Neural network based adaptive control of piezoelectric actuator with unknown hysteresis

This paper proposes a neural network (NN) based adaptive control of piezoelectric actuator with unknown hysteresis. Based on the classical Duhem model described by a differential equation, we explore the explicit solution to the equation and construct a new hysteretic model with a linear model in series with a piecewise continuous nonlinear function. A NN-based dynamic pre-inversion compensator is designed to cancel the effect of the hysteresis. With the incorporation of-the pre-inversion compensator, an adaptive control scheme is proposed to make the position of the piezoelectric actuator track the desired trajectory. The paper has three distinct features. First, it applies NN to approximate complicate piecewise continuous unknown nonlinear functions in the explicit solution to Dubem model. Second, no off-line training is required for the NN. Third, the stability of overall controlled piezoelectric actuator is guaranteed. Simulation results for a practical system illustrate the validation and effectiveness of the proposed method in this paper.