Problem $2$ Let H be a plant with transfer function

H$($s$)=$ A

s$2+$ a$0$

$.$

Next, consider series compensation of the plant with

G$($s$)=$ Kds$2+$ Kps $+$ Ki

s $,$

i$.$e$.,$ a PID compensator.

$1.$ Determine the pole$-$placement equations, that is$,$ given denominator coefficients for the

closed loop transfer function, what are the compensator gains required?

$2.$ What happens to the pole$-$placement equations if the plant is third order?