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Message started by circuit_cook on May 5^th, 2009, 7:44am

Title: question on stability
Post by circuit_cook on May 5^th, 2009, 7:44am

Hi, everyone:

I am a little loss at the control theory.
It says a system is stable if it has all poles in the left half plane. But if an opamp in closed loop has three poles (all in the left plane), we say it is unstable, because PM is negative.
Is the stability mean different thing here? Or does it mean that the stability criterion means that if compensation can be applied to achieve stability, it still meets the criterion?

Judy

Title: Re: question on stability
Post by buddypoor on May 5^th, 2009, 8:08am

circuit_cook wrote on May 5^th, 2009, 7:44am:

Who has said that a closed loop opamp with 3 poles in the LHP has negative PM and is unstable ? This is not the case !
Or did I understand something wrong in your question ?

Title: Re: question on stability
Post by raja.cedt on May 5^th, 2009, 8:55am

hi Judy,
if the poles are in RHP then system is unstable,but if they are in LHP still there is a chance of unstable because it is necessary but not sufficient.Now come to 3 stage op amp,in this case based on poles location you have to decide whether it is stable or not,but most of the times you will get less phase margin(>30) so it wont give satisfactory transient response.

Hope this is useful.

Thanks,
Rajasekhar.

Title: Re: question on stability
Post by circuit_cook on May 5^th, 2009, 9:22am

Hi buddypoor:

I mean a open loop opamp with three left half plane poles before UGB, a limit is on the feedback factor fo it to be stable. Is that anything wrong in my question?

I kind of have the same thought as Raja, that all left half plane poles is a necessary but not always sufficient condition for stability.

I read something called exponentially stability, and also there is the exponentially uniform stability, but too much math for me to get through it all now. So I wonder if the stability we acheive with Bode plot for enough PM margin is a subset of the more broader stability of BIBO. For BIBO the left half plane criterion suffice. For the subset the condition is more stringent?

This question has some similarity to Pancho's question about a system that is stable in Nyquist plot (conditionally stable), but why the 180 phase shift doesn't matter.

Does that comes from Bode plot is only an engineering aid to design, and Nyquist is the golden rule?

Judy

Title: Re: question on stability
Post by pancho_hideboo on May 5^th, 2009, 9:25am

circuit_cook wrote on May 5^th, 2009, 7:44am:

It says a system is stable if it has all poles in the left half plane.
But if an opamp in closed loop has three poles (all in the left plane), we say it is unstable, because PM is negative.

Do you understand open-loop gain, closed-loop gain, GM and PM correctly ?

If no RHP pole in your closed loop gain is achieved by pole-zero cancellation, you have to consider internal stability.
Especially during startup of system or circuits, each block have time difference to reach steady state.
So RHP poles could not be canceled by RHP zeros during startup of system or circuits.

Title: Re: question on stability
Post by circuit_cook on May 5^th, 2009, 9:34am

Hi, Pancho:

Thanks, I mixed it up. the closed loop pole would move to RHP when unstable. the criterion is right.

Judy

Title: Re: question on stability
Post by raja.cedt on May 5^th, 2009, 10:02am

hi Judy,
i think you need some minimum basics on stability.
1.For an open loop system to be stable you should have all LHP poles,otherwise system wont converge for steady input(This is called BIBO stability). In real working analog circuit you will not see RHP poles may be RHP zero(this is what i observed from my exp)
2.For an closed loop now poles will move with feedback, so as to examine the stability bode plot will help (this will take open loop information and feedback factor) otherwise if you are able to find you can roots then no need of bode plot.
3.But in circuits we wont consider BIBO stability because even though it is unstable you may limited by power supply or active device non linearity, so the main concern here is how good step response (this will come from the phase margin)
4.Bode plot is exact in case of all pole system,if zero's are then use nyquist.........use this document..very clear one.
http://www.ee.iitm.ac.in/~nagendra/presentations/20090109vlsiconf/20090109vlsiconf.pdf

hi pancho_hideboo,
from your previous ans i got this doubt, is it possible to cancel RH pole?could you please..i think answer is no.

Title: Re: question on stability
Post by pancho_hideboo on May 5^th, 2009, 10:14am

raja.cedt wrote on May 5^th, 2009, 10:02am:

hi pancho_hideboo, from your previous ans i got this doubt, is it possible to cancel RH pole?could you please..i think answer is no.

Not correct.
We can set zeros in RHP.
For example, assume 2nd order allpass system function which have two zeros in RHP and two poles in LHP.

Title: Re: question on stability
Post by raja.cedt on May 5^th, 2009, 10:23am

hi pancho_hideboo,
ya but is it canceling there?in the magnitude point of view it is canceling,but from phase point of view how it is not canceling?Please don't mind if my concepts are clear.Thanks for spending time.

Thanks,
Rajasekhar.

Title: Re: question on stability
Post by pancho_hideboo on May 5^th, 2009, 10:36am

raja.cedt wrote on May 5^th, 2009, 10:23am:

hi pancho_hideboo, ya but is it canceling there?
in the magnitude point of view it is canceling,
but from phase point of view how it is not canceling?

See text books on control system theory.

The followings might be a little helpful.
http://www.ece.rutgers.edu/~caggweb/Analog/hw5.pdf
http://www.engin.umich.edu/group/ctm/extras/PZ.html