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Control theory: process given, PID settings

  • Thread starter Engineer_s
  • Start date
  • #1
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Homework Statement



Problem:

We want a closed loop control loop for the given process (see bode plot), the control loop requirements are:
  • Steady state error needs to be zero.
  • The gain margin needs to be infinite.
  • The phase margin needs to be 40 degrees.
Questions:
  1. Which controller will be the best choice: P, PI, PID or PD and why?
  2. What are the controller settings needed to reach the requirements for the controller you have chosen.
The bode plot of the process is given:

sFJcIgc.jpg


Homework Equations



Standard controllers in de Laplace domain.

The Attempt at a Solution



My attempt to find a solution:
  • Steady state error needs to be zero. ==> We need an integrator action
  • The gain margin needs to be infinite. ==> the phase is not allowed to cross the -180°.
  • The phase margin needs to be 40 degrees. ==> phase margin at 0 dB crossing.
Since the phase of the process is below -180° we need an extra null in the open loop equation. Therefore we need an derivative action (D-action). This will result in a phase that never crosses the -180°. Since we both need an I-action and D-action the appropriate controller will be a PID-controller.

How can I find the appropriate settings for my controller?

Thanks in advance for helping me out!
 

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Answers and Replies

  • #2
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Anyone?:frown:
 
  • #5
FactChecker
Science Advisor
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I think he means undefined, since he concludes that the phase must stay above -180. I'm afraid that I don't know enough of the subject to know if that is the common way to say it.
 

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