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.
