Optimal pulse-width control of flexible dynamic systems

Abstract

Two of the major problems encountered in precisely positioning the end-effectors of robotic systems are friction and flexibility. With regard to friction, PulseWidth Control (PWC) has been shown to be exceptionally effective for rigid systems. When used to control flexible systems, however, residual vibrations often result, limiting the speed and precision with which an endeffector reaches the desired final position. As an alternative, input shaping provides a technique for timing and sequencing pulses to reduce residual vibration but is typically limited by the minimum possible move distance. By combining features of both PWC and input shaping, an optimal pulse-width controller is developed here that uses two pulses separated in time such that the second pulse cancels vibration induced by the first. The overall distance the system moves and the amplitude of residual vibration are dependent on three parameters: the first pulse width, the second pulse width, and the separation time. Based on minimizing vibration attenuation time, optimal zero vibration (ZV) solutions for these three parameters are found. These solutions provide relationships between position error, pulse widths, and separation time, and are the essence of the optimal pulsewidth controller of this paper. Evaluations of the performance of the controller are done both in simulation and experimentally.