Precise trajectory tracking control of elastic joint manipulators

A flexible control system consisting of a dc servomotor, harmonic drive, flexible shaft, and manipulator arm is considered. The transfer function of the system relating the manipulator arm angle to the desired trajectory angle is derived, including natural frequencies and material damping of the flexible system, as well as proportional integral derivative gains of the control system. It is shown that the dominant roots of the transfer function, which characterize the response of the flexible system, are totally different from that of a rigid system. Material damping is not very effective on the system response. The flexible system is more sensitive to the derivative gain than to the integral gain. For the chosen particular type of trajectory, which is cycloid, the settling time of the system can be related to the rise time of the cycloid, and precise trajectory tracking can be obtained.