The open loop transfer function of a unity feedback system is given by {G}( {s})= {\pi {e}^{-0.25 s}}/{ {s}}. In {G}( {s}) plane, the Nyquist plot of {G}( {s}) passes through the negative real axis at the point

Correct Answer is : (−0.5,j0)

GATE Electrical Engineering (EE) 2019 Solved Paper

Question : 21 of 65

Marks: +1, -0

The open loop transfer function of a unity feedback system is given by

{G}( {s})=\;{π {e}^{-0.25 s}}/{ {s}}

. In

{G}( {s})

plane, the Nyquist plot of

{G}( {s})

passes through the negative real axis at the point

Solution:

Given data:

{G}( {s})=\;{π {e}^{-0.25 {s}}}/{ {s}}

ω_{ {pc}} ⇒ ∠ {G}( {j} ω)=-180^{∘}

-180^{∘}=+90^{∘}+0.25 ω × \;{180^{∘}}/{π}

90^{∘}=\;{45^{∘} ω}/{π} ⇒ ω_{ {pc}}=2 π {r} {/} {sec}

\;\text " Magnitude "\;=\;{π}/{ω_{p c}}=\;{π}/{2 π}=0.5

Inter section point with negative real axis

⇒(-0.5, {j} 0)

Go to Question:

Prev Question

Next Question