Theoretical Basis for Short Maneuver Optimal Pulse-Width Control

Two problems encountered in precision manufacturing are friction and flexibility. With regard to friction, Pulse-Width Control (PWC) has been shown to be exceptionally effective for rigid systems. When used to control flexible systems, however, residual vibrations often result, limiting speed and precision. In a previous related paper, an optimal pulse-width controller was developed that uses two pulses such that the second pulse cancels vibration induced by the first Based on a numerical process minimizing vibration attenuation time, optimal zero vibration (ZV) solutions for the first pulse width, the second pulse width, and the time between pulses were found. Trends in these numerical solutions were also identified that approached limiting values for short maneuvers. In the present paper, a theoretical foundation for these limiting values is derived. This derivation shows that for short maneuvers analytical expressions for pulse widths and timings are easily obtained. These analytical expressions are then used as the basis of an optimal pulse-width controller that is shown to function effectively in both simulation and experiment.