Question

The number of open right half plane poles of $G\left(s\right)=\frac{10}{s^5+2s^4+3s^3+6s^2+5s+3}$ is

• A. $0$
• B. $1$
• C. $2$
• D. $3$

Answer 1

The correct option is C $2$

Characteristic equation
$q\left(s\right)=s^5+2s^4+3s^3+6s^2+5s+3$
$Puttings=\frac{1}{z}$
$q^{\prime }\left(z\right)=3z^5+5z^4+6z^3+3z^2+2z+1$

Routh array is
$\begin{array}{cccc}{z}^5& 3& 6& 2\\ z^4& 5& 3& 1\\ z^3& 21/5& 7/5& \\ z^2& \frac{\frac{63}{5}-\frac{35}{5}}{21}=\frac{4}{3}& 1& \\ z^1& \frac{\frac{28}{15}-\frac{21}{5}}{4/3}=\frac{-35/15}{4/3}=\frac{-7}{4}& & \\ z^0& 1& & \end{array}$

Since sign changes twice in Routh-array, therefore, there are two poles on right half plane.