Why does transfer function modelling give different results?

Hi.

From the command line I am trying to estimate a transfer model (2 poles, 1 zero) that will have good fit to my data. When I compare the model to my output, most of the times the fit is quite well (see first figure below). Sometimes though, the transfer function behaves abnormal and the fitted data is quite odd (see second figure below). My question is what can be the reason for this to happen, does it have to do with my input? My input is just a straight line with positive, constant slope.

Figure 1:

Figure 2:

Answer 1

[Star Strider]

You didn’t post your code so I have to guess. If you’re using one of the nonlinear solvers such as nlinfit, lsqcurvefit, or fminsearch, understand that they are sensitive to the initial parameter estimates you give them. and can get caught in a local minimum. The more you know about your function, the more accurately you can estimate the initial parameter values you give to your function. Even if successful, different function fits will give slightly different parameter estimates, one reason to use nlparci to estimate their confidence intervals.

[Rafi]

I've added a piece of the code to be a little more precise:

    %CODE
% Create iddata for working data
input = x_m;
output = y_m;
Ts = input(2)-input(1);
ze = iddata(output', input',Ts);
sys = tfest(ze,2,2,'Ts',ze.Ts);
transfer = tf(sys.num,sys.den,Ts); % Transfer function estimation
compare(ze, transfer); % Compare transfer function with working data

As I mentioned, the input for my system is the same everytime: a straight line with constant, positive slope. Do you think I need to specify initial parameters for tfest to make the function converge?

[Star Strider]

I have the System Identification Toolbox, but I haven’t used it in a while. I thought you were using one of the nonlinear curve fitting functions. I’ll delete my answer in a few minutes.

[Arkadiy Turevskiy]

Could you attach a mat file with x_m and y_m?