Feedforward control applications often utilize a controller that consists of a lead-lag unit:Develop expressions for the controller output at the kth sampling instant p(k) using the backward difference approximation of the derivatives involved in Gf(s). Compare the discrete-time unit step response of Gf with the continuous-time response when K = 1, ?1 = 5 min, ?2 = 2 and ?t = 1 min.

G(s) = K(TIs + 1) (71 + 12) T2s +1