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sugar

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loop stability
Oct 19^th, 2006, 12:04am

Let's say we have a negative feedback system whose open loop transfor function
T(s) = A(s+100)^2/s^3

As we know, if open loop gain A is large enough, the loop will be stable (from root locus).

But bode plots tell us that if A is very large, at -180 degree phase shift, the gain plot is larger
than 0dB, which means signal will be amplified repeatedly after going through the loop, so
the system should be unstable.

I believe root locus is correct, but what's wrong in bode plot?

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vivkr

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Re: loop stability
Reply #1 - Oct 20^th, 2006, 5:14am

Hi sugar,

This topic has been done to death on this forum before. Please see
the link in a similar topic just a couple of days old.

http://www.designers-guide.org/Forum/YaBB.pl?num=1160990196

ACWWong is right in suggesting that you use the search tool. Often, several such questions and their
answers can be found in previous discussions.

and an older thread to which there is a link:
http://www.designers-guide.org/Forum/YaBB.pl?num=1141283321/2#2

Regards
Vivek

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sugar Community Member Offline Posts: 54	Re: loop stability Reply #2 - Oct 20^th, 2006, 9:08am hi vivek, I don't think the links you suggested answered my question. Bode plot has very clear physical meaning as I describe in the first post, prof. razavi also explained like that in his book. I just want to know what's wrong in that physical explanation.
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vivkr

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Re: loop stability
Reply #3 - Oct 24^th, 2006, 3:49am

Hi sugar,

Consider the fact that the gain and phase margin are measurements made at 2 frequencies alone, and for 1 value of feedback factor. How can they possibly convey all the relevant stability information of a Nyquist plot? Similarly, a Bode plot is still made for just 1 feedback factor.

Under certain assumptions, one may reliably extract stability information from the Bode plot. One basic assumption would be that the gain curve is monotonically decreasing or atleast not increasing. In such systems, there is typically a maximum value of loop gain (dc open loop gain A x feedback factor H) beyond which the loop becomes unstable.

On the other hand, your system has a range of gains (AHmin,AHmax) between which it is stable. This information though readily seen from a Nyquist plot is not seen in a Bode plot which is plotted for a single value of AH. Quite simply put, the Nyquist plot contains far more information than the Bode plot and the latter can never provide all the information about the former.

Does this answer your question?

Regards
Vivek

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ettore

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Re: loop stability
Reply #4 - Oct 27^th, 2006, 2:49am

Hi,

if A is big enough your system is stable. Furthermore Bode and root locus give confirm it in the same way.
As we know. in the Bode plot we must look at the phase margin when the open loop gain is 0db. In your example if A is big enough the phase margin can be a safe 90 degrees.

The fact that when the open loop gain �s still >> 0dB the open loop phase shift equals 180 degrees does not cause instability for the close loop gain.
It is misleading to imagine a recursive signal amplification inside the loop in such condition. It can help to remember that the close loop gain is A(s)/(1-A(s)), if feedback factor is 1. It is straghtforward to see that, no matter what is A(s) phase shift, the close loop gain is always -1.

regards,

Ettore

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ettore New Member Offline Posts: 4	Re: loop stability Reply #5 - Oct 27^th, 2006, 9:57am Ops, of course when the feedback factor is 1 the close loop gain is A(s)/(1+A(s)) and, consequently, if A(s) is big the close loop gain is always 1. The rest should be right.
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