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Question

# Loop transfer function of a feedback system is G(s)H(s)=s+3s2(sâˆ’3). Take the Nyquist contour in the clockwise direction. Then, the Nyquist plot of G(s)H(s) encircles -1+j0

A
once in clockwise direction
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B
twice in colckwise direction
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C
once in anticlockwise direction
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D
twice in anticlockwise direction
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Solution

## The correct option is A once in clockwise direction Nyquist plot of G(s)H(s)=s+3s2(s−3) is as shown below: From the Nyquist plot G(s) H(s) encircle -1+j0 once in clockwise direction. Atlernate solution: Characteristic equation, 1+G(s) H(s)=0 s2(s−3)+(s+3)=0 s3−3s2+s+3=0 using Routh's array, s3s2s1s0∣∣ ∣ ∣ ∣∣11−33203 There are two sign changes, hence two poles in right half of s-plane exist. Z=2,P=1 N=P−Z=−1 One encirclement in clockwise direction.

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