Question

Reduce the block diagram below to a single block representing the transfer function T(S) C(s) R(S) H3(s) Hl(s) R(s) + C(s) Gi(s) G2(s) G3(s) Hz(s) H4(s)

Answer 1

Hz) 0 HHIS + 4,(8) R (3) 19219) elso M218) Huls Step Block G, (3) , H, (3) and 412 H2(8) are forming loop. So, it can be reduced M3LQ B. a ti G16 HG,SHION A 626) Ht92( biz RO P HY

2 Step II shifting the summing point to the Bight side of Gain Block A = G200 and It.com) shifting the take off point (P) to the left side of gain Block A (MASA B A G(S) TA HUS)- A Hyls are Step Blocks B, H3(S.A and G3(8), forming loops 430) 19 BIO IZAB130) A THAGAHY. RUS Now step Ao B, 43(S) HAB H263)) (1799344) R(6) 1+ AB. 40 Il+ A B 13) (14A 4944)

A.B.63 Tele u (+AB4y)(1+Aggte) + ABC13 ABG3 Il+AB43)(1+4449 ♡ R(S) and B= put A = 62 It ₂ M2 G It GIHI Gz Gi G3 (5) RS) (1+ G242) (1HG H I) +9,42H3 it. &n4zdy t it 92Hz (1441H) (144213] G1 G293 11+ 4142)(it 4x13 212 Gi Q2 Q3 (14 9242) (11494.)[1442 42) 4979243)(14 474219243 +4) + G1 9293