GATE Electrical Engineering (EE) 2020 Solved Paper

Question : 64 of 65

Marks: +1, -0

Consider a negative unity feedback system with the forward path transfer function

\;{s^{2}+s+1}/{s^{3}+2 s^{2}+2 s+k}

, where

K

is a positive real number. The value of

K

for which the system will have some of its poles on the imaginary axis is

Solution:

Closed loop characteristic equation

1+G(s) H(s)=0

1+\;{5^{2}+5+1}/{5^{3}+25^{2}+25+k} × 1=0

5^{3}+35^{2}+35+k+1=0

Routh array

\table 5^3;5^2;5;5^0|\table1,3;3,k+1;{8-k}/3,0;k+1,0

For poles on

{j} ω

\;{8-k}/{3}=0 ⇒ k=8

Value of

K=8

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