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

Question

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

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