Obtaining poles and zeros from frequency response magnitude and Phase plot

Question

是否有任何Matlab代码可直接从频率响应图确定极点和零点，任何参考文献将不胜感激。

Answer 1

Obtaining Poles and zeros from experimental data is a nontrivial task. The first step is to visually inspect the estimated FRF. Plot magnitude, phase and coherence all together in one diagram. Some questions to answer:

1. Does the coherence drop below 0.9 in some areas? If so, dont trust the data in this region. If you can do so, improve the experiment in this case. Narrow areas at resonances with bad coherence may be unavoidable. If there is a zero in the FRF, the coherence at this frequency will also be bad. In all other regions, a drop in the coherence may not be permitted. A carefully designed experiment should yield gamma^2 > 0.95 in all areas except at resonances or zeros. Failure to meet this criterion may indicate nonlinearity or high noise.
2. Can you see zeros or poles from the data? Look for peaks and valleys in the mangitude or jumps in the phase. If you see anything, write it down and compare it to your final results.
3. Is there any special structure in the FRF? Are the poles close to each other? Is this an oscillating system? Try to get some insight.

If the structure of the FRF is simple, just do a least square fit. Transform the FRF to a complex representation (FRF = real + i * imag). Then assume that FRF(s) = den(s)/num(s), where numerator and denomninator are polynonmials of chosen order. We obtain FRF*num(s) = den(s). This is linear with respect to the coefficients of num(s) and den(s). Calculate the least squares solution. Do this for different (independent) orders of num and den. Then compute zeros an poles from the polynomials.

If this approach does not succeed you need to understand what the problem is. Software does not help with this important step! Of course once you have some understanding, a more sophisticated approach may yield good results.