Fitting transfer function to amplitude phase data

Hello,

I have amplitude-phase (Bode) data from my experiment, which I have obtained by sweeping a range of frequencies. My system has the delay term exp(-Tau*s). I am looking to fit transfer function models of the form exp(-Tau*s)*(N(s)/(D(s)) to my data with the lowest possible order. Any help would be greatly appreciated!

Thanks and Regards, Hari

Answer 1

[Star Strider]

You are fitting a matrix (amplitude and phase) with your model, so the most appropriate function to use is the Optimization Toolbox function lsqcurvefit. Your objective function will have to produce two outputs (amplitude and phase) to match your data.

[Hari]

Hi Star Strider, Thanks for your answer. I will look into this.

[Star Strider]

My pleasure.

I hope it works for you.

Answer 2

[Arkadiy Turevskiy]

Actually the function specifically created for this task is tfest from System Identification Toolbox. Take a look at the doc page and look at the section "Examples". For the lowest possible order, specify the number of poles =1, and number of zeros =0. If you do not get a good fit, try to increase the number of poles and zeros.

tfest takes your data as an input argument. Data has to be in the idfrd format. You will need to convert your mag-phase data to complex-valued response with something like this:

>>response=mag.*exp(i*phase);

[Hari]

Thanks for your answer. I have tried 'tfest' by taking known transfer function models. But tfest really struggles to fit when the order is higher with big polynomial coeffiecients. I am expecting an order of 10 with big polynomial coeffiecients .

I tried 'fitfrd' which is slightly better, but still has problems at higher orders.

[Hari]

Now I am thinking of some sort of optimisation for best polyfit after specifying the order.