NASA is developing remote manipulators that can be used to extend the hand and the power of humankind through space by means of radio. A concept of a remote manipulator is shown. The closed-loop control is shown schematically. Assuming an average distance of 238,855 miles from Earth to the Moon, the time delay T in transmission of a communication signal is 1.28 seconds. The operator uses a control stick to control 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 approximately 30°. Evaluate the percentage steady-state error for this system for a step input.
(b) To reduce the steady-state error for a position command input to 5%, add a lag compensation network in cascade with K\. Plot the step response.