What does infinite phase margin mean of a transfer function and is this even practical in the real world?

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Roger van Rensburg
Roger van Rensburg 2015-6-19
回答： Roger van Rensburg 2015-7-26
Goodday all,
I've stabilized a very unstable inverted pendulum system using state-feedback. When I analyze stability using frequency response by observing the bode plot in Matlab, I found the magnitude in the gain margin plot below the 0db line for all frequencies (see bode attached). This causes my phase margin to be infinite but does cross the -180 degree line in the phase margin plot that gives me a finite gain margin. I don't understand the significance of the infinite phase margin, is it good or bad for a system or even practical? I know from tutorials that the higher the gain and phase margin the better the stability.

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Craig
Craig 2015-7-22
A few ways to interpret an infinite phase margin is:
  • you can rotate your frequency response plot on the Nyquist diagram and never changed your encirclement condition
  • this means your system can robustly handle phase uncertainty and time delays
-craig

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Roger van Rensburg
Roger van Rensburg 2015-7-26
Hi Craig, thanks for the reply. I have also read that some mathematical models will have infinite gain/phase margins, if course no real-physical system is possible to have infinite margins but will be an indication to the designer that the real-physical system has large margins.
Interestingly enough, I obtained state feedback gains using a LQR to stabilize the system and when I plot the open loop frequency response of the system I get a gain margin of -6bB and phase margin of 60deg. This is really interesting because my SIMO system holds stability for some variance of parameters in my mathematical model. Don't know if a LQG will provide better robustness for linear-time-variant systems? I will try this next. Or would there be a better alternative in controller design in terms of robustness?
Thanks.
Roger

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