GATE 2017 EE (EE2) – Question 46

Control Systems · Transient and Steady-state analysis of linear time invariant systems · 2 marks · Multiple choice

Which transfer function gives the greatest unit-step peak overshoot?

$100/(s^2+10s+100)$
$100/(s^2+15s+100)$
$100/(s^2+5s+100)$
$100/(s^2+20s+100)$

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Correct answer: (C) $100/(s^2+5s+100)$

Explanation

All have natural frequency ωn=10 rad/s. Compare the s coefficient with 2ζωn: their damping ratios are 0.5,0.75,0.25 and 1.

For an underdamped second-order system, $M_p=e^{-\pi\zeta/\sqrt{1-\zeta^2}}$, which decreases as ζ increases. The smallest damping ratio is 0.25, giving the largest overshoot. Hence **C**.

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