Why are gain & phase margins not reliable tests of stabi

[aryajur]

Gain and Phase Margins

Why are gain and Phase margins not reliable tests of stability. If anybody can give a case wherethey fail, it will be helpful

 

[suvendu]

Re: Gain and Phase Margins

for stability gain and phase mergin both should be positive.some system transer function arises in control system where gain mergin and phase mergin both are ∞(infinity).in that case u can not say abt stability of the system perfectly.eg.1/s

 

[tanghua_0407]

Gain and Phase Margins

i don't what you mean!

 

[gszczesz]

Re: Gain and Phase Margins

Gain and Phase margin give the stability of the system as currently described. In other words, given the simulated loading conditions, they will describe if your system will be stable.

Unconditional stabilty is different: it states that no matter what load you present on the output/input, the system will never become unstable. For that you need to do SP simulations and either plot load/source stability circles or look at the beta/Kf factors to see if you have unconditional stability. The load/source stability circles will plot what impedances at a given frequency will cause oscillations.

Greg

 

[aryajur]

Re: Gain and Phase Margins

Thomas Lee Book says that Gain and Phase Margin may not be enough to tell about the stability of a system in all cases. Thats what I want to explore, are there any systems which do have Gain and phase margin which would normally be interpreted as stable and will actually not be.

 

[VVV]

Re: Gain and Phase Margins

One situation I can imagine is when the gain or phase characteristics are such that a relatively small change in gain will make the crossover frequency change and at this new crossover frequency the phase margin is inadequate. Or the gain margin may become inadequate at some frequency.

Look at the picture (not accurate, just to illustrate the point). If the gain drops slightly, the phase margin at the new crossover frequency is no longer adequate.
Changes in gain can occur due to process variations, ageing, etc.

 

[aryajur]

Re: Gain and Phase Margins

Wow thats a really nics example, just wondering 1 more thing, would Nyquist stability criteria indicate the potential of increased instability in this case. I forgot the Nyquist criteria. I think I will study it again.

 

[nebisman]

Re: Gain and Phase Margins

Search in this forum the book "feedback control systems using matlab" by Dr. Lurie and read de chapter three. Here, he presents a key concept that clarify you question.


neb,...

 

[VVV]

Re: Gain and Phase Margins

You would see it in a Nyquist plot, too. Bode diagrams are actually another way of representing the info in the Nyquist plot.

I tried to draw a Nyquist plot whose Bode plot would be similar to the situation examined earlier. Note that the phase margin you measure is rather adequate.
But note also that the plot passes close to the critical point (the bump). That means that a slight decrease in gain would make it intersect the unit circle (gain=0dB) close to the critical point and so you would have little phase margin left in that case.

The point is that gain and phase margin provide part of the answer to the stability of the system, but you should also look at the overall plot to see if there are possible signs of trouble.

 

[nebisman]

Re: Gain and Phase Margins

Do you know any experiments or circuits where linear analysis can be completely valid, for using this keypoint from practical viewpoint?.

Nyquist-test stability-gain margin phese margin, conditional stability practical experiments for students

 

[scottieman]

Re: Gain and Phase Margins

may I post a open question on this topic for brainstorming?

Consider a amplifier, its open loop transfer function has two poles (assume all loading effects are included due to any closed-loop connection), which are all above the 0dB line.

Then, if I connect this amplifier into unity-gain feedback, should this amplifier stable or not?

Scottie

 

[nebisman]

Re: Gain and Phase Margins

This is always estable because stabilty margins are all positive. I have heard that at high frecuencies non minimum phase zeros are present in amplifiers and we should considetate the effect of this zeros over nyquist diagram.


nebisman

 

[leonlin]

Re: Gain and Phase Margins

I connect this amplifier into unity-gain feedback, should this amplifier stable or not

 

[dasong]

Re: Gain and Phase Margins

I hadn't studied the auto-control ,who can tell me,is it very important for system design.