Bandwidth analysis of a system with multidimensional input

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HaMo 2019-10-16

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https://ww2.mathworks.cn/matlabcentral/answers/485569-bandwidth-analysis-of-a-system-with-multidimensional-input

评论： Star Strider 2019-10-20

采纳的回答： Star Strider

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I am playing around with the built-in bandwidth function.

I can intuitively understand what is going on under the hood for a transfer function with scalar input and scalar output. However, how is the band width computed when the input is a vector of length > 1?

For instance, as in this example from the documentation:

A   = [-2 -1; 1 0];
B   = [1; 0];
C   = [1 2];
D   = 1;
sys = ss(A,B,C,D);
bandwidth(sys)

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Star Strider 2019-10-16

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https://ww2.mathworks.cn/matlabcentral/answers/485569-bandwidth-analysis-of-a-system-with-multidimensional-input#answer_396542

The length of the input vector is likely irrelevant, and is not even an argument to the bandwidth function. Note however that the bandwidth function only applies to SISO systems, or arrays of SISO systems (Find Bandwidth of Model Array), so it would not apply to MISO or MIMO systems.

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HaMo 2019-10-20

在 MATLAB Online 中打开

After testing out a few different ideas in Matlab, I suddenly had an Eureka moment. This is the answer I was looking for:

A = [-2,-1;1,0];
B = [1;0];
C = [1,2];
D = 1;
% Laplace transformation:
% sX = AX + BU
% Y  = CX + D
%
% (sI - A)X = BU
% X = inv(sI - A) B U
% Y = C inv(sI - A) B U + D
% H(s) = C inv(sI - A) B 
sys = ss(A,B,C,D);
bandwidth(sys)
%% Built-in bode plot
figure(1)
bode(sys);
%% Home-made bode plot
s = (i*10.^(-2:.1:2))/(2*pi);    % Input frequencies
freq_response = nan(size(s));    % Frequency response vector
for i=1:length(s)
    freq_response(i) = C / (s(i) * eye(length(A)) - A) * B + D;
end
figure(2)
% Magnitude plot
subplot(2,1,1)
semilogx(abs(s), 10*log(abs(freq_response)))
% Phase plot
subplot(2,1,2)
semilogx(abs(s), 180/pi*phase(freq_response));