Question

R+ E vo UA G G b) Given the block diagram as shown, R and D are inputs and G, G, and H, are transfer functions. D a) Using only the block diagram reduction method*, find the transfer function C/R in terms of G, G2, and H2 HA Using only the block diagram reduction method*, find the transfer function E/D in terms of G, G, and Hz. c) Using either the block diagram reduction method* or the equation method, find the transfer function E/R in terms of G,, G2, and Hz. d) Using either the block diagram reduction method* or the equation method, find the transfer function C/D in terms of G, G2, and H2 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

R D Given Block E Digram IGI + G2 to a) Finding of c out-put, Rinput [0:0] * * * PID for D=0 GI flood G2 RID=0 R E For R=0,670 هو عبا و انا E For C,D=0 for R=0 , Gz , Hq Ave Negiliwly Feedbacked. GI G2 R It G2 H2 - 3 Gi, Ga Are in Cascade and negativly Feedbacked 14GH2 with Gi G2 It G2 H2 G. Go 드 R = loro It G1 G2 It G₂H2 + G, G2 It G2 H2 رط EO 1.R.O. D REO, CO [R, cao D G2

G, H2 Are Negitivly feedbacked. 42 1+62 H2 E GI -G, G2 It G2 H2 - GIG2 1+ GiGat 2112 1+ G1 G2 It G₂ H2 C) o loco 0,C=0 G G2 H2 E R 92 Go H₂H2 E GI R I + G G2 It Galty Git G, G2 H2 It G G2 tkz Itz D) RO 41 G2 H21 als Ge It G₂ H 2 Gs 17 G1 G2 It Go H2 ITG G2 + G282

characlerstic Equation : 1+G, G2 + G2H2 For All.