Diffrent results using tf(ss(A,B,C,D)) or Cinv(sI-A)*B+D

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rupprechtt 2019-9-7

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评论： rupprechtt 2019-9-7

采纳的回答： Raj

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Why do I obtain diffrent results?

A = rand(3,3);
B = rand(3,1);
C = rand(4,3);
D = rand(4,1);
% using matlab function
tf1 = tf(ss(A,B,C,D));
% calculated by hand
s = zpk('s');
tf2 = D + C*inv(s*eye(3)-A)*B;

Does anyone have an idea why tf1-tf2 is not zero?

Thank you

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Raj 2019-9-7

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The results are not different. They are same. Minor differences can be due to numerical/computational tolerances and accuracy. At any given natural frequency, magnitude of (tf1-tf2) is indeed very close to zero. You can check the similarity yourself by comparing their bode plots like this:

bode(tf1)
hold on
bode(tf2)

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Raj 2019-9-7

Why are you 'unhappy' with the result of bode(tf1-tf2)? The magnitude of the difference as I mentioned earlier is in the order of 10^-13 which is very very small for almost any practical aspect.

You need even higher precision?