How would you try to model a system with the presented step response?

Dear all,

I am a beginner in System Analysis and would like to be advised on transfer function design.

 I am given the measured step response of a system as shown above and I am trying to design a transfer function that models the underlying system. Obviously, the system is more than first order, since the overshoot would otherwise not be reproducable. If second order, it goes beyond my current understanding on how to design a transfer function reproducing a similar step response. I would really appreciate tips or guidelines on system design for this special case. Thank you in advance and best wishes from Germany!

Answer 1

[Star Strider]

The System Identification Toolbox is designed for problems such as this.

If you have the Signal Processing Toolbox, and you know the input to the system as well, my first approach would be the invfreqz function.

[Star Strider]

Dennis’s ‘Answer’:

Thank you, and I do, input is a step function of amplitude 3.5, approximately. However, there must be rules on how to choose appropriate nz and np for such problems, say, 'you need at least two poles to resemble that behaviour' ..

[Star Strider]

You need as many poles and zeros as required to model your system to the desired degree of fidelity.

I use the ‘full’ number of input arguments, then cut and try:

[b,a] = invfreqz(h,w,n,m,wt,iter,tol)

occasionally omitting the ‘weight’ vector.

Answer 2

[Dennis]

Thank you, and I do, input is a step function of amplitude 3.5, approximately. However, there must be rules on how to choose appropriate nz and np for such problems, say, 'you need at least two poles to resemble that behaviour' ..