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GATE 2014
Hard
A step change of magnitude 2 is introduced into a system having the transfer function G(s)=2/(s²+2s+4). The percent overshoot is _____
16.4 %(± 0.4 accepted)
Explanation
Comparing to Kp·ωn²/(s²+2ζωns+ωn²): ωn²=4 ⟹ ωn=2; 2ζωn=2 ⟹ ζ=0.5. Percent overshoot=exp(−ζπ/√(1−ζ²))×100=exp(−0.5π/√0.75)×100=exp(−1.814)×100≈16.3%. (The input magnitude doesn't affect the % overshoot for a linear system.)
Source: GATE CH 2014 (2014)
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