Question

Consider the statndard negative feedback configuration with
$G\left(s\right)=\frac{s^2+0.2s+100}{s^2-0.2s+100}andH\left(s\right)=\frac{1}{2}.$
The number of clockwise encirclements of (-1, 0) in the Nyquist plot of the Loop transfer-function G(s) H(s) is

• A. 0

Answer 1

The correct option is A 0
$G\left(s\right)=\frac{s^2+0.2s+100}{s^2-0.2s+100},H\left(s\right)=\frac{1}{2}$

$q\left(s\right)=1+G\left(s\right)H\left(s\right)=0$

$=3s^2-0.2s+300=0$

This system is unstable with two roots in right side of S-plane.

$\therefore P-N=2$
$P=2$ is OLTF has two poles in right side of s-plane.
$\therefore$ $N=0$

Or,
Nyquiest plot:


$\because (-1,0)$ lies outside the circle,
$\therefore$ $N=0$