Estimation of transfer function
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Hello,
I would like to estimate a transfer function based on the experimental data (magnitude, phase and frequency. I was trying to use pem function but it does not work well. For example in my system I have a derivative and my transfer function should be something like: (as^2+bs)/(a1s^3+b1s^2+c1s+d1). I cannot get it in the estimation model. It gives me something like as^2+bs+c. I do not want "c" parameter. There is any estimation function that allows me to settle my searching function not only number of orders? I mean user0searching parameter? If is there any how I can do it?
Thank you for any response.
Kamil
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Arnaud Miege
le 6 Juin 2011
For frequency-domain data, there are three types of id models supported by the System Identification Toolbox(see documentation):
For your application, I would recommend the latter. Choose the correct order for your system and once you have your estimated state-space matrices, you can use the tf command from the Control System Toolbox to convert it to a transfer function.
HTH,
Arnaud
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Rajiv Singh
le 6 Juin 2011
There is also the "grey box" approach that lets you parametrize your model any way you like. For this, write a MATLAB function that takes in a, b, a1, b1, c1 and d1 as input arguments and returns a state-space form of the model as output arguments. Use this file to create an "idgrey" model object whose parameters (your a, b, a1,..) can be estimated to fit data. You will need to derive the expressions for SS matrices to begin with. A controls textbook (e.g., Linear Analysis by Kailath) would show you some common forms.
for details on grey-box modeling. Also see http://www.mathworks.com/products/sysid/demos.html?file=/products/demos/shipping/ident/iddemo7.html
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