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

[LM741]

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?

 

[Maxwell]

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.

 

[LM741]

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

 

[SGT]

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.

 

[LM741]

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

 

[SGT]

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.

 

[LM741]

i'll go do some reading up on it . thanks very much