P10.18 NASA is developing remote manipulators that can be used to extend the hand and the power of hu

mankind through space by means of radio. A concept of a remote manipulator is shown in Figure P10.18(a)

[11, 22]. The closed-loop control is shown schemati

cally in Figure P10.18(b). Assuming an average dis

tance of 238,855 miles from Earth to the Moon, the time delay T in transmission of a communication sig

nal is 1.28 s. The operator uses a control stick to con

trol remotely the manipulator placed on the Moon to assist in geological experiments, and the TV display to access the response of the manipulator. The time constant of the manipulator is 1 4 second.

(a) Set the gain K1 so that the system has a phase margin of P M. . = 30°. Evaluate the percentage steady-state error for this system for a step input. (b)

To reduce the steady-state error for a position com

mand input to 5%, add a lag compensation network in cascade with K1. Plot the step response.