GATE EE 2016 Set 2 — Question 60
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Control Systems → Time-Domain Analysis → First & Second-Order Response
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Question
A second-order real system has the following properties:
a) the damping ratio and undamped natural frequency rad/s,
b) the steady state value of the output, to a unit step input, is 1.02.
The transfer function of the system is
a) the damping ratio and undamped natural frequency rad/s,
b) the steady state value of the output, to a unit step input, is 1.02.
The transfer function of the system is
Correct answer
(B) (102)/(s² + 10s + 100)
Solution
The standard form of a second-order transfer function is .
Given:
rad/s
Steady state value for unit step input .
So, the denominator is .
Given , we have .
This matches option (B).
Given:
rad/s
Steady state value for unit step input .
1.Calculate the denominator coefficients:
So, the denominator is .
2.Determine the steady state gain :
For a unit step input, the steady state value is .Given , we have .
3.Form the transfer function:
.This matches option (B).
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