A spacecraft with a camera is shown in Figure $($a$).$ The camera slews about $16$ in a canted plane relative to the base. Reaction jets stabilize the base against the reaction torques from the slewing motors. Suppose that the rotational speed control for the camera slewing has a plant transfer function

$G(s)=\frac{1}{(s+1)(s+2)(s+4)}$

A proportional plus derivative controller is used in a system as shown in Figure $($b$)$ where

$G_c(s)=K_p+K_{D}s,$

and where $K_p>0$ and $K_D>0.$ Obtain and plot the relationship between $K_p$ and $K_D$ that results in a stable closed$-$loop system.

$($a$)$

Figure: $($a$)$ Spacecraft with camera; $($b$)$ control system with feedback.