Why do i get a different pzmap if i use idtf or ss representation of the same system

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Guillaume FOURNIER 2019-6-18

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https://ww2.mathworks.cn/matlabcentral/answers/467633-why-do-i-get-a-different-pzmap-if-i-use-idtf-or-ss-representation-of-the-same-system

评论： Guillaume FOURNIER 2019-6-19

Hello,

I noticed a behaviour i cannot explain.

idtf, idpoly, ss, from what i understood, is just a matter of writing or convention to describe a system. Because they describe the same system, they should have the same poles and zeros, therefore the same pzmap.

I have a continuous SISO model. If i do pzmap of the ss, i get one pole of multiplicity N, the order of my system, and N zeros as well.

if i do pzmap of the idtf representing the same system, i get N poles and N zeros. Zeros do not match perfectly but are quite close.

Does anyone has an explanation?

Thanks in advance for your help

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Answer 1

Raj 2019-6-19

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https://ww2.mathworks.cn/matlabcentral/answers/467633-why-do-i-get-a-different-pzmap-if-i-use-idtf-or-ss-representation-of-the-same-system#answer_379859

I assume you are doing something like this:

G = idtf(num,den)
M=tf(num,den)
N=ss(G)

Now you expect G ,M and N to be identical and have same pzmap since they are basically the same system. However there may be small differences due to numerical computation accuracy issues if your system is of high order.

See the section "Recommended Working Representation" here:

https://in.mathworks.com/help/control/ug/conversion-between-model-types.html#f3-1039600

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Guillaume FOURNIER 2019-6-19

The order of my system is 19. I don't know if that can be considered high.

In my case, i need to use a state space approach. Luckily my needs are in line with Mathworks recommendations (thanks for the link). Let's say these discrepencies come from numerical issues.

Thanks for your answer and your time

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