Pid Controller

• 1 PID controller in SOBEK
• 2 Aim of this document
• 3 Conclusion
• 4 Mass-Spring-Damper system
  • 4.1 Energy of Mass-Spring-Damper system
• 5 Feedback loop, PID-controller
  • 5.1 Unit impulse function
  • 5.2 Unit step function
• 6 PID controller (positional)
  • 6.1 Proportional term
  • 6.2 Derivative term
  • 6.3 Integral term
• 7 PID controller (velocity)
• 8 Determine coefficients from experiments
• 9 Numerical discretisation
  • 9.1 Mass-Spring-Damper system as system of first order PDE's
  • 9.2 PID controller (positional)
    • 9.2.1 Implicit Mass-Spring-Damper system with explicit PID-controller
    • 9.2.2 Implicit Mass-Spring-Damper system with implicit PID-controller
    • 9.2.3 Corrected Mass-Spring-Damper system while using an explicit PID controller
  • 9.3 PID controller (velocity)
    • 9.3.1 Implicit Mass-Spring-Damper system with explicit velocity PID controller
    • 9.3.2 Implicit Mass-Spring-Damper system with implicit velocity PID controller
    • 9.3.3 Corrected Mass-Spring-Damper system while using an explicit velocity PID controller
• 10 Experiments
  • 10.1 Solutions determined by Maplesoft
  • 10.2 Numerical experiments
    • 10.2.1 Time integration method
    • 10.2.2 Convergence behaviour
• References