GATE EC 2019 Set 1 — Question 42
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Control Systems → System Modelling → Block Diagram Reduction
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Question
The block diagram of a system is illustrated in the figure shown, where is the input and is the output. The transfer function is

Correct answer
(B) H(s) = (s²+1)/(s³+2s²+s+1)
Solution
Let be the signal after the first summing junction. From the block diagram, we can write the following equations:
1.The output of the second summing junction is .
2.The output of the system is .
3.The first summing junction has two feedback paths, one from and one from , both with negative feedback. Thus, .
Substituting the expressions for and in terms of :Now, substitute back into the expression for :The transfer function is .This corresponds to option (B).Continue learning with Success Tracker
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