Feedback and control (Any control experts?)

[PM3295]

Someone asked me this question:

When we have a negative-feedback system:

We know; The system will be stable as long as the overall gain stays below 0dB (with some margin)when we reach -180° phase shift point.

a) What happens if the phase shift goes to +180°, for some reason, and the gain is more than 0dB?
b) What happens if the phase goes to more than +180° (say +200°, 250°) with more than 0dB gain?

I looked through my old books but can't find any example of a negative-feedback system having large positive phase shifts.
All the examples only deal with stability issues approaching the -180° point.

I hope some control expert can clarify this.

[optikon]

Someone asked me this question:

When we have a negative-feedback system:

We know; The system will be stable as long as the overall gain stays below 0dB (with some margin)when we reach -180° phase shift point.

a) What happens if the phase shift goes to +180°, for some reason, and the gain is more than 0dB?
b) What happens if the phase goes to more than +180° (say +200°, 250°) with more than 0dB gain?

I looked through my old books but can't find any example of a negative-feedback system having large positive phase shifts.
All the examples only deal with stability issues approaching the -180° point.

I hope some control expert can clarify this.

You just have to consider the whole phase shift around the loop of the feedback system. It answers all your questions about stability.
a) If the overall loop achieves a total of 360 degrees or more with > 0 dB gain, you will have instability
b) See "a"

[PM3295]

So, basically we only need to look at either +180° or -180° and if the gain is > 0 it will be unstable?

[optikon]

So, basically we only need to look at either +180° or -180° and if the gain is > 0 it will be unstable?

I think the 180 phase requirement you are thinking about might come from the fact that your forward path has already contributed 180 degrees phase shift. Is this correct? I think that is the standard control system model. But the actual condition for instability is the loop (forward and feedback) must achieve 360 or more phase with a loop gain > 0dB.

The previous statement is general and covers all feedback cases. What is the model you are thinking about?

[PM3295]

I think the 180 phase requirement you are thinking about might come from the fact that your forward path has already contributed 180 degrees phase shift. Is this correct? I think that is the standard control system model.

That is the case. I have no specific model in mind.

[nordiceng]

  When the phase shift goes to 180°, the control system is most likely will be unstable

[Old_but_Alive]

its not just a go-no  go situation.

There must be a margin away from the raw gain <1 at 180

there is a need to be some way away from that situation.

have a look at

http://www.ridleyengineering.com/loop-stability-requirements.html

this next one is a bit heavy, but try it

http://www.eeng.nuim.ie/~rfarrell/EE301/notes/EE309_notes_18.pdf

[bigtoy]

Consider a simple example, with a constant DC input. With 180 degree phase shift and gain > 1, the output will increase in value each time we "go around the loop". So the output will increase without bound.