The system phase margin frequency is given as omega1 17

Question

1. With the aid of a block diagram of a PID controller, show the expression of its output in the time domain.

2. A PID compensator is to be designed for the system given by the following translation function;

G(s)H(s) = 4/s(s+1)(s+2)

The system phase margin frequency is given as ω₁ =1.7 radsec^-1 and the required phase angle is 50°. Obtain the respective values of the PID controller.