Consider the unit step response of a unity feedback control system whose open loop transfer function is
$G (s) = \frac{1}{s (s + 1)}$
The maximum overshoot is equal to

0.143

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0.153

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0.163

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0.173

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Solution

The correct option is C 0.163
$G (s) = \frac{1}{s (s + 1)}$

$∴ C h a r a c t e r i s t i c e q u a t i o n = 1 + G (s)$

$= s^{2} + s + 1$

On comparing with
$s^{2} + 2 ξ ω_{n} s + ω_{n}^{2}$

$W e h a v e, ξ = 0.5$

$∴ M_{ρ} = e^{⎛ ⎜ ⎝ \frac{- ξ π}{\sqrt{1 - ξ^{2}}} ⎞ ⎟ ⎠} = 0.1630$

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Consider the unit step response of a unity feedback control system whose open loop transfer function is G(s)=1s(s+1) The maximum overshoot is equal to

The correct option is C 0.163G(s)=1s(s+1) ∴ Characteristic equation =1+G(s) =s2+s+1 On comparing with s2+2ξωns+ω2n We have, ξ=0.5 ∴Mρ=e⎛⎜⎝−ξπ√1−ξ2⎞⎟⎠=0.1630

Consider the unit step response of a unity feedback control system whose open loop transfer function is
$G (s) = \frac{1}{s (s + 1)}$
The maximum overshoot is equal to