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Stability analysis and weird behaviour

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CAMALEAO

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Hi everyone.

When plotting the closed loop stability analysis, what happens if the gain crosses the 0dB more than once? Say, three times?

The same for the phase margin plot, what happens of it "crosses" the 0deg more that once?

Regards.
 

You'll evaluate the Nyquist stability criterion. Find various previous threads about the topic at Edaboard.
 

Hi everyone.

When plotting the closed loop stability analysis, what happens if the gain crosses the 0dB more than once? Say, three times?

The same for the phase margin plot, what happens of it "crosses" the 0deg more that once?

Regards.

I suppose you are speaking about the loop gain behaviour (0 db crossings)?
The Nyquist criterion requires analysis of the open loop (loop gain) for checking the closed-loop stability.
 

Hi, Thanks both for your comment.

I am using cadence. I don't know how o plot Nyquist for stability analysis in cadence, do you know? I am using STB to evaluate the closed-loop feedback.
 

it is the last crossing - of the phase past 180 (360) degrees that counts, measure the gain margin there ...
 

if the open-loop gain is higher than 1 (=0dB) and the phase shift is higher than 180° at the same frequency of the open-loop characteristic your system is unstable.
you don't need to plot Nyquist-curve to check this, just go through the magnitude and phase points and check the above condition.
 

@frankrose, can you please elaborate? In this case, when the phase shift reaches 0deg, I have a reasonable gain.

How can I simulate Nyquist plot in cadence?
 

if the open-loop gain is higher than 1 (=0dB) and the phase shift is higher than 180° at the same frequency of the open-loop characteristic your system is unstable.
you don't need to plot Nyquist-curve to check this, just go through the magnitude and phase points and check the above condition.

Not necessarily, the system can be conditional stable. We can’t trust our intuition in this case, and neither in the previous case.
 

unfortunately post #6 is not strictly correct - it is a last crossing that matters, the phase can go to -360 (reinforcing) at gains higher than one as long as there is a later crossing ( the phase has to come up and then down again ) where the gain is <1 for -360 deg lag. This happens more often than you might think in real world systems - esp for buck converters ...
 

You are right, I forgot about conditional stability, but Bode plot also should represent that. Nyquist curve is necessary?
 

Nyquist and bode plot are different representations of the same data. The point is that for loop gain functions with more than one crossing of the 0 dB line, you need to evaluate the full Nyquist criterion. I feel that it's more visual in the Nyquist plot (# of encirclements of the critical point), but you have the same information in the bode plot.
 

The point is that for loop gain functions with more than one crossing of the 0 dB line, you need to evaluate the full Nyquist criterion.
For specifically that example it is not necessary.

You can arrive to the conclusion from the Nyquist plot that the system is stable if the gain is less than 1 (0 dB) at all following frequencies: -180º-n*360º ("n" is natural number including 0). -only valid for the specific case quoted.

You can see the above statement comes from the Nyquist plot.
 

For specifically that example it is not necessary.
Which example? The original post doesn't specify a scenario.

if the gain is less than 1 (0 dB) at all following frequencies: -180º-n*360º ("n" is natural number including 0).
Not sure how frequency can be expressed in degree.
 

Which example? The original post doesn't specify a scenario.
Your example. The one that has multiple gain crossover frequencies.

Not sure how frequency can be expressed in degree.
The gain must be evaluated at frequencies of the loop gain that has the phase equal to -180º-n*360º ("n" is natural number including 0).
 

O.K., that's not my example, it's the original question of CAMALEO.

For specifically that example it is not necessary.
I don't see that the question is restricted to the trivial case k=0 (no encirclements of the critical point). In the more interesting, and less intuitively understandable cases your condition is not fulfilled but the system is conditionally stable, though.
 

I should add that the simplified Nyquist criterion - no intersections of the real axis left of the critical point is applicable for most electronic feedback systems. From the electronic circuits design viewpoint, it's not so important that you need to apply the general Nyquist criterion for some control systems.


There are many previous discussions at Edaboard about stability analysis. Unfortunately some appended papers from older threads have been deleted in the last years. There's however an interesting link that's still actual (thanks to LvW)

https://www.cds.caltech.edu/~murray/amwiki/Main_Page


I also repost two papers from the previous discussion
 

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    CataM

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Thank you so much for all your comments. I will read these pdfs FvM and come back to you.

Meanwhile, do you guys now if it is possible to simulate nyquist or better saying, plot nyquist in cadence/spectre?
 

do you guys now if it is possible to simulate nyquist or better saying, plot nyquist in cadence/spectre?
Plot real part vs imaginary part of the quantity of interest. AC analysis needed.
 

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