# 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!

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Engineer_s
Anyone?