Diffrent results using tf(ss(A,B,C,D)) or C*inv(s*I-A)*B+D

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rupprechtt
rupprechtt 2019-9-7
评论： rupprechtt 2019-9-7
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
Raj 2019-9-7
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
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?
Capture.JPG
rupprechtt
rupprechtt 2019-9-7
Uhh.. my bad!
I have overlooked the factors .. (what an idiot)
Thanks a lot!

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