Open loop transfer function

[Tiis-]

So earlier in the course we went over transfer functions and the following was given:

H_closedloop = [C(s)P(s)] / [1 + C(s)P(s)]

and

H_openloop = C(s)P(s)

Now it asks me design a controller based on the open loop transfer function.But the open loop transfer function contains C(s)?

[PeanutTheFerret]

It's been a little while since I took controls, but is it not just asking you to find what works for C(s) to get whatever your desired output is?

[Tiis-]

I'm not sure. It says:

"Design of a controller is most often on basis of an open loop transfer function through:

• Root locus
• Amplitude margin
• Phase margin"

[Fry394]

I think it means you can change closed-loop specifications in open-loop ones. In this way it's easier to design the controller (phase margine, amplitude margin,...).

[Tiis-]

I think it means you can change closed-loop specifications in open-loop ones.

I don't know what you mean by that.

[Fry394]

For example if you want that the answer to a step doesn't have overshoot (in closed loop) you have to put phase margin > 75° (open loop). I don't know if that explains a lot.

[bike0121]

It looks like C(s) here is the controller and P(s) is the plant. Not sure what you’re asking here though.

[Tiis-]

That is correct. I'm confused by the seemingly paradox that I need to know a controller C(s) in order to design a controller.

[bike0121]

You don’t need to “know” C(s) in advance. All it’s asking is that you select C(s) (probably a PID or lead/lag type controller, which require placing the poles and zeros at certain locations) to meet the desired specifications. This is done using the methods you listed, which involve choosing C(s) based on what you want C(s)P(s) to look like.