GATE EE 2021 Set 1 — Question 56
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Control Systems → Time-Domain Analysis → First & Second-Order Response
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Question
Consider a closed-loop system as shown. is the plant transfer function and is the compensator. For a unit-step input, the output response has damped oscillations. The damped natural frequency is __________ rad/s. (Round off to 2 decimal places.)
Correct answer
10.8 to 11
Solution
The characteristic equation of the closed-loop system is given by .
Given and , we have:Comparing with the standard second-order characteristic equation :
rad/s
The damped natural frequency is given by:
Given and , we have:Comparing with the standard second-order characteristic equation :
rad/s
The damped natural frequency is given by:
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