Bode Plot for stability Interpretation help needed ?

Thread Starter

mishra87

Joined Jan 17, 2016
906
The Loop gain and phase plot a control loop is shown below. Please comment on the
stability of the system.
Also, comment on the system stability if the gain (alone) of the system changes significantly.
1616005288289.png
 

MrAl

Joined Jun 17, 2014
8,063
The Loop gain and phase plot a control loop is shown below. Please comment on the
stability of the system.
Also, comment on the system stability if the gain (alone) of the system changes significantly.
View attachment 233007
Well what have you learned about this so far?
What do you know about the gain and phase relationship for stability?

Actually though you are supposed to show your first attempt to solve this in the Homework section.
 

LvW

Joined Jun 13, 2013
1,213
In your case (three zero crossings for the phase function) you have to apply the FULL Nyquist criterion.
(Result: Stable).
 

Thread Starter

mishra87

Joined Jan 17, 2016
906
Well what have you learned about this so far?
What do you know about the gain and phase relationship for stability?

Actually though you are supposed to show your first attempt to solve this in the Homework section.
Hi Thanks for
The Loop gain and phase plot a control loop is shown below. Please comment on the
stability of the system.
Also, comment on the system stability if the gain (alone) of the system changes significantly.
View attachment 233007
Well what have you learned about this so far?
What do you know about the gain and phase relationship for stability?

Actually though you are supposed to show your first attempt to solve this in the Homework section.
Hi,
Thanks for your reply !

My understanding this Gain and phase plot is as per below.

PHASE MARGIN : At corner frequency f3 Gain plot crosses the 0db line and let us assume the PM positive i.e.45deg so the stable.
Gain MARGIN : At corner frequency f1 phase plot crosses 0db line and GM is negative so it leads instability
At corner frequency f2 phase plot crosses 0db line and GM is negative so it leads instability
At corner frequency f4 phase plot crosses 0db line and GM is positive so it leads stability


So the overall system is unstable as GM is changing insignificantly.


I do hope some more comments on this particular system stability.

1616326343686.png
 

Attachments

LvW

Joined Jun 13, 2013
1,213
So the overall system is unstable as GM is changing insignificantly.
No, your conclusion is not correct. The concepts of phase and gain margins cannot be applied because the loop gain exhibits three crossings of the zero deg line. As I have written in my answer#3 you have to apply the FULL Nyquist criterion.
 

Thread Starter

mishra87

Joined Jan 17, 2016
906
No, your conclusion is not correct. The concepts of phase and gain margins cannot be applied because the loop gain exhibits three crossings of the zero deg line. As I have written in my answer#3 you have to apply the FULL Nyquist criterion.
Hello,

Thanks for reply !
Could you please explain about at some extent ?
The reason for saying stable system as i see using bode diagram it is unstable system.
Thanks in advance !
 

Thread Starter

mishra87

Joined Jan 17, 2016
906
No, your conclusion is not correct. The concepts of phase and gain margins cannot be applied because the loop gain exhibits three crossings of the zero deg line. As I have written in my answer#3 you have to apply the FULL Nyquist criterion.
1616338893634.png
 

LvW

Joined Jun 13, 2013
1,213
Hello,

Thanks for reply !
Could you please explain about at some extent ?
The reason for saying stable system as i see using bode diagram it is unstable system.
Thanks in advance !
There is not much to explain.
* In general, the stability of a system with feedback can be checked using the Nyquist criterion (complex s-plane).
* In some cases, however, a simplified form of this criterion may be used. This simplification leads to the concept of gain and phase margin. This simplified form may be used for phase functions only which cross the 0-deg. line once (see the example in your last post).
* You must not be confused because of the -180deg. Sometimes the minus sign at the summing junction is included in the definition for the loop gain - and sometimes it is not. That`s all!
 
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