Question

R E UA Given the block diagram as shown, R and D are inputs and G, G, and H, are transfer functions. a) Using only the block diagram reduction G G method", find the transfer function C/R in terms of G, G, and H. H, b) 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, 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, Gy, 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

JD C G2 R Gi H2 ca) finding the transfor function & In the question, it is given that there are two input (R&D) will finding the transfor function of of set D=0 с Gi G2 ITG₂ H2 R pe G, G2 It G2 H2 Gi G2 1HG2 H2 R C It GIG2 I+G2H2 CS Scanned with CamScanner

G, G2 cz ITG₂ H2 + G, GL b while finding the trams for function & keep R=0, D с G2 Gi H2 B С Gil G2 HGHL D. G2 GI l+G2 H2 ula G1 G₂ 1HG₂ H2 e while finding the transfer function keep D=0. Scand with CS Camsc.

с R Gi G2 H2 с E R Gi G2 HG2 H2 с R-c E- (R-C.).G, E. G2 -7 2 HG22 from Equation @f @ E = R. G- Gj. E. G2 14 G2 H2 [ " R.GI 14 G1 G2 It Gala . ] E El It G2 Hz + G, G2 1+ G2 H2 G, CI+ G₂ H2) 14 G₂ H2 + GIGA E I! Gi (lt G2 H2 ) It GiG2 +G₂ H2 il ules CS Scanned with CamScanner

(d) while finding transfer function of keep R=0. D с E Go Gi H2 D sh G2 → C 6 Gy 1HG2H2 E.+D. 0 C. Gil (E+D). G2 C = ItG2 H2 E.G2 1HG₂H2 D. G2 14 G2H2 from Equation and D. G2 CE G2 ... G + I+G2H2 1+G2 H2 D. G2 c[in I- Gi G2 It G₂ H2 It G2 H2 c[ 1+ G2 H₂ - G G2 1927 = _D. G2 D.G2 14 G2 H2 C 1+ G2 H2 G12 ola D It G₂ H₂ - G1 G2 CS Scanned with CamScanner

(e) from the question @ G, G2 clar It G2H2 + G, G2 1+ G12H2 +GIGA = 0 11 characteristic Equation CS Scanned with CamScanner