Question

The forward transfer function of a unity feedback system is
$G\left(s\right)=\frac{K(s^2+1)}{(s+1)(s+2)}.$

The system is stable for

• A. K < - 1
• B. K > - 1
• C. K < - 2
• D. K > - 1

Answer 1

The correct option is B K > - 1

Close loop transfer function of the system is
$T\left(s\right)=\frac{G\left(s\right)}{1+G\left(s\right)}=\frac{K(s^2+1)}{(K+1)s^2+3s+K+2}$

$\therefore$ the characteristic equation is given by
$(K+1)s^2+3s+K+2=0$
For the system to be stable all the coefficient should be of same sign

$\therefore K+1>0=K>-1$
$andK+2>0=K>-2$

$\therefore$ The system is stable for K > - 1.