# Bode Plot for stability Interpretation help needed ?

#### mishra87

Joined Jan 17, 2016
1,000
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.

#### MrAl

Joined Jun 17, 2014
10,599
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
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
1,669
In your case (three zero crossings for the phase function) you have to apply the FULL Nyquist criterion.
(Result: Stable).

#### mishra87

Joined Jan 17, 2016
1,000
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
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,

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.

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#### mishra87

Joined Jan 17, 2016
1,000
Hi Guys,

I am still waiting for some one to respond this topic.

Regards,

#### LvW

Joined Jun 13, 2013
1,669
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.

#### mishra87

Joined Jan 17, 2016
1,000
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,

The reason for saying stable system as i see using bode diagram it is unstable system.

#### mishra87

Joined Jan 17, 2016
1,000
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.

#### mishra87

Joined Jan 17, 2016
1,000
This plot is something different as phase plot crosses 0deg line not -180deg line.

#### LvW

Joined Jun 13, 2013
1,669
Hello,