Question

A closed loop system has the characteristic equation given by $s^3+K{s}^2+(K+2)s+3=0$. For this system to be stable, which one of the following conditions should be satisfied?

• A. 0 < K < 0.5
• B. 0.5 < K < 1
• C. 0 < K < 1
• D. K > 1

Answer 1

The correct option is D K > 1

Characteristic equation is,

$s^3+K{s}^2+(K+2)s+3=0$

For this system to be stable, using Routh's criterion, we can write,

$3<K(K+2)$

or $K^2+2K-3>0$

or $(K+3)(K-1)>0$

Here, the valid answer will be out of all the options given.

i,e. $K>1$.