Consider the control system,
where

The value of / is known to change slowly with time, although, for design purposes, the nominal value is chosen to be J = 25.
(a) Design a PID compensator (denoted by Gc(s)) to achieve a phase margin greater than 45° and a bandwidth less than 4 rad/s.
(b) Using the PID controller designed in part (a), develop an m-file script to generate a plot of the phase margin as J varies from 10 to 40. At what J is the closed-loop system unstable?

Transcribed Image Text:

G(s) = 2