Question

Consider a closed-loop system shown in Figure(A) below. the root locus for its is shown in Figure (B). the closed loop transfer function for the system is

• A. $\frac{K}{1+(0.5s+1)(10s+1)}$
• B. $\frac{K}{(s+2)(s+0.1)}$
• C. $\frac{K}{1+K(0.5s+1)(10s+1)}$
• D. $\frac{K}{K+0.2(0.5s+1)(10s+1)}$

Answer 1

The correct option is D $\frac{K}{K+0.2(0.5s+1)(10s+1)}$

$G\left(s\right)=\frac{1}{(s+0.1)(s+2)}$
$T.F.=\frac{K.G\left(s\right)}{1+KG\left(s\right)}$
$T.F=\frac{\frac{K}{(s+0.1)(s+2)}}{1+\frac{K}{(s+0.1)(s+2)}}$
$T.F=\frac{K}{(s+0.1)(s+2)+K}$
$T.F=\frac{K}{K+0.2(1+10s)(1+0.5s)}$