Question

A closed loop system is shown in figure.


Range of K in which system is stable

• A. K > 0
• B. K < 12
• C. K > 12
• D. 0 < K < 12

Answer 1

The correct option is D 0 < K < 12

Characteristic equation of system is,

$1+\frac{K}{s(s+1)(s+3)}=0$

$s^3+4s^2+3s+K=0$

Routh-Hurwitz method,


According to Routh-Hurwitz criteria, for a stable system, first column of Routh array should have positive sign
$\frac{12-K}{4}>0$
and $K<12$

$K>0$

Common range is $0<K<12$