A spacecraft with a camera is shown in Figure AP6.6(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) = 1 / (s + 1)(s + 2)(s + 4).
A proportional plus derivative controller is used in a system as shown in Figure AP6.6(b), where
Gc(s) = KP + KDs,
and where KP > 0 and KD > 0. Obtain and plot the relationship between KP and KD that results in a stable closed-loop system.
Figure AP6.6
(a) Spacecraft with a camera.
(b) Feedback control system.

Camera Solar panel Boom Tats) Controller Plant Es) R(s)