GATE EC 2015 Set 2 — Question 30
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Control Systems → System Modelling → Signal Flow & Mason's Gain
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Question
For the signal flow graph shown in the figure, the value of is

Correct answer
(B) (G₁ G₂ G₃ G₄)/(1 + G₁ G₂ H₁ + G₃ G₄ H₂ + G₂ G₃ H₃ + G₁ G₂ G₃ G₄ H₁ H₂)
Solution
To find the transfer function , we use Mason's Gain Formula:
Loops and do not share any common nodes. Their product is:
All other pairs of loops touch each other.
1.Forward Path:
There is only one forward path from to :2.Individual Loops:
- : with gain
- : with gain
- : with gain
Loops and do not share any common nodes. Their product is:
All other pairs of loops touch each other.
4.Calculate :
5.Calculate :
Since the forward path touches all loops, .6.Transfer Function:
This corresponds to option (B).Continue learning with Success Tracker
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