A PD controller is used in a control system having a first-order process and a first-order sensor as shown below.

Ysp Gc(s) Gp (s) Gs (s) where Gc = K. (1 + tds); Gp = 1/(Tp s +1); Gs = 1/(Ts s +1). = = S (a) Find expressions for and t for the closed-loop response. (b) If Tp 1 min, Ts = 10 sec, find Kc so that $ = 0.7 for the two cases: (1) TD = 0, (2) TD = 3 = = sec. (c) For servo control, compare the offset and period realized for both cases, and comment on the advantage of adding the derivative mode