A New Hysteresis Model for Piezoelectric Actuators With Application to Precision Trajectory Control

Piezoelectric actuators with their sub-nanometer resolution and fast frequency response are becoming increasingly important in today’s micro-and nano-positioning technology. Along this line, this paper undertakes the development of a nonlinear modeling, system identification and control framework for piezoelectric actuators used in such positioning systems. More specifically, a general nonlinear modeling framework for a single piezoelectric actuator combined with a novel method for describing its hysteretic nonlinearity is proposed. For the actuator generated force, a polynomial form of the nonlinearity is assumed, and the time-varying history-dependent parameters of this polynomial are identified through the observed hysteretic characteristics of the actuator. Experimental results demonstrates the validity of the proposed the modeling and identification framework for an in-house high resolution piezoelectric-based stager with capacitive position sensor. Utilizing Lyapunov method and the sliding mode control strategy, the control force acting on the actuator is then designed such that the high frequency tracking control and the asymptotic stability of the system are attained. Simulation results indicate that controller suppresses the high frequency tracking error significantly, noticeably improving the tracking performance.