system identification

For a second order differential equation of a mechanical system m*(xdbldot) + c*(xdot)+k*(x)=F1*t)+F2*exp(i*2*omega*t) the unknown parameters 'c' which represents system damping and F1 and F2 which represent forcing functions need to be estimated. I have vibration signature in frequency domain to be used for input. How do i use system identification in Matlab for the same ?

Thanks, Sumit.

Answer 1

[Rajiv Singh]

By vibration signature, do you mean the frequency responses from the two inputs to the output? Are F1 and F2 constants? Is the system of equations complex (you show exp(i*2*omega*t) which is a complex number)?

Given frequency response measurements, there are various functions that can produce a model that fit the measured response - n4sid, oe, pem, and in R2012a, also tfest, procest, ssest. For structured estimation, you can also use grey box modeling techniques (idgrey/pem in R2011b or earlier, greyest in R2012a), but for simple systems like yours (unless I missed something; see questions above), functions like OE and PEM can deliver the results, provided you do have the right data.

[SUMIT]

The system of equations is complex including both transverse directions, say r=x+j*y. Frequency response is FFT of the individual responses.

[Rajiv Singh]

So what type of data do you have? It is FFT of complex time-domain input and output measurements (possibly complex)? If so, the standard identification methods that I mentioned before still apply. You can package the data as iddata object with domain = frequency. You will need to generate FFT values for a frequency range that is symmetric around origin. The result of estimation will be a complex model.

Perhaps you could post some example data to put the discussions to more concrete terms?