Use matlab identification tool to estimate the transfer function of the vibrating system

There are many functions in the Matlab identification toolbox. Here is a simple example to show how to use the estimated system transfer function.

For example, our task is to know the input and output of the system, but the system is unknown. It is a black box, and we need to estimate the transfer characteristics of the system .

Our system input and output data are as follows

 The system is unknown, we solve for the system response by estimating the power spectrum

 Transfer function estimate - MATLAB tfestimate

 The system frequency response is obtained by dividing the cross-power spectrum and the self-power spectrum

[pxx,f1] = pwelch(x,window,noverlpap,Nfft,fs);

[pyx ,f2]= cpsd(y,x,window,noverlpap,Nfft,fs);

tfunc=pyx./pxx;

We get the system frequency response (magnitude and phase)

plot(f,(abs(tfunc)));
title('Transmission tf amplitude small range');
xlim([0,20]);
 

plot(f,(angle(tfunc)));
title('Transmission tf phase small range');
xlim([0,20]);
ypf = angle(tfunc);

 That 's exactly the same frequency response as we're using

The transfer function of the system is estimated as follows

Create Frequency Response Object

sysfr = idfrd(ResponseData,Frequency,Ts) creates a discrete-time idfrd object that stores the frequency response ResponseData of a linear system at frequency values Frequency. Ts is the sample time. For a continuous-time system, set Ts to 0.

sys = arx(data,[na nb nk]) estimates the parameters of an ARX or an AR idpoly model sys using a least-squares method and the polynomial orders specified in [na nb nk]. The model properties include covariances (parameter uncertainties) and goodness of fit between the estimated and measured data.

 The above na nb nk are respectively, the number of denominator coefficients, the number of numerator coefficients and delay

Unfortunately, we don't know the number of poles and zeros of this unknown system (or the order of the polynomial)

ypf = abs(tfunc);
xpf = f;

frdobj = idfrd(ypf,xpf,1/fs);

modelobj = arx(frdobj,[4 3 0])

modeltf = tf(modelobj);

b = cell2mat(get(modeltf,'Numerator'));
a = cell2mat(get(modeltf,'Denominator'));

Estimated system response, the characteristics of the two peaks have been simulated

 

unit shock

step(modeltf)

Transfer Function

pole-zero form

 zplane pole-zero plot