$($Please show work and circle$/$box final answers$)$

$(\backslash$phi $($s$))/(\backslash$delta $\_($a$)($s$))=(1)/($s$($s$-2))$

where $\backslash$phi is the roll angle and $\backslash$delta $\_($a$)$ is the aileron deflection.

a$(\backslash$phi $($s$))/(\backslash$delta $\_($a$)($s$)).$Based on the open$-$loop pole locations, determine whether the open$-$loop aircraft

system is stable or not. Clearly explain why or why not.

b$(\backslash$phi $($s$))/(\backslash$delta $\_($a$)($s$))$ as the plant

transfer function G$\_($p$)($s$),$ design a closed$-$loop control system as shown in the following

block diagram:

In the given block diagram, the controller is a Proportional$-$Derivative $($PD$)$ controller of

the form: G$\_($c$)($s$)=$K$\_($p$)+$K$\_($d$)$s$,$ where K$\_($p$)$ is the proportional gain and K$\_($d$)$ is the derivative

gain. Determine the controller gains K$\_($p$)$ and K$\_($d$)$ such that the closed$-$loop system poles are

located at s$\_(1)=-3$ and s$\_(1)=-4.$