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8.21. Find C/R for Fig. 8-71, using Equation (8.2). G₁ G₁ R H₁ H₂ Fig. 8-71 G₁ G₂

8.21. Find C/R for Fig. 8-71, using Equation (8.2). G₁ G₁ R H₁ H₂ Fig. 8-71 G₁ G₂

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
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Pls answer 8.21
CHAP. 8] SIGNAL FLOW GRAPHS 203 = The signal flow graph is given in Fig. 8-70. We have P₁ = G₁G₂, P₂=G₂G₁3, P₁₁-G₂ H₂, A = 1 + G₂ H₂, A₁ A₂ = 1, and = P₁A₁ + P₂A₂_G₂(G₁ + G₂) 1+ G₂H₂ = = R G₂ 1 R G3 -H₂ Fig. 8-70 Putting G, G₁G₂H₂, we obtain C/R=G₁G₂ and the system transfer function becomes open-loop. 8.20. Determine the elements for a canonical feedback system for the system of Problem 8.10. From Problem 8.10, P₁ = G₁G₂G3, P₂ = G₁, A = 1 + G₂ H₁ − G₁G₂ H₁ + G₂G, H₂, A₁ = 1, and A₂ = A. From Equation (8.3) we have 2 GP,A,G,G₂G₁ + G₁ + G₂G₂ H₁ - G₁G₂G₁H₁ +G₂G₂G4H₂ i-1 and from Equation (8.4) we obtain A-1 G₂H₁G₁G₂H₂ +G₂GH₂ H = G G₁G₂G3 + G₁+G₂G4 H₁ - G₁G₂G4 H₁ + G₂G₂G₁ H₂ Supplementary Problems 8.21. Find C/R for Fig. 8-71, using Equation (8.2). G₂ G₁ G₁ G₂ R C Fig. 8-71 8.22. Determine a set of canonical feedback system transfer functions for the preceding problem, using Equations (8.3) and (8.4). + G₁ H₂ H₂
Transcribed Image Text:CHAP. 8] SIGNAL FLOW GRAPHS 203 = The signal flow graph is given in Fig. 8-70. We have P₁ = G₁G₂, P₂=G₂G₁3, P₁₁-G₂ H₂, A = 1 + G₂ H₂, A₁ A₂ = 1, and = P₁A₁ + P₂A₂_G₂(G₁ + G₂) 1+ G₂H₂ = = R G₂ 1 R G3 -H₂ Fig. 8-70 Putting G, G₁G₂H₂, we obtain C/R=G₁G₂ and the system transfer function becomes open-loop. 8.20. Determine the elements for a canonical feedback system for the system of Problem 8.10. From Problem 8.10, P₁ = G₁G₂G3, P₂ = G₁, A = 1 + G₂ H₁ − G₁G₂ H₁ + G₂G, H₂, A₁ = 1, and A₂ = A. From Equation (8.3) we have 2 GP,A,G,G₂G₁ + G₁ + G₂G₂ H₁ - G₁G₂G₁H₁ +G₂G₂G4H₂ i-1 and from Equation (8.4) we obtain A-1 G₂H₁G₁G₂H₂ +G₂GH₂ H = G G₁G₂G3 + G₁+G₂G4 H₁ - G₁G₂G4 H₁ + G₂G₂G₁ H₂ Supplementary Problems 8.21. Find C/R for Fig. 8-71, using Equation (8.2). G₂ G₁ G₁ G₂ R C Fig. 8-71 8.22. Determine a set of canonical feedback system transfer functions for the preceding problem, using Equations (8.3) and (8.4). + G₁ H₂ H₂
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