GATE EE 2022 Set 1 — Question 39
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Control Systems → System Modelling → Block Diagram Reduction
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Question
The damping ratio and undamped natural frequency of a closed loop system as shown in the figure, are denoted as and , respectively. The values of and are
Correct answer
(A) = 0.5 and ωₙ = 10 rad/s
Solution
Let's find the closed-loop transfer function .
1.The inner loop has a forward path of and a unity negative feedback. Its transfer function is .
2.The overall forward path is .
3.The system has unity negative feedback, so .
4.Comparing with the standard second-order form :
- rad/s.
- .
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