Question

4. Given the block diagram as shown, and D are inputs and G, G2, and H, are transfer functions. a) Using only the block diagram reduction R+ G method*, find the transfer function C/R in terms of G, G, and Hz. H b) Using only the block diagram reduction method*, find the transfer function E/D in terms of G, G2, and Hz. c) Using either the block diagram reduction method* or the equation method, find the transfer function E/R in terms of G, G, and Hz. d) Using either the block diagram reduction method* or the equation method, find the transfer function C/D in terms of G, G, and Hz. e) Identify clearly the characteristic function of the system. NOTE: All stages of block diagram reduction must be clearly shown until you arrive at the last simple closed loop diagram and then the final open-loop equivalent with the transfer function in question. In addition, the final transfer function must be simplified, i.e., no fraction(s) over fraction(s).

Answer 1

Answer: Given that D R E Gi 672 с H₂K a) The transfer function § - Coutput , R input (o=o] صال for D=0 GU G2 >c E R for R=0,020 poln E H2 for CD=0 for Rao ی را Hz are. negitivity feedbacked Gu G2 R I+G 42 ㅋC vis GI G 1+G G₂ are in cascade and negitivity and negitivity feed backed with G, G2 1HG, 42 ula 1 + G, G2 it G242 G, G. 2 ItG₂H₂ +G, G2

b) The transfer function ula R-0,6 CR,C=0] GI G2 H₂ cence lis G2 H2 are negitivity feed backed G2 HG₂ H2 -G71 olm -G,672 It G₂H2 1+ G, G2 1+GH2 -G, G2 1+ G₂ H₂ +G, G₂ the transfer function. € R E -boxca R 'D,C=0 E R Gi G2 H2K

€ R 3 Gi G2 1HG₂H2 E GI R 1 + G, G2 HGH2 6 2 G,+GqH 1 + G, 69+G242 d) the transfer function:- éleco GI G2 > 7с H2 G2 1+G₂H2 G, G2 i + HG₂H2 G2 ofn 2 1HG, G + G₂ H₂ e) characteristic cquation:- HG, G₂ + G₂ Hz for all,