GATE EC 2016 Set 2 — Question 29
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Control Systems → Differential Equations → Laplace Transforms & Applications
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Question
The response of the system to the unit step input is . The value of at is _________
Correct answer
0.96 to 1.04
Solution
Given the transfer function of the system is .
The input is a unit step , so its Laplace transform is .
The output in the s-domain is given by:
We need to find the value of the derivative of the output at , i.e., .
Let . The Laplace transform of is:
Assuming the system is initially at rest (zero initial conditions), . Thus:
According to the Initial Value Theorem:
Dividing numerator and denominator by :
Therefore, the value of at is 1.
The input is a unit step , so its Laplace transform is .
The output in the s-domain is given by:
We need to find the value of the derivative of the output at , i.e., .
Let . The Laplace transform of is:
Assuming the system is initially at rest (zero initial conditions), . Thus:
According to the Initial Value Theorem:
Dividing numerator and denominator by :
Therefore, the value of at is 1.
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