Question

3. There is a block diagram as shown in Fig. G1 G2 G3 Fig. 2 (a) Convert the block diagram to a signal flow (b) Obtain its transfer function (G(s)-C(s)/R(s)) (c) As G -K.G3 G3 and its inputrt) is unit step, obtain the 50 condition of the P-controller(G1) for c(t) not to oscillate.

Answer 1

"(a) rightarrow signal flow graph (b) rightarrow C(s)/R(s) = rightarrow Forward path = G_1 G_2 leftarrow M_1 individual loops materialimplication -G_2 G_3, -G_1 G_2 gain mainsole's Rule C(s)/R(s) = Sigma^n_k = 1 M_k Delta_k/Delta Delta = 1 - (individual loops) M_k - forward path Delta_k - The value of Delta which is not touch the k^th path. \r\n M_1 = G_1 G_2, Delta_1 = 1 C(s)/R(s) = M_1 Delta_1/Delta = G_1 G_2/1 -[(-G_2 G_3) = (-G_2 G_2)] C(s)/R(s) = G_1 G_2/1 + G_1 G_2 + G_2 G_3 (c) G_1 = K_1,. G_2 = 50/S(S + 1), G_3 = S/50 C(s)/R(s) = k_1 50/S(S + 1)/1 + K_1 50/S(S + 1) + 50/S(S + 1) S/50 = K_1 50/S(S + 1) + K_1 50 + S C(s)/R(s) = 50 k_1/S^2 + 2S + 50K_1----(1) From (1) rightarrow characteristic equation materialimplication S^2 + 2S + 50 K_1 = 0 From R-H criteria S^2