Advanced hysteresis compensation and adaptive control for piezoelectric actuators in micro-nano systems

This paper addresses the challenge of hysteresis nonlinearity in piezoelectric actuators, which critically limits their precision in micro-nano positioning systems. While these actuators are valued for their fast response and high precision, their performance is compromised by inherent hysteresis, particularly under dynamic conditions where rate-dependent and asymmetric behaviors are prominent. To overcome this limitation, we propose an advanced composite control strategy that combines feedforward compensation with adaptive feedback control. The core of our approach is a novel rate-dependent generalized Prandtl-Ishlinskii (RD-GPI) model, which accurately captures complex hysteresis behaviors through the incorporation of dynamic thresholds and dead-zone operators. An analytical inverse model, derived from the RD-GPI framework and combined with adaptive control strategies, provides effective feedforward compensation to suppress hysteresis effects. The algorithm requires tuning solely the differential gain, significantly reducing adjustable parameters. System stability is rigorously validated via the Lyapunov method. Experimental results confirm the composite approach’s efficacy, demonstrating superior dynamic control accuracy and offering a robust, generalizable framework for hysteresis compensation in precision optical and nanotechnology applications.