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

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

Answer 1

[Raj]

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)

[rupprechtt]

Hi thank you,

I checked the similarity, but I am very unhappy with the result of

bode(tf1-tf2)

Do you know how I can increase numerical accuracy?

[Raj]

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?

[rupprechtt]

Uhh.. my bad!

I have overlooked the factors .. (what an idiot)

Thanks a lot!