SOLUTION

The stability of a feedback system can be determined from the Bode plot of the Frequency response of the open-loop system. This stability is usually based upon the Nyquist criterion for stability.

Gain margin (GM): The gain margin of the system defines by how much the system gain can be increased so that the system moves on the edge of stability.

A large gain margin or a large phase margin indicates a very stable feedback system but usually a very sluggish response.

If the open-loop frequency response shows gain greater than or equal to unity when the phase shift is -180° then the closed-loop system is not stable or highly oscillatory.

If the phase shift of the open-loop response is -180° or more negative than -180° when the gain is unity then the closed-loop system is unstable.

Gain margin and phase margin are frequently used for frequency response specifications by designers. Usually a Gain margin of about 6 dB or a Phase margin of 30 – 35° results in a reasonably good degree of relative stability.