Solution bi 62 1/s ½ Vs 9. -a₂ Y(s) = X(s) ΣΡΟΚ Δ 199 Forward Paths P₁ = b Loops L = -91 S Y(s) b2 P₁₂ = bi P3- 52 S3 ; L3= 53 -92 52. X(s) PA, PA + P3D3 - { sum of Lep} + { two non touching Loops DK= Y(s) = X(S) 1- { sum of non-touching Loop. Gains by +b₂ (5, +b₁ (55)) (s² + αis² +α₂s + α3) /53 bs² + b₂s +b3 S³ +9₁s² + a₂s +93 Y(s) = X(s)

Introductory Circuit Analysis (13th Edition)
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ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
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Modern Control Engineering, Volume 4, Chapter 3. I would like to know the details of the method for the origin of the equation in the red circle. Thank you in advance for your answer.
Solution
bi
62
1/s
½
Vs
9.
-a₂
Y(s) =
X(s)
ΣΡΟΚ
Δ
199
Forward Paths P₁ = b
Loops L =
-91
S
Y(s)
b2
P₁₂ = bi
P3-
52
S3
;
L3= 53
-92
52.
X(s)
PA, PA + P3D3
-
{ sum of Lep} + {
two non
touching
Loops
DK=
Y(s)
=
X(S)
1-
{
sum of non-touching Loop.
Gains
by +b₂ (5, +b₁ (55))
(s² + αis² +α₂s + α3) /53
bs² + b₂s +b3
S³ +9₁s² + a₂s +93
Y(s)
=
X(s)
Transcribed Image Text:Solution bi 62 1/s ½ Vs 9. -a₂ Y(s) = X(s) ΣΡΟΚ Δ 199 Forward Paths P₁ = b Loops L = -91 S Y(s) b2 P₁₂ = bi P3- 52 S3 ; L3= 53 -92 52. X(s) PA, PA + P3D3 - { sum of Lep} + { two non touching Loops DK= Y(s) = X(S) 1- { sum of non-touching Loop. Gains by +b₂ (5, +b₁ (55)) (s² + αis² +α₂s + α3) /53 bs² + b₂s +b3 S³ +9₁s² + a₂s +93 Y(s) = X(s)
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