Dynamic compensation and H∞H∞ control for piezoelectric actuators based on the inverse Bouc–Wen model

• We propose a rate-dependent inverse-Bouc–Wen model to compensate the trajectory error.
• The proposed open loop rate-dependent inverse-Bouc–Wen compensator model has enhanced the performance of the PZT.
• The proposed compensator can be widely applied in all kinds of situations with rate-dependent hysteresis problems.

Piezoelectric actuator, which is widely used in micro-/nano-manipulation, often demonstrates nonlinear rate-dependent hysteresis characteristics. This paper proposes a Bouc–Wen model based inverse hysteresis compensator for rate-dependent hysteresis in PZT. The classical Bouc–Wen model for hysteresis is introduced firstly, then the identification of the parameters through the particle swarm optimization (PSO) method is conducted. A novel modified inverse Bouc–Wen model is proposed and verified through experiment. The proposed modified inverse Bouc–Wen model with a parametric selector constructs a real-time online rate-dependent compensator for handling PZT's hysteresis. During experiments of tracking multi-frequency composed of signals, the rate-dependent hysteresis of the PZT can be consistently compensated. The experimental results show that the proposed open loop hysteresis canceling method greatly improves the PZT's tracking control accuracy.