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Bandwidth analysis of a system with multidimensional input

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HaMo 2019 年 10 月 16 日
コメント済み: Star Strider 2019 年 10 月 20 日
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);

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Star Strider
Star Strider 2019 年 10 月 16 日
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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Star Strider
Star Strider 2019 年 10 月 16 日
As always, my pleasure!
If you are taking a course in modern control, or linear control systems (it goes by several names), this will all be cleared up for you as the course proceeds. If you have not taken such a course, I definitely recommend it. An excellent text (in my opinion, and the one we used when I took a linear control systems course) is Chi-Tsong Chen Linear system Theory and Design (ISBN 0-19-511777-8). We used an earlier edition, and I still use it (this is the third edition) as my primary reference.
HaMo 2019 年 10 月 20 日
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);
%% Built-in bode plot
%% 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;
% Magnitude plot
semilogx(abs(s), 10*log(abs(freq_response)))
% Phase plot
semilogx(abs(s), 180/pi*phase(freq_response));
Star Strider
Star Strider 2019 年 10 月 20 日
That example (from the documentation) is a SISO system.


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