How can I use allmargin() with non-unity feedback?

Hello!

I have a (MIMO) feedback system of which I would like to estimate the stability margins using allmargin(). Looking at the documentation of this function, it takes as input the loop gain L and assumes unity feedback, such that the system can be modelled as the figure below:

However, my system has some controller in the negative feedback path, such that the system looks as follows:

Is it possible to compute the stability margins of such a system using allmargin()?

Answer 1

[Paul]

Hi Erik,

What's the loop transfer function, L(s), from which one could compute the stability margins (having already determined the closed-loop system is stable)?

In other words, are you asking about the math? Or do you know the math and are just asking how implement the math in Matlab?

[Erik]

Hi Paul,

Thanks for your response! I suppose I'm asking about a bit of both... it's been a while since I've looked at control systems. Let me try to rephrase.

The two systems sketched above have different closed-loop transfer functions; for system (1) and for system (2). However, since they both see the same loop gain , the stability margins for both systems seem to be equivalent. Is this correct?

[Paul]

Yes, that's correct.

[Erik]

Perfect, thanks! Sorry for the (ultimately) trivial question.

[Sam Chak]

Hi @Erik

Personally, I have a preference for system (1), where the compensator is positioned on the feedback path. However, I acknowledge that system (2) may be more intuitive for most designers who prioritize driving the error to zero.