GATE EC 2016 Set 1 — Question 56
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Control Systems → Time-Domain Analysis → First & Second-Order Response
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Question
The open-loop transfer function of a unity-feedback control system is given byFor the peak overshoot of the closed-loop system to a unit step input to be 10%, the value of is
Correct answer
2.7 to 3
Solution
For a unity feedback system with open-loop transfer function , the closed-loop transfer function is:Comparing this with the standard second-order characteristic equation :
1.
2.
The peak overshoot is given as 10% or 0.1. The formula for peak overshoot is:Taking the natural logarithm on both sides:Squaring both sides:Now, substitute :Thus, the value of is approximately 2.86, which falls within the official range of 2.7 to 3.0.Continue learning with Success Tracker
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