MIMO Singular Value Plot Producing 5 lines not 2 lines

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bullseye1440
bullseye1440 2018-12-12
评论： wenlong 2020-11-10
It was my understanding that singular value plots are only to plot a maximum and minimum singular value transfer functions for a MIMO system. So I would expect to see two sets of lines for my sigma() plot. This system is plotting five sets for both the open and closed loop singular value plots. Any ideas as to why?
% open-loop continuous
% state matrix
A = [-0.238 0 -1 0.0207 0;
-16.78 -2.14 0.029 0 0;
7.11 0.035 -0.264 0 0;
0 1 0 0 0;
0 0 1 0 0];
% control effectiveness/distribution matrix
B = [-0.0005 0.0177 -0.0048 0 0;
4.97 4.33 20.33 28.62 0.17;
-0.225 -2.88 -0.862 -1.32 -0.008;
0 0 0 0 0;
0 0 0 0 0];
C = eye(5);
D = zeros(size(C));
% Gain matrix, calucated using LQRD with Ts = 0.1 seconds
K1 =
[0.1587 0.0281 0.0375 0.0492 0.2219;
-0.7110 -0.0137 -0.4046 -0.0271 -0.7802;
0.0656 0.0116 0.0162 0.0203 0.0918;
0.0920 0.0162 0.0213 0.0283 0.1281;
0.0005 0.0001 0.0001 0.0002 0.0008];
% Open loop system SV plot
sys1 = ss(A,B,C,D);
H = tf(sys1);
% plot open loop
figure()
sigma(H)
grid on
% plot closed loop
figure()
sigma(K1*H)
grid on
SDR_SV_OL.png
SDR_SV_CL.png
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Mark Sherstan
Mark Sherstan 2018-12-13
Was looking at some controls stuff and came across MIMO systems similar to your question. If you do a plot of the singular values of your state space representation you can get the max and mim gain and phase margins for all the transfer functions in the MIMO. Maybe thats what your prof was reffering to?
wenlong
wenlong 2020-11-10
Dear Mark,
I tested sigma for 4 inputs, 9 states and 9 outputs, 4 inputs, 9 states and 4outputs, both I got 4 plots. When I tested it for SISO transfer functions, I got the same as bode gain plot. I have some question about sigma function:
1 What does each plot mean? Does it mean for each pair of input-output?
2 If 1 was right, which pair did it mean?
3 If 1 was not right, what did mean for?
4 How could I get max and min gain from sigma plot?
Thanks, sincerely

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