GATE EC 2019 Set 1 — Question 41
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Control Systems → Time-Domain Analysis → First & Second-Order Response
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Question
Consider a causal second-order system with the transfer function with a unit-step as an input. Let be the corresponding output. The time taken by the system output to reach 94% of its steady-state value , rounded off to two decimal places, is
Correct answer
(B) 4.50
Solution
The transfer function is . For a unit-step input , the output is:Using partial fraction expansion:Taking the inverse Laplace transform:The steady-state value is . We need to find such that :Solving for by trial or numerical methods:
For , .
For , .
Thus, is the closest option.
For , .
For , .
Thus, is the closest option.
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