Question

The first two rows in the Routh table for the characteristic equation of a certain closed-loop control system are given as

$\begin{array}{ccc}{s}^3& 1& (2k+3)\\ s^2& 2K& 4\end{array}$

The range of $K$ for which the system is stable is

• A. $-2.0<K<0.5$
• B. $0<K<0.5$
• C. $0<K<\infty$
• D. $0.5<K<\infty$

Answer 1

The correct option is D $0.5<K<\infty$

$\begin{array}{ccc}{s}^3& 1& (2K+3)\\ s^2& 2K& 4\\ s^1& \frac{4K^2+6K-4}{2K}& 0\\ s^0& 4& \end{array}$
For stability,
$K>0$
$4K^2+6K-4>0$
$2K^2+3K-2>0$
$(2K-1)(K+2)>0$
$\Rightarrow K>\frac{1}{2}or,K<-2....\left(ii\right)$
Hence,
$0.5<K<\infty$