Design of a waveform tracking system for a piezoelectric actuator

Abstract

In this work an adaptive model-based predictive control (AMPC) is designed for high-frequency waveform tracking by a PZT bimorph actuator in industrial vibratory feeding. Since the actuator has a narrow bandwidth and significant dynamic hysteresis, the waveform tracking process contains both linear and non-linear errors and the coupling effect between these two needs to be considered before effective compensation can be implemented to obtain a precise vibration trajectory. In the adaptive control, two parallel loops were employed, a linear compensation loop and a non-linear offset loop, to suppress the hybrid errors and let the error eventually converge to an acceptable level by iteration. Since the system varies much more slowly than the control loops, a quasi-time invariant system is assumed in the modelling process and a single-layer neural network is used to compensate the system floating adaptively. Due to the fact that in this application the smoothness of the actuator motion waveform is of critical importance to ensure the mechanical force configuration required in industrial application, each driving waveform must be adapted as a whole, not as a series of discrete input points. Therefore instead of applying a set-point tracking method, a self-tuning process is used in the predictive filter design of the current cycle, and corresponding control is delayed to waveform generation of the next cycle. The control algorithm is then implemented into experiment for vibratory feeding and the result shows satisfactory hysteresis suppression and good waveform tracking.