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Determine if the system is stable? How is this done? Is this at one frequency? Is the Loop gain is A x B x C = 0.5 Should phase angles be added together = 173 degrees? Should I be considering the open loop or the the loop gain? The only info i have been given in material regarding stability is that at any frequency if the loop gain is greater than 1 and the the phase lag is 180 degrees then it is unstable. The course is only an intro the control engineering but I have no clue where to start with this. The material is terrible and provides very little info.

This is the entire question. There is no other information with it.

Thanks all for your help

Zephon
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  • Welcome to EE.SE! Is the above info the *only* info given in the question ? If so, you may not be able to use the Laplace transform method. Since you hinted that you have not learned Lapalace transforms, please mention the methods you have learned so far to measure stability. Please use the [edit] link below the question to add more details. – AJN May 03 '21 at 01:31
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    For stability, you can use the [Barkhausen criterion](https://en.wikipedia.org/wiki/Barkhausen_stability_criterion) or [Nyquist criterion](https://en.wikipedia.org/wiki/Nyquist_stability_criterion). Are you familiar with those ? In short you can check if the *open-loop* gain is less than or greater than 1 **and** if the open loop phase is a multiple of 360 degrees. Are you familiar with the terms open loop gain, open loop phase etc ? – AJN May 03 '21 at 01:34
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    @AJN I don't think you can use Barkhausen criterion for a particular frequency to claim that the system is stable, but, for a particular frequency you might be able to claim that it is unstable. – jDAQ May 03 '21 at 02:57
  • Hi thank you very much for your responses. The course i am doing is only introductory. the only info i have been given for stability is if there is a phase shift 180 degrees and gain is 1 then the system is unstable. – Zephon May 03 '21 at 08:02
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    Are all the phase angles really positive? – Chu May 03 '21 at 10:30
  • @jDAQ I agree. I was thinking that the system will not oscillate at the *given* frequency. I didn't think that there could be other frequencies at which the system could enter diverging oscillations. – AJN May 03 '21 at 12:00
  • I’m voting to close this question because homework needs an attempt at a solution – Voltage Spike May 14 '21 at 18:10

1 Answers1

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  1. Find the transfer function in Laplace domain.
  2. Find the poles.
  3. If Re{p_i} < 0 for all the poles the system is stable. Or in other words if all the poles are left of the Im axis, the system is stable. (This is only true for causal systems, which this system is.)

Here is a previous question that might help you understand better: https://electronics.stackexchange.com/questions/29647/how-to-determine-a-system-is-stable-using-pole-zero-analysis#:~:text=In%20summary%2C%20if%20you%20have,closed%2Dloop%20system%20is%20stable.

Emre Mutlu
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  • hi. thank you for your answer :) can you provide any more detail on how to do it? There is nothing in my learning material about laplace and ive never studied control engineering before now. – Zephon May 02 '21 at 22:45
  • @Zephon I don't really know how one could learn System theory without Laplace transform. All my books are in German so I cant recommend anything in English. But a quick google search on "System Stability" should provide you with answers. – Emre Mutlu May 02 '21 at 22:50
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    Take a look on a Laplace transform table to do the transform. Don't bother trying to calculate per hand. – Emre Mutlu May 02 '21 at 22:52
  • How can i figure out what the transfer function is? – Zephon May 02 '21 at 23:08
  • In this case it is (A*B)/(1+A*B*C), in laplace domain – Emre Mutlu May 02 '21 at 23:11
  • Brian Douglas has a great series of YouTube videos on controls you may find helpful. e.g. https://youtu.be/yf09OrHa520 – relayman357 May 03 '21 at 01:26
  • I think there isn't info in the question to do a Laplace transform. Instead, data at a single frequency seems to be given. OP can just use the gain (G >? 1) and phase criteria (P =? n*360). – AJN May 03 '21 at 01:29
  • Thanks so much for your help! Is the Loop gain is A x B x C = 0.5 Should phase angles be added together = 173 degrees? Should I be considering the open loop or the the loop gain? The only info i have been given in material regarding stability is that at any frequency if the loop gain is greater than 1 and the the phase lag is 180 degrees then it is unstable. – Zephon May 03 '21 at 08:29