Question

For the system shown in figure, $S=-2.75$ lies on the root locus if $K$ is

• A. 0.3

Answer 1

The correct option is A 0.3

The open loop transfer function of the system
$G\left(s\right)H\left(s\right)=\frac{K(s+3)\times 10}{(s+2)}$

In order to lie a point $s=-2.75,$the angle condition must be satisfy and therefore the magnitude condition is
$|G\left(s\right)H\left(s\right){|}_{s=-2.75}=1$

$={\begin{array}{c}\frac{10K\sqrt{s^2+3^2}}{\sqrt{s^2+2^2}}\end{array}|}_{s=-2.75}=1$

$=\frac{10K\sqrt{(3-2.75{)}^2}}{\sqrt{(2-2.75{)}^2}}=1$

$=\frac{0.25\times 10K}{0.75}orK=0.3$