GATE EE 2014 Set 3 — Question 27
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Control Systems → System Modelling → Signal Flow & Mason's Gain
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Question
The signal flow graph of a system is shown below. is the input and is the output.
Assuming, and , the input-output transfer function, of the system is given by
Assuming, and , the input-output transfer function, of the system is given by
Correct answer
(C) G(s) = (b₁ s + b₀)/(s² + a₁ s + a₀)
Solution
Using Mason's Gain Formula:
Substituting and :
Note: Based on standard SFG structures for canonical forms in control systems, the intended answer for this topology is typically (C).
1.Forward Paths:
- (Path through to the node after the first integrator)
- (Path through and both integrators)
- (Path 1 touches all loops)
- (Path 2 touches all loops)
Substituting and :
Note: Based on standard SFG structures for canonical forms in control systems, the intended answer for this topology is typically (C).
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