Control theory: process given, PID settings

[Engineer_s]

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:

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!

 

[Engineer_s]

Anyone?

 

[FactChecker]

Position your zeros and poles at the frequencies needed to bent the response magnitude graph as desired. See https://web.njit.edu/~levkov/classes_files/ECE232/Handouts/Frequency Response.pdf )

 

[berkeman]

The gain margin needs to be infinite.

How does one manage to get infinite gain margin? I guess I'm missing something...

https://microchip.wdfiles.com/local--files/asp0107:phase-gain-margin/gain_phase_margin2.png

 

[FactChecker]

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.