MATLAB: Creating PTn transfer function by

ptntransfer function

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.

Best Answer

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.
Related Question