Consider a unity$-$feedback system with the following transfer function for the plant and

controller:

G$($s$)=$ K

s$2.$

The closed$-$loop system needs to be designed to have a settling time of $1\mathrm{.}667$ s and $16\mathrm{.}3\%$

overshoot. Design a controller that utilizes a lead compensator with the compensator zero

placed at $-1.$ Determine the location of the desired poles, the location of the compensator

pole, and the controller proportional gain.

$2$