A hydrobot is under consideration for remote exploration under the ice of Europa, a moon of the

Question:

A hydrobot is under consideration for remote exploration under the ice of Europa, a moon of the giant planet Jupiter. Figure DP4.6(a) shows one artistic version of the mission. The hydrobot is a self-propelled underwater vehicle that would analyze the chemical composition of the water in a search for signs of life. An important aspect of the vehicle is a controlled vertical descent lo depth in the presence of underwater currents. A simplified control feedback system is shown in Figure DP4.6(b). The parameter J > 0 is the pitching moment of inertia.
(a) Suppose that Gc(s) = K. For what range of K is the system stable?
(b) What is the steady-state error to a unit step disturbance when Gc(s) = K?
(c) Suppose that Gc(s) = Kp + KDs. For what range of Kp and KD is the system stable?
(d) What is the steady-slate error to a unit step disturbance when Gc(s) = Kp + KDs?
Figure DP4.6
(a) Europa exploration under the ice.
(b) Feedback system.