Different Results of allmargin() and margin()

Hello,

I am currently analyzing the stabiity margins of my MIMO open-loop with 2 inputs (find ol_sys attached) . Therefore I tried both, the margin() and the allmargin() commands.

- allmargin(-ol_sys, Focus=[0.001 Inf]) delivers a low Gain Margin at 0.0414 rad/s, however, the bodeplots of the system do not have a phase transition of -180° at this freqeuncy

- margin(-ol_sys(1,1)) and margin(-ol_sys(2,2)) deliver similar Phase margins, but different GM, which are in line with the corresponding Bode Plots

I am wondering if there is a error in the allmargin() calculation or why there is a different resut. Would be awesome if someone can help me.

Cheers,

Florian

Answer 1

[Paul]

Hi Florian,

For a MIMO system, allmargin computes the margins of each loop with all other loops are closed. However, the command margin(-ol_sys(1,1)) doesn't know about any other loops.

Consider

load ol_sys
s = allmargin(-ol_sys,Focus=[0.001,inf]);

These are the margins at the first input with the loop closed on the second input (don't know why they are slightly different than your result)

s(1)

ans = struct with fields:
     GainMargin: 0.0636
    GMFrequency: 0.0374
    PhaseMargin: 84.4117
    PMFrequency: 11.0574
    DelayMargin: 0.1332
    DMFrequency: 11.0574
         Stable: 1

Manually close the second loop

L = feedback(-ol_sys,diag([0 1]));

and compute the margins on the first loop

allmargin(L(1,1),Focus=[0.001,inf])

ans = struct with fields:
     GainMargin: 0.0636
    GMFrequency: 0.0374
    PhaseMargin: 84.4117
    PMFrequency: 11.0574
    DelayMargin: 0.1332
    DMFrequency: 11.0574
         Stable: 1

which yields the same result as above.

Now use margin on the first loop with the second loop closed to visualize the result.

margin(L(1,1))