( 30 points) A PD controller is used in a control system having a first-order process and a first-order sensor as shown below. where Gc=Kc(1+D);Gp=1/(ps+1);Gs=1/(ss+1) (a) (10) Find expressions for and for the closed-loop response. (b) (10) If p=1min,s=10sec, find Kc so that =0.7 for the two cases: (1) D=0, (2) D= 3sec. (c) (10) For servo control, compare the offset and period realized for both cases, and comment on the advantage of adding the derivative mode