GATE Electrical Engineering (EE) 2020 Solved Paper

Question : 14 of 65

Marks: +1, -0

Consider a negative unity feedback system with forward path transfer function

G(s)=\;{K}/{(s+a)(s-b)(s+c)}

, where

K, a, b, c

are positive real numbers. For a Nyquist path enclosing the entire imaginary axis and right half of the s-plane in the clockwise direction, the Nyquist plot of

(1+G(s))

, encircles the origin of

(1+G(s))

-plane once in the clockwise direction and never passes through this origin for a certain value of

{K}

. Then, the number of poles of

\;{G(s)}/{1+G(s)}

lying in the open right half of the s-plane is

Your Answer:

Validate

Solution:

G(s)=\;{k}/{(s+a)(s-b)(s+c)}

No. of open loop poles in right half of s plane

P=1

Nyquist plot encircles the origin of

(1+ {G}( {s}))

plane once in clockwise direction

N=-1

We know that

N=P-Z

Z=P-N

=1-(-1)=2

No. of closed loop polos

Z=2

No. of closed loop poles lying in the right half of s plane

=2

Go to Question:

Prev Question

Next Question