Question

A system described by the transfer function $H\left(s\right)=\frac{1}{s^3+\alpha s^2+Ks+3}$ is stable.
The constraints on $\alpha$ and $K$ are

• A. $\alpha >0,\alpha K<3$
• B. $\alpha >0,\alpha K>3$
• C. $\alpha <0,\alpha K>3$
• D. $\alpha <0,\alpha K<3$

Answer 1

The correct option is B $\alpha >0,\alpha K>3$

The characteristic equation is,
$s^3+\alpha s^1+Ks+3=0$
Routh table is
$\begin{array}{ccc}{s}^3& 1& K\\ s^2& \alpha & 3\\ s^1& \frac{\alpha K-3}{\alpha }& 0\\ s^0& 3& 0\end{array}$
For system to be stable
$\alpha >0,\frac{\alpha K-3}{\alpha }>0$
$\alpha K>3$