MATLAB: What can you tell/deduce by looking at the plots of magnitude and phase of a frequency response function

dynamicsfrequency response functionmagnitudephase

What can you tell/deduce by looking at the plots of magnitude and phase of a frequency response function?

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Okay, now I get it.

Actually, there are lots of things to tell. For instance, by looking at the magnitude plot, you can see at which frequency a single pole, double poles or complex conjugate poles take place. If -20dB/decade change happens at that frequency, you say it is a single pole. If -40dB/decade change happens at that frequency, you say it is a double pole. If a resonance peak takes place, which means immediate rise and fall at a specific frequency, it means complex conjugate poles. For zero, the situation is vice versa, which means there will be positive changes instead negative ones, like 20dB/decade, 40dB/decade...

For phase plots, you should think it this way: For a transfer function, if you do mathematical calculations in frequency domain, you will see that its phase at a specific frequency is the difference between its zeros and poles. Therefore, one can easily see that any zero will bring positive phase, while pole will bring negative phase. Therefore, for negative poles and zeros, you should see what I say, in other words, stable zeros and poles.

That is all for now. We can discuss further later.

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MATLAB: Open loop stability: Bode – Pole zero plot mismatch

You did not post your system, so it is a bit hard to figure out what is going on, especially when you say that you see poles moving to RHP in Spice.

Going purely on the plots you provided (poe zero map primarily) I tried to construct a model that would create similar plots.

sys=zpk([2.4*10^9*j -2.4*10^9*j], [-0.0000001 -11.5*10^7+1.2*10^9*j  -11.5*10^7-1.2*10^9*j],-100000000);
subplot(121);bode(sys);grid;
subplot(122);pzmap(sys);
xlim([-1.5e+8 2e+7]);

The first subplot shows full bode plot. If you focus on the region you are looking at, you will see similar plot to what you show:

subplot(121); bode(sys, {1e+9*0.1034 1e+9*2.8278}); grid;

Now if you zoom in bode plot magnitude that looks similar to your plot.

If you do

allmargin(sys)

you will see phase margins at first two crossovers are negative and phase margin at 3rd crossover is positive.

If you do

isstable(sys)

you will see the system is stable because all poles are in the left half plane, even though one of them is essentially at the origin.

Bottom line: even though you see negative phase margins, this system is stable, as all poles lie in the LHP. Hope this helps.

MATLAB: How to force tfest to estimate the process with “only real poles”

TFEST cannot guarantee real poles.

If you can work with <=3 poles and <=1 zero, try PROCEST. This is a process model estimator.
Otherwise, consider a grey-box formulation where your parameters are the real poles. See for example:

https://www.mathworks.com/help/ident/ug/estimate-complex-conjugate-poles-and-zeros-using-grey-box-model.html

The downside to using grey-box approach is that you will need to initialize the parameter values manually; the software will not do that for you. You can run TFEST and use the poles of the resulting model to may be take a guess at the initial real pole values for grey-box estimation.

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Related Solutions

MATLAB: Open loop stability: Bode – Pole zero plot mismatch

MATLAB: How to force tfest to estimate the process with “only real poles”

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