Creating PTn transfer function by

2020 3 26
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更新时间：2020 3 27
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Hi
I have results ofthe response of a system on different inputs.
I want to create a couple transfer functions of the from TF = k/(Ts+1)^n, with n=1 or 2 or 3. So 'k' and 'T' need to be determined.
Is it possible in matlab to generate a response of this transfer function with unknown 'k' and 'T'. Because I would like to determine them by minimising the the mean square error of the response of the transfer function and the real response of the system.

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Star Strider
Star Strider 2020-3-26

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To fit them in the time domain:
syms k s T
TF1 = k/(T*s+1);
TF2 = k/(T*s+1)^2;
TF3 = k/(T*s+1)^3;
TF1t = ilaplace(TF1);
TF1fcn = matlabFunction(TF1t);
TF2t = ilaplace(TF2);
TF2fcn = matlabFunction(TF2t);
TF3t = ilaplace(TF3);
TF3fcn = matlabFunction(TF3t);
B0 = [T0; k0];
B = lsqcurvefit(@(b,t),TF1fcn(b(1),b(2),t), B0, xdata, ydata);
and similarly for the others, where ‘xdata’ and ‘ydata’ are the time and amplitude data.
The System Identification Toolbox, for all its strengths, is not intended for this sort of parameter estimation.

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Ruben Dumas
Ruben Dumas 2020-3-27
I did not expect an answer this quick, thank you!
It works for most simple input signals, but for something like a chirp signal I couldn't get it to run. I tried to laplace transform the input signal u(t) -> U(s) and multiply it with the TF1/2/3 so when I transform U(s)*TF1/2/3 back I could get y(t). But it works with multisine signals so it is not that big of a deal.
Thank you again for the answer!
Star Strider
Star Strider 2020-3-27
As always, my pleasure!

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