Minimizing Residual Vibration in Short-Maneuver Pulse-Width Control

Two problems encountered in precision manufacturing are friction and flexibility. With regard to friction, pulse-width control has been shown to be exceptionally effective for rigid systems; however, when used to control flexible systems residual vibrations often result, limiting speed and precision. In previous work, a pulse-width controller was developed that uses two pulses in sequence such that the second pulse minimizes vibration induced by the first. This controller used a brute-force numerical process and obtained solutions similar to optimal zero vibration techniques. Additionally, trends in numerical solutions were identified that approached limiting values for short pulse durations. In the present paper, a theoretical foundation for these limiting values is derived. This derivation shows that for short maneuvers approximate analytical expressions for pulse-widths and their application times are easily obtained. These analytical expressions are used as the basis of a pulse-width controller that is shown to effectively minimize residual vibration in simulations and experiments.