[SOLVED] Enough information to determine stability?

[E-design]

If only the following data are known in a negative feedback system is it possible to make a conclusion about stability or not?

 

[LvW]

If only the following data are known in a negative feedback system is it possible to make a conclusion about stability or not?

No, it is not possible because it is not known
a) if this is loop gain, closed-loop gain or something else,
b) if the condition for applying the BODE criterion is fufilled (frequency region to small)

 

[E-design]

That was my feeling as well (not enough information), although this came up in a interview question of one of my friends recently. He had only 2 choices of answers. Is this system stable or not.

 

[LvW]

That was my feeling as well (not enough information), although this came up in a interview question of one of my friends recently. He had only 2 choices of answers. Is this system stable or not.

Perhaps the interviewer did want exactly this as an answer - namely that additional information is needed.

 

[FvM]

Whe must presume the diagram is showing loop gain, otherwise it would be totally unrelated to stability.

The loop gain characteristic will have at least one unity gain crosspoint at higher frequencies. Without knowing the respective phase margin of this and possible additional crosspoints, the question can't be answered, I think.

 

[E-design]

Perhaps the interviewer did want exactly this as an answer - namely that additional information is needed.

He told me there were only two blocks to mark on the form (interview had a paper test part as well as verbal)

Is the system stable?
A- Yes
B- No

 

[dave9000]

The expected answer is NO, since the gain is greater then 0 dB for a phase shift of 180°

 

[crutschow]

The system has only 20° of phase margin at 0dB gain and has no gain margin (gain is +9.6dB) at 180° phase so it would seem that the system is unstable and the answer is b- No.

 

[mtwieg]

The expected answer is NO, since the gain is greater then 0 dB for a phase shift of 180°

The system has only 20° of phase margin at 0dB gain and has no gain margin (gain is +9.6dB) at 180° phase so it would seem that the system is unstable and the answer is b- No.

This assumes that there is another another 180 degree phase shift in the feedback due to an inverting error amp or something. But since that's not given in the problem, then this isn't necessarily true.

It's an awful, poorly designed question and your friend got screwed.

 

[dave9000]

This assumes that there is another another 180 degree phase shift in the feedback due to an inverting error amp or something.

The original post says "in a negative feedback system"

 

[varunkant2k]

The system has only 20° of phase margin at 0dB gain and has no gain margin (gain is +9.6dB) at 180° phase so it would seem that the system is unstable and the answer is b- No.

If we see the question and image as it says, this is the correct answer.

 

[LvW]

If we see the question and image as it says, this is the correct answer.

Remember, that there are conditionally stable systems and that the BODE stability criterion (based on phase and gain margins) is not always applicable. It may be used when there is only one single cross-over frequency of the phase function. This is not the case for the system under discussion (see FvM's post #5).
Perhaps one should take into consideration that also interviewers are not errorless.

 

[dave9000]

The loop has a positive gain of 3 at 0.3Hz: I cannot imagine a linear system being stable given this premiss, whatever the loop gain may be outside the given frequency range.

 

[mtwieg]

The original post says "in a negative feedback system"

Yes, but that doesn't mean the amp is or isn't actually included in that plot. Often when looking a bode plots of closed loops, you actually include the entire loop, including the error amp, and thus you look for crossings of 360 degrees, not 180.

And FwM/LvW also bring up to valid point that bode plots often aren't sufficient for actually determining stability. Especially in the case where there are multiple crossings of 180/360 degrees of phase. A nyquist plot is necessary for that.

 

[dave9000]

And FwM/LvW also bring up to valid point that bode plots often aren't sufficient for actually determining stability. Especially in the case where there are multiple crossings of 180/360 degrees of phase. A nyquist plot is necessary for that.

Yes, I agree that you cannot say if the system is stable unless you have full information. But you can say that it is not stable from this bit of info - I cannot point to the theory, but it looks clear to me.

 

[LvW]

The loop has a positive gain of 3 at 0.3Hz: I cannot imagine a linear system being stable given this premiss, whatever the loop gain may be outside the given frequency range.

I can agree to you - insofar as it is not easy to imagine stability for such a system. However, sometimes it is not sufficient to rely on the "common sense".
Example: In the present case, the phase function goes for rising frequencies from +160 deg to +180 deg (equivalent: from -200 deg to -180 deg). Then, it will further rise to e.g. -150 deg and certainly will again cross the -180 deg line at f=fx . This is the normal behaviour for each real system that exhibits a rising negative phase angle for high frequencies.
Assuming that the magnitude at f=fx will be again below 0 dB the system will be stable if the open lopp is closed with a "-1" subtractor.
This can be proved by a suitable Nyquist plot because the critical point "-1" will remain left to the Nyquist contour.
This explains my claim that some information is missing.
(The above assumes that the graph as given by E-design belongs to the product of all loop components - except the phase inversion due to the "-1" subtractor element).

Regards
LvW