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

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.

Answer 1

[Craig]

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

Answer 2

[Roger van Rensburg]

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