MIMO Singular Value Plot Producing 5 lines not 2 lines

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

[Mark Sherstan]

Where did you see that sigma should only plot the max and min tf? It was my understanding that it should plot one for every output and since your system has 5 outputs, 5 inputs, and 5 states the 5 makes sense from my end.

[bullseye1440]

Thank you for your comment!

Maybe I didn't quite have the correct understanding of how sigma worked. I am taking a controls class right now and my professor had implied that singular value plots are only used to plot maximum and minimum transfer functions for MIMO systems. I had assumed this meant that the plot would only show the maximum and minimum transfer functions as a result.

[Mark Sherstan]

I looked through the sigma documentation and dont see any reference to maximums or minimums. You can adjust the frequencies and a couple other things but looks like you will always get multiple plots. Perhaps your prof meant you can use the plot to find the maximuma and minimum transfer functions? I would confirm with them in case it becomes testable later.

[Mark Sherstan]

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]

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