Question

The forward path transfer function of a unity negative feedback system is given by $G\left(s\right)=\frac{K}{(s+2)(s-1)}$
The value of $K$ which will place both the poles of the closed-loop system at the same location is

• A. 2.25

Answer 1

The correct option is A 2.25

Given that, $G\left(s\right)=\frac{K}{(s+2)(s-1)}$

Using root locus method, the break point can be obtain as

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

$\Rightarrow 1+\frac{K}{(s+2)(s-1)}=0$

$orK=-(s+2)(s-1)$

$\Rightarrow \frac{dK}{ds}=-2s-1=0$

$ors=-0.5$

To have, both the poles at the same directions

$|G\left(s\right){|}_{s=0.5}=1$

$K=2.25$