How Can You Calculate the Phase Margin of an Unstable System?

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Discussion Overview

The discussion revolves around the calculation of phase margin for an unstable system, particularly in the context of control theory. Participants explore the implications of negative phase and gain margins as revealed by Nyquist plots, and the conditions under which these margins can be interpreted or utilized.

Discussion Character

  • Debate/contested
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • One participant questions how to find the phase margin of an unstable system, noting that the Nyquist plot indicates instability.
  • Another participant asserts that the signal phase margin (SPM) is defined as the largest additional phase angle a system can tolerate before becoming unstable.
  • A different participant expresses confusion over the necessity of phase margin in the context of an unstable system, questioning the validity of calculating it when the system is already unstable.
  • One participant states that the gain and phase margins of an unstable system are negative, providing an approximate gain margin value and suggesting that a certain gain increase is needed for stability.
  • Another participant argues that both phase and gain adjustments are necessary to stabilize the system, challenging the interpretation of phase and gain margins in this context.
  • A later reply suggests that negative margins indicate the need for compensation to achieve stability, mentioning the use of a lead compensator as a potential solution.

Areas of Agreement / Disagreement

Participants express differing views on the interpretation and relevance of phase and gain margins for unstable systems. There is no consensus on whether these margins can be classified as such when the system is already unstable.

Contextual Notes

Limitations include the ambiguity surrounding the definitions of phase and gain margins in the context of instability, as well as the potential need for additional compensatory measures to achieve stability.

LM741
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hey

can you find the phase/gain margin of unstable system. I am asked for the phase margin of this system, but the nyquist plot reveals that -1 is encicled verfiying that the system is unstable,.. how can you get a phase margin of an unstable system?
 
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I don't believe so. The definition of the signal phase margin (SPM) is the largest additional phase angle the system can accept without becoming unstable.
 
i concur, but then why is the PM required??

that's what i figured...but the question asks for a phase margin...unless my judgement on the stability of the system is incorrect... I've just included the nyquist plot as an attachement so this can be vrified.

many thanks
 

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The gain and phase margins of an unstable system are negative. In your case the gain margin is approximately -2.1dB, meaning that you should increase your gain by more than 2 dB, without altering the phase, in order to make your system stable.
 
but surely i should need to change my phase too (because like you said my pahse margin is negative)

this still does not make sense because if you look at the definitions of phase/ gain margin - it is the amount (phase/gain) you can add to the system BEFORE it BECOMES unstable...

here, we have an unstable system initially, and we have evaluted the values needed to make it stable...however can one classify these as phase/gain margins..?
thanks for reply
 
We normally use gain and phase margins for positive values. If you have negative values for the margins you should compensate the system in order to make it positive.
In most cases a lead compensator can do the job. A lead compensator is a system with a zero near the origin and a pole very far to the LHP. Such a system has a negative phase, so it can stabilize the whole system.
 
i'll go do some reading up on it . thanks very much
 

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