A process with transfer function is controlled with a P controller with positive gain kc. (a) For what value of kc is the gain margin 2? (b) For what value of kc is the phase margin 30°? (c) Use...

A process with transfer function

is controlled with a P controller with positive gain kc.

(a) For what value of kc is the gain margin 2?

(b) For what value of kc is the phase margin 30°?

(c) Use MATLAB or Maple to calculate and plot the response of the closed-loop system to a unit step change in the set point for the values of kc found in (a) and (b).

(d) If there is an unmodeled dead time θ in the process transfer function, what value of the dead time in each case will drive the system to the verge of instability? Solve (a), (b) and (d) algebraically and then validate your results using MATLAB.