control executions should be fully
coordinated with governing responses.
2. Coordination of Controllers. Where multiple controls are used, they
should be fully coordinated with one another to avoid interaction and
hunting.
3. Stable Controls. Each control should be stable and should act to
correct errors and not create them.
4. Data Display. Adequate display of pertinent parameters should be
provided for dispatchers and operators.
5. Channels. Although the number of information channels should be
kept at a minimum, their use must be carefully considered if they can
serve vital purposes, such as providing appropriate feedback for control
or pertinent information for display.
6. Operating Ease. Since supplementary controls are tools to help dispatchers and operators do a better job, they should be designed to ease
operating problems and not complicate them. Controls should be easy to
comprehend and easy to cut in or out of service.
7. Safety. Controls should be inherently safe and should be self-disabling, with appropriate alarms, if faults occur in their performance or in
the channels that connect them to sources of information and locations of
regulation.
Specific Steps for Achieving a Solution. Steps in the solution of the
generation control problem on both single area and multiple area systems
are summarized in Table 1. There are two steps on a single area system,
and three on a multiple area system.

CONTROL OF INTERCONNECTED POWER SYSTEMS
TABLE

1.

17-11

THE GENERATION CONTHOL PROBLEM FOR AN
INTERCONNECTED SYSTEl\I

For a Single Area System
Step 1
Achieve correct total
system generation, i.e.,
match total system
generation to total system load.
System governing.
Defined as:
An unchanging system
Criterion:
frequency.
Achieved by: Natural regulation.

Objective:

For a Multiple Area System
Step 1
Objective:

Achieve correct total
system generation, i.e.,
match total system
generation to total system load.
System governing.
Defined as:
Criterion:
An unchanging system
frequency.
Achieved by: Natural regUlation.
Step 2
Objective:

Allocate total system
generation among the
areas so that each follows its own load
changes and does its
share of frequency regulation, i.e., so that
total area generation
equals total area load
±scheduled area net
interchange.
Defined as:
Area regulation.
Criterion:
Area net interchange
is on schedule, i.e.,
area requirement is
reduced to zero.
Achieved by: Net interchange tie
line bias control.

Step 2
Allocate total system
genera tion among
alternative system
sources for optimum
economy.
Economy dispatch.
Defined as:
Sources loaded to equal
Criterion:
incremental costs of
power delivered.
Achieved by: Computation and control systems. See
Sects. 8 and 9.

Objective:

Step 3
Allocate total area
generation among
alternative area
sources for optimum
economy.
Defined as:
Economy dispatch.
Criterion:
Sources loaded to equal
incremental costs of
power delivered.
Achieved by: Computation and control systems. See
Sects. 8 and 9.
Objective:

17-12

INDUSTRIAL CONTROL SYSTEMS

Specific Steps for a Single Area System. There are two specific steps
in the solution of the generation control problem in a single area interconnection. The first is to achieve the correct total system generation;
the second is to allocate this total among alternative system sources for
optimum economy.
Step 1. Satisfying Total System Demand. This step is achieved when
total system generation matches total system load. The criterion for determining when total demand has been satisfied is an unchanging system
frequency. It is important to note that this does not mean a unique frequency, such as 60 cycles, but rather an unvarying frequency, at whatever
level then prevails. It means an absence of acceleration or deceleration
of the system.
Step 2. Allocating Total System Generation among Alternative Sources.
Applicable criteria for this step, and various computation and control
techniques for satisfying these criteria are discussed in Sects. 8 and 9.
Specific Steps for a Multiple Area Interconnection. There are three
steps in the solution of the generation control problem on a multiple area
interconnection. The first is to achieve the correct total system generation, the second is to allocate the total system generation appropriately
among the areas of the interconnection, and the third is to allocate each
area's generation among its alternative sources for optimum economy.
Step 1. Satisfying Total System Demand. This first step is the same
on the multiple area system as it is on a single area system. An unchanging system frequency, zero acceleration, is the criterion that confirms a
match between total system generation and total system load.
Step 2. Allocating Total System Generation among the Areas. This
step for a multiple area system has no counterpart on a single area system. Its objective is to assign to each area the load changes that occur
within its boundaries. Total area generation will accordingly vary in
the manner that total area load varies. The two may not be equal, however, but may be displaced by a fixed amount corresponding to the prevailing interchange schedule between the area and the rest of the system.
Maintenance of such interchange at its scheduled value is the criterion
that the area generation is being adjusted to match changes in its own
area load.
Step 3. Allocating Total Area Generation among Alternative Sources.
This step for the multiple area system is comparable to step 2 of the single
area system, except that here it is the total area generation that is allocated among alternative area sources for optimum economy. The criteria that define such allocation, and computation and control techniques
utilized to achieve them, are discussed in Sects. 8 and 9.

CONTROL OF INTERCONNECTED POWER SYSTEMS

17-13

Regulation

The term regulation applies generically to the matching of generation
and load, to the transfer of generation among sources, and to the adjustment of stored spinning energy of a system to achieve a desired frequency.
It is achieved on present-day power systems by direct speed governing
action or by supplementary adjustment of speed governors. The following subsections define more specifically the types of regulating effects encountered and utilized in generation control systems.
Governing Regulation. The term governing regulation defines two
effects. It applies to the adjustment of generator output by the action
of turbine governors responding to changes in system speed; this adjustment is identified as generation governing. It also applies to the variation of connected load with changes in system frequency, identified as
load governing. Both of these effects are frequently referred to as natural
governing or natural regulation.
Supplementary Regulation. Turbine speed governors are normally
equipped with a motor-driven adjustment that shifts the speed-output relationship of the generator. Operation of this device either manually
or through automatic means varies the generation or speed level of the
unit. Such operation is defined as supplementary regulation. It is also
referred to as imposed regulation.
System Governing. The term system governing applies on an interconnected system to the matching of total generation to total load by
governing action. It is governing regulation or natural regulation for
the system as a whole. It is the aggregate effect of all the generator
speed governors of the system plus any coefficient of system load as a
function of system frequency. It is step 1 in the regulation of single area
and multiple area interconnections (see Table 1). Area Regulation. The term area regulation defines supplementary
regulation applied, manually or automatically, to area generator speed
governors, to cause each area to follow its own load changes and do its
share of frequency regulation. It represents step 2 of the multiple area
control problem.
Economy Dispatch. The term economy dispatch defines supplementary regulation applied, manually or automatically, to generator speed
governors on either single area or multiple area systems, to allocate generation changes among alternative sources for optimum economy. Synonymous terms are economic loading, incremental loading and sustained
assignment. In general, economy dispatch is achieved when alternative
sources of an area are loaded to equal incremental costs of power delivered,
as defined and discussed in Sect. 8. Economy dispatch represents step 2

17-14

INDUSTRIAL CONTROL SYSTEMS

in the single area control problem and step 3 in the multiple area ,control
problem.
Load-Frequency Control. The term load-frequency control or frequency-load control has been used since the earliest days of the generation
control art to identify generically supplementary regulatian by automatic means responsive to frequency, time error, source loading, tie line
pawer flow, area generation, and combinations of these ar related parameter.s.
Area Control. The term area control is a contractian of area-wide
generation control. On a single area system it would be synonymous with
automatic economy dispatch. On a multiple area system, to which the
term is more generally applied, it infers that the automatic control equipment is performing both area regulation and economy dispatch, thus fulfilling both steps, 2 and' 3 of the multiple area problem. It may do so.
in a single step or in successive steps. In the single step execution, all
area generation changes are allocated in accordance with the ecanomy
dispatch program. In the aggregate such allocations provide the necessary area regulation. Such single step execution minimizes generation
changes within the area. Each change is allocated ance to the area source
where it is to. remain in accordance with the economy dispatch program.
Wh~n the sources involved in such allocatian cannat be responsive enough
to provide the desired area regulation, gene'ration changes are initially
assigned elsewhere in the area for more rapid response, and then they are
assigned in a subsequent step to the sources that are to retain them an
the economy dispatch basis.
Area Assist. The term area assist or area assist action defines the component of area control that involves assignment of generatian changes
temporarily within the area for mare rapid or extensive area regulation,
before making the assignment to the sources of the area that are to retain
the ,changes on the econamy dispatch basis. A synonymous term is initial
assignment, as distinguished fram the economy dispatch sustained assignment. It is also. identified as fringe control, swing control, and proportional action. On a single area system, the equivalent of area assist action is achieved by system governing, and no. supplementary regulation
is required for this purpose. On a multiple area system, area assist if desired would be part of the supplementary control.
Economy Interchange. The term economy interchange applies to the
intentional supply af excess lower cost energy from a company which has
it a'vailable to a company which can use it to displace its own higher
cost energy. On a single area interconnection, econamy interchange occurs when ane company adjusts its generation on an economy dispatch
schedule, in accordance with step 2 of the single area problem, to accam-

CONTROL OF INTERCONNECTED POWER SYSTEMS

17·15

modate another company's load change. On a multiple area interconnection, economy interchange between areas is achieved by setting and holding interarea tie line schedules in accordance with step 2 of the multiple
area problem.
Summary of the Generation Control Problem

Steps in the solution of the generation control problem for both single
area and multiple area systems have been summarized in Table 1. Figure
7 summarizes the factors to be considered in allocating total generation
Factors influencing economy
r~--------In-cre-m-en-tal----~A~----------------~,
Availability
of
sources

efficiency
of each
source

Required
total
generation

High and low
limit of
each source

Fuel
costs

Transmission
losses

Desired generation
for
each source

Assimilation
and
computation

Reserve
requirements

Transmission
line
limitations

Hydro
conditions

,

Permissible
rate of
change
of
sources

Rate of
change
of
customer
load
v

I

FIG. 7.

for economy dispatch, step 2 of the single area problem, and step 3 of the
multiple area problem.
Classification of Control Systems

Control systems. may be broadly classified by the portions of the integrated control problem which they undertake to solve and by the nature
of the programming technique used when multiple source loading is involved. They may be additionally subdivided by the nature of the common reference used for establishing source loadings. Also, in some of the
subdivisions, optional arrangements, as will be individually specified, may
be included. .

17-16

INDUSTRIAL CONTROL SYSTEMS

Data on classifications and subdivisions, based on the categories sug..;
gested in Refs. 4 and 5, are included in the following paragraphs; their use
makes for considerable convenience in describing the general nature of
alternative approaches to the solution of generation control problems.
The categories described apply fully to multiple area systems and partially to single area systems. It should be noted that in practice some
control installations incorporate combinations of various classes and types.
Summary of Classifications. The three general classifications of control systems and the three subdivisions in the first class are as follows:
Class I. Area regulation only
Type 1. Single source regulation.
Type 2. Multiple source regulation, single source output reference.
Type 3. Multiple source regulation, area requirement reference.
Class II. Economy dispatch, flexible programming.
Class III. Economy dispatch, fixed programming.
The subsections that follow discuss the area regulation techniques of
Class I controls. For illustrative diagrams and a discussion of Class II
and Class III economy dispatch systems, and of the three types of controIs in each of these classes, see Sect. 8 of this chapter.
Class I Control, Area Regulation Only

This is a control system which undertakes to provide area regulation
only. Such control is area assist control. Economy dispatch within the
area, if practiced at all, is achieved by direct manual adjustment of the
generation levels of area sources.
Subdivisions in this class are defined by whether control is on a single
unit or multiple unit basis, and by the nature of the reference for multiple
unit loading.
Class I, Type I, Single Source Regulation. In this execution a Class
I control is applied to a single generating unit. A block diagram would
be Fig. 44 in Sect. 8, with control applied to source GA only. Such control
is usually undesirable, since it would generally impose too large a regulating burden on the unit. Very few installations of this type remain currently in operation. Control is preferably applied to several units, thereby
spreading the regulation.
Class I, Type 2, Multiple Source Regulation, Single Source Output
Reference. Here control is applied simultaneously to two or more units.
Participating sources are automatically loaded with respect to the load
level on one of them which is designated as the master. A schematic for
such a control would be similar to Fig. 44 in Sect. 8, but with control

CONTROL OF INTERCONNECTED POWER SYSTEMS

17-17

applied to a limited number of units in the area. A few early installations
of this type remain in operation.
Class I, Type 3, Multiple Source Regulation, Area Requirement
Reference. In this execution a Class I control is applied to two or more
units. Participating sources are automatically loaded with respect to a
reference derived from area requirement, which is defined in Sect. 6. See
Fig. 64 in Sect. 9 for a block diagram of such a control. Very few installations use this arrangement by itself. It is frequently used, however,
in combination with Class II and Class III economy dispatch systems to
achieve area assist control as discussed in Sect. 9.
4. SYSTEM GOVERNING

System regulation, matching total generation output to total load demand-step 1 of Table 1-is achieved by governing action. There are
two components to such governing action. One is generation governing,
the other load governing.
Generation Governing
General Nature of a Speed Governor. Speed governors are arranged
to vary prime mover input automatically in response to changes in system
speed. A speed sensitive element, usually a flyball assembly, is responsive to changes in speed and operates through suitable amplifying servos
to adjust prime mover input until system acceleration or deceleration is
arrested. A simplified schematic of a speed governing system is shown
in Fig. 8. To permit parallel operation of prime movers, the speed-output
governing characteristic of each is of a drooping nature. The extent of
the droop determines how much speed change is required to induce a
given change in output.
R
Increasing speed
decreases
turbine input

R
L

~

f

------........~---------,

FIG. 8. Simplified schematic of flyball governor which regulates speed and output
of generator G by controlling input to turbine T. Motor M permits application of
supplementary control by adjustment of pivot point f. Up\vard adjustment of f
raises output, downward adjustment lowers output.

17-18

INDUSTRIAL CONTROL SYSTEMS

Speed Changer. Speed governing systems are equipped with a supplementary means-identified as a speed changer-for shifting the speedoutput relationship. The manner in which these supplementary means
are utilized to allocate generation changes to various sources is discussed
in Sect. 5.
The Speed-Output Characteristic. Figure 9 shows a hypothetical

G

- -JFrequency - ___
ie.Ql!f~ ~E.

~ __

_

I
I

G

o

100%
Unit generation

FIG. 9. Hypothetical generator governing characteristic.

speed-power output governing characteristic. It is shown as a straight
line. Assuming a single unit system, and starting with output Go at 60
cycles, the figure shows how conditions move from point 10 to 11 as a new
load AL is added and frequency is reduced by AF.
In practice, speed-output characteristics are not straight lines over the
full range of generator operation as shown in Fig. 9. Instead, the drooping characteristic has an irregular pattern, as shown typically in Fig. 10.
On steam units, such irregularities result from the characteristics of steam
inlet valves.
Steady-State Speed Regulation. For a single turbine, steady-state
speed regulation is defined Ole£. 6) as the change in steady-state speed,
expressed in percent of rated speed, when output is gradually reduced from
rated to zero power. For purposes of the present discussion, it may be
regarded as the percent of nominal frequency ·which will cause generator
output to change from no load to full load. A synonymous term is percent droop. It is graphically represented in Fig. 10 by the slope of the
dash line.

CONTROL OF INTERCONNECTED POWER SYSTEMS

17-19

~

,,~

~

~,~

,

~
, r--~"

o

\

'~
100%

Unit generation

FIG. 10. Typical generator-governing characteristic. [Source: E. E. George, Elec.
World, 23, 85 (1945),]

Steady-State Incremental Speed Regulation. For a single unit, the
steady-state incremental speed regulation is defined, at a given steady-

state speed and power output, as the rate of change of steady-state speed
with respect to power output, expressed in percent of rated speed (Ref.
6). A synonymous term is percent incremental droop. For a characteristic as shown in Fig. 10, it is a variable from no load to full load. It is
graphically represented in this figure by the slope of each of the segments
that make up the overall characteristic.
Prevailing Natural Generation Governing Characteristic. In analyzing generation control problems, an important term is the prevailing
natural generation governing characteristic. It may apply to a unit, an
area, or a system. For each of them, it has the same basic meaning that
steady-state incremental speed regulation has for a unit, but it may be
expressed in different terms.
For a Single Unit. The prevailing natural generation governing characteristic for a single unit is identical to the steady-state incremental
speed regulation of the unit. It may be expressed as the same percentage
droop. It may also be expressed in percent capacity per one-tenth cycle
or megawatts per one-tenth cycle, in which cases for a 60-cycle system the
following relations (see Ref. 7) apply:
(1)

100
N=-.

(2)

N'=-.

6D
M

6D

17-20

INDUSTRIAL CONTROL SYSTEMS

where N is the prevailing natural generation governing characteristic in
percent of unit capacity per one-tenth cycle,
D is the steady-state incremental speed regulation in percent,
N' is the prevailing natural generation governing characteristic in
megawatts per one-tenth cycle,
M is the unit capacity.
Thus, for example, applying eq. (1), a steady-state incremental speed
regulation of 8% corresponds to a prevailing natural generation governing
characteristic of approximately 2% of capacity per one-tenth cycle.
For an Area. An area will include a large number of generators of
different types and sizes, with governors of correspondingly different
sensitivities, dead bands, response times, and incremental speed regulation characteristics. At any given time, and for a given set of prevailing
conditions, the area taken as a whole will have a characteristic generation response to speed and load changes. The prevailing natural generation governing characteristic for the area is defined by this aggregate
response. Since it is made up of a number of nonlinear components, it
is itself not likely to be linear over an appreciable range. However, over
the small ranges of speed change and load change usually considered,
it may, for a given combination of generators and loading, be regarded
as linear. It is usually expressed in percent per one-tenth cycle or in
megawatts per one-tenth cycle. For the former, the base used for the
percentage computation must be identified. It may be area spinning
capacity, prevailing area generation, or area peak load. The characteristic may also be expressed as a percent droop by using the relations of
eqs. (1) and (2), where N, N', D, and M would each apply to the area
instead of to a unit. Typical area characteristics may run from 1 to 3%
of spinning capacity per one-tenth cycle.
For an Interconnected System. The prevailing natural generation governing characteristic for a system defines the generation response of the
complete interconnection to changes in system speed or load. The characteristic is usually expressed in percent per one-tenth cycle or in megawatts per one-tenth cycle. For the former, the base for the percentage
computation may be system spinning capacity, prevailing system generation, or system peak load, as specified. The characteristic may also be
expressed as a percent droop by using the relations of eqs. (1) and (2),
where N, N', D, and M would each apply to the system instead of to a
unit. Typical system characteristics may run from 1 to 3% of spinning
capacity per one-tenth cycle.

CONTROL OF INTERCONNECTED POWER SYSTEMS

17-21

Load Governing

On most power systems total connected load has a frequency coefficient,
load increasing with increasing speed. This adds a component of selfgoverning to the system. For example, when new load is added causing
system speed to decelerate, the lowered system speed results in a lower
effective rating of the already connected load, thereby making some of the
prevailing generation available for the new load and decreasing the need
for increased generation.
Natural Load Governing Characteristic. The term natural load governing characteristic defines the frequency coefficient of connected load of
an area or system. It is a measure of the change in the rating of connected load with frequency. It may be expressed in percent per one-tenth
cycle or in megawatts per one-tenth cycle. For the former, the base for
the percentage computation should be the 60-cycle rating of the connected
load. Frequently, for convenience in computation and analysis, the
reference base is made the same as the reference base for the prevailing
natural generation governing characteristic, namely, spinning capacity,
prevailing generation, or peak load. Typical values for this characteristic
lie in the range of 0.3 to 0.5ro per one-tenth cycle.
Combined Governing

In practice, system regulation is achieved by the combined effects of
generation governing and load governing.
Prevailing Natural Combined Governing Characteristic. The term
prevailing natural combined governing characteristic defines the overall
response of an area or system to changes in speed or load. It is a measure
of the net generation response to such changes, taking into account the
load governing effect as well as the generation governing effect. It may
be expressed in percent per one-tenth cycle or in megawatts per one-tenth
cycle. For the former, the base for the percentage computation may be
spinning capacity, prevailing generation, or peak load.
The generation governing characteristic is a negative quantity, denoting the increase in generation with decrease in frequency. The load
governing characteristic is positive, reflecting the decrease of rated load
with decrease in frequency. The two may be combined as an algebraic
difference or an arithmetic sum to obtain the combined governing characteristic. The latter, like the generation characteristic, is negative,
reflecting an aggregate increase in generation for a decrease in frequency.
vVhen both characteristics are expressed in megawatts per one-tenth
cycle, they can be combined directly. vVhen each is expressed as a percentage, they can be combined provided the same base reference has been
used for each percentage value.

INDUSTRIAL CONTROL SYSTEMS

17-22

Combined governing characteristics encountered in practice may run
for individual areas from 1 to 4% of spinning capacity per one-tenth cycle,
corresponding [see eq. (1)] to system droops of approximately 160/0 and
4% respectively.
Graphical Repr,esentation

Figures 11 and 12 illustrate the responses of generation governing, load
governing, and combined governing on an isolated area, for a step func60.2
G

60.1
>.
u

c

~ 60.0

C"

~

LJ..

59.9

L'I

L

G

58.8

GA

LA

Area generation
Area load

+
+

(Curves GG and
(Curves LL and
(Curves GG and
(Curves LL and

G'G')
L'L')
G'G')
L'L')

FIG. 11. Generation governing and load governing responses on an isolated area A
for a step function load increase and zero load characteristic. G A and LA are initial
generation and load respectively.

tion load increase. In each case, initial conditions are at 10 . GG is the
generation governing characteristic, LL the load governing characteristic,
and CC, where shown, the combined governing characteristic. It is assumed that for the small changes being considered, the characteristics may
be shown as straight lines. Load is increased from LL to L'L'. These
figures illustrate how system governing regulation achieves a match between total generation and total load of the area. For comments on
supplementary regulation which shifts the generation characteristic from
GG to G'G', see Sect. 5.
Zero Load Characteristic. This is the case illustrated in Fig. 11. The
load has zero frequency coefficient, as shown by LL being a vertical line.
Initial conditions are defined by the intersection of the GG-LL characteristics, point 10 • After the load increase, the new conditions are defined by

17-23

CONTROL OF INTERCONNECTED POWER SYSTEMS
60.2,-----r-----,.-----.------.---...,.------,

>.
u

c:

~
CT

60.0

1-----+----I-----~~---1I__-----""tE-------1

59.9

I----+----+--/--t----j-

Q)

Lt
.-"Q.-~----I

G

L
59.8

c

L--_ _-L-_ _--'-_ _ _.l.--_ _- ' -_ _---'-_ _- - - - '

GA

LA
Area generation
Effective area load
Rated 60-cycle connected load

+
+

(Curves GG
(Curves LL
(Curves GG
(Curves LL

and G'G')
and L'L')
and G'G')
and L'L')
(Curv~s CC and C'C')

FIG. 12. Generation governing, load governing, and combined governing responses
on an isolated area for a step function load increase and a positive load characteristic.

the intersection of the GG-L'L' characteristics, point II. Speed is decreased, and generation governing has increased generator output to balance the new load at II.
Positive Load Characteristic. This is the case illustrated in Fig. 12.
Here the connected load has a positive coefficient of change with frequency, shown by the sloping LL characteristic. The GG and LL characteristics may be combined into the CC characteristic, with proper consideration to the par