Design a time-delay compensator (Smith predictor) for

where G_v = G_m = 1 and θ = 1. Show closed-loop responses for unit step set-point and disturbance changes (G_d = G_p). Use an IMC PI controller with τ_c = 3 (Case A in Table 12.1).

-Os G, %3D 5s + 1 Table 12.1 IMC Controller Settings for Parallel-Form PID Controller (Chien and Fruehauf, 1990) Case Model KK K TS +1 K T, + T, B T, + T2 (T,s + 1)(t,s + 1) K 257 25t T?g + 2%ts + 1 25 K(-s +1) B > 0 7?s + 25ts + 1 25t D 25t 25 K 2 27. +t 27,t 2t, +t K 2t. + t s(ts + 1) Ke- G TS +1 T +0 Ke-s Ts +1 2t +0 K(t,s + 1)e-s (T,s + 1)(t,s + 1) T, T; = (T, + T, T3)T3 T, + Tz = T3 I, + T, = T3 T, + T, - T3 OIN