Question

Please solve both parts a and b step-by-step using the block reduction method ONLY.

Q4 a) (1 mark) The figure below shows a block diagram of a control system, obtain the transfer function [Y(s)/R(s)]N=0 N(S) R(5) Y(s) Gy(s) Ge(s) H(s) b) (2 marks) The figure below shows a closed-loop system with a reference input and disturbance input. Obtain transfer functions C(s)/R(s) and C(s)/D(S) of the system shown. Use block diagram reduction method only. GF D(S) R(S) Es) U(5) Cs) GC G G H

Answer 1

(མ） N(s） Ris) + 6-Cs) Hts) We are asked to find Yis) R(s) ཚེར་ས་ ས་ ད་ Inso. RCS) Gols) Y(s) ཀs (s） H(s）

111 R(S) 1+GE(S) HCS) Gpls) 1+ Gpls) HIS) →y(s) > R(s) Gp(s)[1 + GC687 H (s)] 1+ Gpls) HIS) →y(s) * YCS) Gpso 1 + GeCs) H(s)] RCS) N(S) - 1 + Gp(s) H(S) (ط) Gwen system is: DIS2 RCS) + Gf TGo + & Get Gp CLS) Tak C(s) Ris) | 24sao DLS) 20 GCF) + + G1 Gc →) Gp RCS) H Gf GiGp G1 + R(S) Go • Gp c(s) H

GfG 1 Gp RCS) + GCG , Gp CCS) H RCS) Gf G1 Gp Go G, Gp 1+Gc G, GpH t →C(s) R(3) GCG, Gp *G&G, Gpt 17GG, GpH → cos) CCS) RCS G1 GpGf + GCG, Gp ITG GqGpH DCS) = 0 CCS) - Grapes = G, Gop Cap + Ga Gap GE GEH + G, GC Gp R(3) D(S)-0 1+ Gc G1 GpH CCS D(S) R(S) -0 D(S) Go Gil to Gpl -H D(S) - Gpl (Cs) E -G1GCH Gp 1+GqGp GCH CCS D(S) D(S)[R(s=0 >(S) GP 1+ Gp G G CH