GATE EC 2016 Set 2 — Question 55
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Control Systems → Time-Domain Analysis → First & Second-Order Response
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Question
In the feedback system shown below .
The step response of the closed-loop system should have minimum settling time and have no overshoot.The required value of gain to achieve this is ________
Correct answer
0.95 to 1.05
Solution
To find the required gain , we first determine the closed-loop transfer function :The characteristic equation is . Comparing this with the standard second-order characteristic equation , we get:
1.
2.
For the system to have no overshoot, the damping ratio must satisfy :For minimum settling time without overshoot, we need the system to be as fast as possible while remaining non-oscillatory. For , the poles are real and located at . The dominant pole is . To minimize settling time, we want this dominant pole to be as far to the left as possible, which occurs when is minimized. This happens at .At , the system is critically damped (), which provides the fastest response without any overshoot. Therefore, .Continue learning with Success Tracker
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