Surf respresentation of a transfer function depending on the frequency and the gain of the feedback

Hi,

Please I would like to know if it is possible to plot a transfer function that depends on the variable "s" but also the gain of the feedback.

I give you below the part of my program that is related to my question. (A,B,C,D and alpha are defined already).

sys=ss(A,B,C,D);

gain=1;

H=tf(gain*[1 2*alpha alpha^2],[1  0]);

BF=feedback(sys,H,2,2);

bode BF(1,1);

This program is perfectly working and I can plot the bode diagram of BF(1,1) for example directly.

What I want to do though, is to plot BF(1,1) for different values of the variable gain, let's say for gain varying from 1 to 100, and to have then a 3D representation of BF(1,1) according to the parameter "s" (the frequency) and the parameter gain in the feedback function.

I hope that my question is clear and I hope I find an answer for it.

Thank you,

Answer 1

[Teja Muppirala]

You can loop over different values of "gain" and collect the results in a matrix and then plot it as a surface.

rng(0)
sys=rss(3,2,2);
alpha = 1;
gainList = 1:100;
w = logspace(-1,3,51);

magSurf = [];
for n = 1:numel(gainList)
    gain = gainList(n);
    H=tf(gain*[1 2*alpha alpha^2],[1  0]);
    BF=feedback(sys,H,2,2);

      [mag,phase] = bode(BF(1,1),w);
      magSurf(n,:) = mag(:);
end

surf(w,gainList,20*log10(magSurf));
set(gca,'Xscale','log')
xlabel('Frequency (rad/s)');
ylabel('gain')
zlabel('Magnitude BF(1,1) dB')