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Ro R (Σ D(s) 1 s(s+1) Consider the system shown in Fig. 4.26, where (s+a)² s² +w² D(s) = K- OY (a) Prove that if the system is stable, it is capable of tracking a sinusoidal reference input r = sin wot with zero steady-state error. (Look at the transfer function from R to E and consider the gain at wo.) Fig 4.26
The general unity feedback system shown in Fig. 4.30 has disturbance inputs w₁, w, and w, and is asymptotically stable. Also, K₁I(+216) 31 (5+P1) G₁ (8) = RO" Σ G₂ (s) G₂ (8) = (a) Show that the system is of Type 0, Type ₁, and Type (+12) with respect to disturbance inputs wi, w₂, and we respectively. Σ K₂ s G₂(3) (+226) 1(8+P2) م * (Σ oy Fig 4.30