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+tDs);Gp=1/(tps+1);Gs=1/(tss+1). - Find expressions for z and t for the closed-loop response. - If tp=1min,ts=10sec, find Kc so that z=0.7 for the two cases: (1) tD=0,(2)tD=3 sec. - For servo control, compare the offset and period realized for both cases, and comment on the advantage of adding the derivative mode. 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+tDs);Gp=1/(tps+1);Gs=1/(tss+1). - Find expressions for z and t for the closed-loop response. - If tp=1min,ts=10sec, find Kc so that z=0.7 for the two cases: (1) tD=0,(2)tD=3 sec. - For servo control, compare the offset and period realized for both cases, and comment on the advantage of adding the derivative mode