Given transfer function L(s) as a ratio of polynomials of s, I know that we can find gain margin (GM) and phase margin (PM) by using a Nyquist or Bode plot.
From a Nyquist plot:
- Find a point where the Nyquist plot of L(jw) crosses negative x axis, then GM=1/|L(jw)| at that point.
- Draw a circle from origin with radius 1, and find an intersection of Nyquist plot of L(jw) with unit circle. PM is the smallest angle that is required for Nyquist plot to be rotated clock-wise in order for that point on intersection to touch -1 on x axis.
From a Bode plot: here is an answer.
Question: Lets say I am not able to plot Nyquist and Bode plots, but I need to find GM and PM.
- Is there any way to find exact GM and PM?
- Is there any easy way to approximate it?