GATE EE 2026 Set 1 — Question 13
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Control Systems → Time-Domain Analysis → First & Second-Order Response
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Question
The Laplace transform of the step response of a system is given by The rise time is defined as the time taken for the response to go from 0.1 to 0.9 of its final value. The settling time is defined as the time taken for the response to reach 0.98 of its final value.For this system, the rise time (), settling time (), and time constant (), all expressed in seconds, are
Correct answer
(A) Tᵣ = 0.022, Tₛ = 0.04, T_c = 0.01
Solution
Given the step response .
The transfer function is obtained by dividing the step response by the input :
.
This is a first-order system with time constant s.
The time-domain response is .
The final value is .
s.
Thus, .
The transfer function is obtained by dividing the step response by the input :
.
This is a first-order system with time constant s.
The time-domain response is .
The final value is .
1.Rise time ():
s.
2.Settling time ():
s. Thus, .
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