How can I design a lag compensator with a specific phase margin and velocity static error constant?

So I am asked to design a lag compensator via frequency response so that the static velocity error constant of the control system is 6 times the uncompensated system and the phase margin of the control system is at least 30 degrees. The open-loop transfer function is given. How can I design a lag compensator in Matlab under these conditions?

Answer 1

[Sam Chak]

Hi @Bilal Antaki

More info about the open-loop transfer function of the uncompensated system should be provided.

From one of Google search results, it shows that the Static Velocity Error Constant is defined as

where is the open-loop transfer function.

If is the plant in the uncompensated system and a lag compensator is used to compensate the s system so that the Static Velocity Error Constant requirement is

.

Since the open-loop transfer function of the compensated system is given by , then

Design Task (Part 1):

Can you determine the lag compensation gain in ?

Design Task (Part 2):

Requires you to select the values for T and c with such that the phase margin is at least 30°.

This one, I think you can use the bode() command to design

[mag, phase, wout] = bode(sys)

[Sam Chak]

Hi @Bilal Antaki

I have fixed the mistakes. I think this time around should be okay. If you have any formulas from your lecture or textbooks on the topic, please provide them because I rely on Wikipedia and Google search.

[Bilal Antaki]

Yes now everything is fine. Thanks alot :). I will make sure to do so next time.

[Sam Chak]

Good to hear that it works out fine, @Bilal Antaki. If you find this mini tutorial helpful, please consider accepting ✔ and voting 👍 the Answer as a token of appreciation.

Edit: By the way, I have changed to c in to avoid having the same parameter in the plant .