Question

PROBLEMS B-2-1. Simplify the block diagram shown in Figure 2-29 and obtain the closed-loop transfer function C(s)/RS). B-2-2. Simplify the block diagram shown in Figure 2-30 and obtain the closed-loop transfer function C(s)/R(s). B-2-3. Simplify the block diagram shown in Figure 2-31 and obtain the closed-loop transfer function C(s)/R(S). G1 R(S) CS) Figure 2-29 Block diagram of a system. Figure 2-30 Block diagram of a system. Figure 2-31 Block diagram of a system.

Answer 1

2-29 RO 4) Renato forward- 37 -CCS) forogne-2 for hard 1= Git 62 for word 2 = 3 - Go t(s) ca) Gitar Gg G4 Git on feed back Network CO — R(S) 1+ (6 +92) (9744) G+ G2 R(S) It 6, 93-G, G4 + G2 - GaGa 12-30 do PA RO) Porward for word = Hi- te

stept sa ROI Rait to Tazt 192 .ca forward feedback HI H2 porward - Cascade Git! Reed back > 622 + G2 (Hi-H2) Cascade = - (wit) CCS) RG) (1+2CH-H2) c (3) = R(3) ont G, G2 it G2 Hi - GrH2 Note R(A) 3 - CU) Спје ers) - forward 4t 2 RB ) = G,*92 ) 25 ras) ai (92 Cascade Poco te. It ca HHH 5 k Ecco 1TCH feedback © 29 ha 1992

12-31] Ros tp tas ir n e tasso stepe R(3) COD) Hok Step 2 R13 Paralled Reedback G2 Reedback sata TGHz Ho Peedback = 1+9272 Paralled Block = anthi Cascade

step 3 Самсоd4 = (- 14 (4) an s+H, Gз 1+12По ко Тъя , тих, Can +h 43 + Cn feed back ПнЗ uter 4 feedback - 42 43-н, саз 1 S2 - hа. 1 + 42 42 + 3 Нs #Слайг 2113 (п. Соз-н, сат |-- Спn Нn - С . 13+ Gg 1 How peadbouk Cascade with an G2 G2 G8th, 93 - П1 Спа Нn + Спо 43 ta + Cng A, B, 1 Again writy feed back Сл a na G, Ching Hy К(0) |-- Спn Ha+( n ts CngН, 13 - Со Cmg - Cnya 1,

Answer 2

Refer to Figure 2.29 in the textbook.

In Figure 2.29, the two blocks are connected in parallel.

Therefore, the resultant is, .

In Figure 2.29, the two blocks are connected in parallel.

Therefore, the resultant is, .

Draw the reduced block diagram.

Figure 1

In Figure 1, the blocks and forms a feedback loop.

Calculate the closed loop transfer function, .

Therefore, the closed loop transfer function, is .