11.8 Repeat Problem 11.6 for the case of a real proportional-derivative controller with transfer function Gc(s)=kc(1+Ds)/(1+Ds).

11.8 Repeat problem 11.6 for the case of a real proportional-derivative (PD) controller with transfer function Gc(s)=kc(1+DS)/(1+DS). Consider the closed loop system shown in Figure P.11.6 where the transfer function of the process is that of a second order system, i.e. Gp(s)=2s2+2s+1kp Figure P.11.6. If the controller is a P controller (Gc(s)=kc) a) determine the closed loop transfer function b) determine the offset to a unit step change of the set point Also, simulate the response of the output y(t) to a unit step change in the set point, for the following values of process parameters: kp=1,=0.5,=0.5 and the following values of controller parameters: kc=10,D=0.1,=0.1 Compare your result to the case D=0. What do you observe