MATLAB: Do i get a different pzmap if i use idtf or ss representation of the same system

MATLABpzmapstate-spaceSystem Identification Toolboxtransfer function

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

Best Answer

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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MATLAB: Do state space and its equivalent transfer function models yield different step responses

Hi there,

Examine the state-space model sys_ss:

>> sys_ss

Note that it has a non-unity E matrix. This happens because your H, a pure derivative, is improper. The connect command represents that block as a two-state ss with a non-unity E matrix - a descriptor ss. When connect builds the interconnected system, it preserves those states, so it yields a descriptor system.

And that means that your call to ss2tf, which only uses A,B,C, and D, is missing part of the dynamics of the system. sys_tf doesn't represent the same dynamics as sys_ss.

This is one of the reasons that ss2tf is not a great command to use when converting from ss to tf form. Try this instead:

>> sys_tf = tf(sys_ss)

This time when you plot the step responses, they match up. Also, tf removes those two extra states.

You can also reduce and simplify sys_ss into explicit form (E = 1) using the 'explicit' option of the ss command:

>> sys_ss_ex = ss(sys_ss,'explicit')

Now all of the system dynamics are described by A,B,C, and D.

For more information about explicit and descriptor state-space models, see the reference page for ss.

>> doc ss

Hope this helps!

MATLAB: How to remove delay from idtf object

You will need an invertible realization. Try high order transfer function estimations with no delays. Or, if the estimated model with delays is a good/accurate model, compute its frequency response (freqresp), invert it, and fit a transfer function to the inverse frequency response.

For literally just removing the delay you can do model.ioDelay= 0

Best Answer

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