Question

Consider open loop transfer function of unity negative feedback system as $G\left(s\right)=\frac{K(s^2+16)}{s(s+4)}$breakaway point is /are :

• A. -9.65
• B. -1.66
• C. -166 : -9.65
• D. 9.65

Answer 1

The correct option is B -1.66

Characteristics equation of this system is
$1+G\left(s\right)H\left(s\right)=0$

$1+\frac{K(s^2+16)}{s(s+4)}=0$

Breakaway points can be calculated as

$k=\frac{-s(s+4)}{s^2+16}$

Differentiating above equation with respect to 's'

$\frac{dK}{dS}=\frac{(s^2+16)(-2s-4)+(s^2+4s)\left(2s\right)}{(s^2+16{)}^2}$

$Putting\frac{dK}{dS}=0$

$Weget(s^2+16)(2s+4)=(s^2+4s)\left(2s\right)$

$\Rightarrow s^2+Bs-16=0$

Solving above equation we get

$S_1,S_2=1.66,9.65$



As the point S = -1.66 lies on root locus, therefore this is valid breakaway point