convert a transfer function to controllable and observable canonical form

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TALAL alghattami
TALAL alghattami 2020-3-29
编辑： Arkadiy Turevskiy 2024-6-18
Hi, I want to convert a transfer function to controllable and observable canonical form for the
num = [4];
den = [1 0.8 4];
Gp = tf (num , den)
Gp =
4
---------------
s^2 + 0.8 s + 4

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Star Strider
Star Strider 2020-3-29
编辑：Arkadiy Turevskiy 2024-6-18
num = [4];
den = [1 0.8 4];
Gp = tf (num , den);
The canon function requesting the 'companion' canonical form directly produces the observable canonical form:
GpssObs = canon(Gp,'companion')
GpssObsA = GpssObs.A
GpssObsB = GpssObs.B
GpssObsC = GpssObs.C
GpssObsD = GpssObs.D
producing:
GpssObsA =
0 -4
1 -0.8
GpssObsB =
1
0
GpssObsC =
0 4
GpssObsD =
0
The controllable canonical form is then:
GpssConA = GpssObsA.'
GpssConB = GpssObsC.'
GpssConC = GpssObsB.'
GpssConD = GpssObsD
producing:
GpssConA =
0 1
-4 -0.8
GpssConB =
0
4
GpssConC =
1 0
GpssConD =
0
Se the documentation section on: Canonical State-Space Realizations for a full discussion.
Update by Arkadiy Turevskiy at MathWorks on 6/18/2024
The answer above is valid for the software release that was current at the time the answer was posted. As of R2024a the doc link is still correct, but a different function should be used to compute controllable and observable forms.
Please use the function compreal, and set the argument type to "c" or "o" for controllable and observable forms respectively.
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Bill Tubbs
Bill Tubbs 2021-2-5
The outputs in this answer (for observable and controllable forms) do not match my class notes or other documentation I found online, for example here and here. The differences are in the B and C matrices.
Sean Doherty
Sean Doherty 2021-9-4
Star Strider. This MATLAB example contradicts the documentation (https://uk.mathworks.com/help/control/ug/canonical-state-space-realizations.html)
documentaion says observable canonical form has:
in example: n = 2, b0 = 0, bn1 = 0; b2 = 4, a0 = 1, a1 = 0.8, a0 = 0.4 should give:
B0 = [4 0]'
C0 = [0 1]
MATLAB example gives:
B0 = [1 0]'
C0 = [0 4]
Documentation is correct, MATLAB's canon() is wrong?

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TALAL alghattami
TALAL alghattami 2020-3-31
for the given matric how can i designe observer and pole placment and then implement the designe in simulink
apreicate your support
deno=[1 0.8 4];
num=[4];
Gp=(num,deno)
A =[0 1 ; -4 - -0.8];
B =[0;4];
C =[1 0];
D =[0];
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Branislav Hatala
Branislav Hatala 2020-12-16
I would like to ask how can I convert SIMO system to controllable form. I did not find anything about SIMO or MIMO systems and this cannot be applied since C and B matrices will result in frong dimensions.

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