The open loop transfer function of a unity feedback system is given by Gs - 3e-2sss-2The gain and phase crossover frequencies in rad-sec are- respectively

Gain cross frequency where gain is 1. |G(s)| = 1 nbsp; ⇒3ω (ω ^2+4)^1/2=1 ⇒9ω ^2(ω ^2+4)=1 ⇒ω _gc = 1.26 Phase cross over frequency, where ∠ GH = 180^∘ ⇒ω _pc ...

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The open loop transfer function of a unity feedback system is given by $G (s) = \frac{3 e^{- 2 s}}{s (s + 2)}$
The gain and phase crossover frequencies in rad/sec are, respectively

0.632 a n d 1.26

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0.632 a n d 0.485

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0.485 a n d 0.632

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1.26 a n d 0.632

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Solution

The correct option is D $1.26 a n d 0.632$
Gain cross frequency where gain is $1.$
$| G (s) | = 1$
$\Rightarrow \frac{3}{ω (ω^{2} + 4)^{1 / 2}} = 1$ $\Rightarrow \frac{9}{ω^{2} (ω^{2} + 4)} = 1$ $\Rightarrow ω_{g c} = 1.26$
Phase cross over frequency, where
$∠ G H = - 180^{\circ}$
$\Rightarrow ω_{p c} = 0.632 (\frac{ω_{ϕ}}{2} = cot 2 ω ϕ)$

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The open loop transfer function of a unity feedback system is given by G(s)=3e−2ss(s+2) The gain and phase crossover frequencies in rad/sec are, respectively

The correct option is D 1.26 and 0.632Gain cross frequency where gain is 1. |G(s)|=1 ⇒3ω(ω2+4)1/2=1 ⇒9ω2(ω2+4)=1 ⇒ωgc=1.26 Phase cross over frequency, where ∠GH=−180∘ ⇒ωpc=0.632(ωϕ2=cot2ωϕ)

The open loop transfer function of a unity feedback system is given by $G (s) = \frac{3 e^{- 2 s}}{s (s + 2)}$
The gain and phase crossover frequencies in rad/sec are, respectively