Hint: you can use Matlab or SciLab for solving (b) and (c).

Bode diagram of frequency response can be used find GM.

In a standard feedback control system, assume G(s)= GvGpGm has the transfer function G(s)=s+12e0.2e and GD(s)=G(s). (a) If a PI controller is employed to control the system, please find the PI controller settings when the direct synthesis method with c=1.0 was used based on the desired response (Y/Ysp)d= eqs/(tcs+1). (b) By using this PI controller tuning parameter, what will be the response y(t) when a unit setpoint change is applied. (c) what will be the response of y(t) if a unit step disturbance change is applied. (d) What will be the gain margin (GM) of this controller design