Interpretation of diskmargin()

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Ömer Faruk Arslan 2022-2-7

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https://ww2.mathworks.cn/matlabcentral/answers/1644535-interpretation-of-diskmargin

编辑： Ömer Faruk Arslan 2022-2-8

Hello everyone,

I need to design a SISO controller and I want to check its robustness by using diskmargin() approach instead of classical gain & phase margins. However, I could not understand how to approach these values that are given by a struct.

Minimum gain margin, maximum gain margin etc. I have noticed that, we can obtain maximum gain at only 0 phase shift, then what is the difference between this & classical gain margin?

How diskmargin approach can be usefull to design robust controllers?

Thanks in advance.

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Paul 2022-2-7

Does this doc page help?

Ömer Faruk Arslan 2022-2-7

Thanks for advise, I saw that page but I did not understand the efficiency of diskmargin. Can we use an ellipse to define a larger stable region?

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Answer 1

Paul 2022-2-8

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The essence of a robust control system is that all points on the Nyquist plot of the loop transfer function be at a "far" distance from the -1 point. The classical gain and phase margins are measures of that distance at two points on the Nyquist plot: where it crosses the real axis and where it crosses the unit circle.

The disk margin is another measure of how far away the Nyquist plot stays away from the -1 point. Other metrics can be defined as well. I suppose you could define the exclusion region as an ellipse, but I don't think you can do that using diskmargin().

The diskmargin() results GainMargin and PhaseMargin, in general, aren't really margins IMO. Rather, they are parameters that provide some insight into where the disk sits in the complex plane. The actual margin is quantified by DiskMargin and/or WorstCasePerturbation. Though I guess it's true that GainMargin and PhaseMargin are lower bounds on the classical gain and phase margins.

From a design perspective, if you design the compensator C so that L = C*P stays outside a disk of specified size (alpha) and skew (sigma) then one might consider that a robust design. Of course, the specifications for alpha and sigma are still up to the designer.

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Ömer Faruk Arslan 2022-2-8

编辑：Ömer Faruk Arslan 2022-2-8

Thank you Paul. I understand that, the given upper & lower margin values are definining location of the disk on the complex plane. It does not mean that we can reach maximum gain & phase simultaneously, or we can hold large gain margin for large spectrum of phase shift.

Defining a different geometric shape rather than disk, maybe more beneficial in terms of tracing larger stable points. I will go on with it. Thanks.

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