Question

Consider a unity feedback system, as in the figure shown, with an integral compensator $\frac{K}{s}$ and open-loop transfer function
$G\left(s\right)=\frac{1}{s^2+3s+2}$
where $K>0$ . The positive value of $K$ for which there are exactly two poles of the unity feedback system on the $j\omega$ is equal to (rounded off to two decimal places)

• A. 6

Answer 1

The correct option is A 6

$\frac{Y\left(s\right)}{X\left(s\right)}=\frac{K}{s^3+3s^2+2s+K}$

Two poles of this system lie on the $j\omega$ axis when the system is marginally stable.

$k_{mar}=3\times 2=6$