NMPC-Based Trajectory Tracking Control of a Piezoelectric Ceramic Actuator Using the Bouc–Wen Model

Abstract

Piezoelectric ceramic actuators provide high-resolution motion but exhibit path-dependent hysteresis and mechanical dynamics that degrade trajectory tracking, particularly under time-varying commands. This paper develops a nonlinear model predictive control (NMPC) method based on a standard Bouc-Wen hysteresis model coupled with second-order actuator dynamics. The voltage rate is selected as the manipulated variable and the actual driving voltage is retained as a system state, allowing voltage-magnitude and voltage-rate constraints to be handled within a unified optimization problem without introducing a separate inverse hysteresis compensator. The objective penalizes displacement tracking error, output velocity, voltage rate, and voltage-rate variation to balance accuracy and control smoothness. Model parameters are initialized from experimental input-output data by least squares and subsequently refined within a limited range. Simulations under step, sinusoidal, and triangular references compare NMPC with proportional-integral-derivative (PID) and sliding mode control (SMC) under identical conditions. Both nonlinear controllers outperform PID. Relative to SMC, NMPC reduces RMSE by 81.03%, 84.06%, and 82.99% for the three trajectories, respectively, and achieves the lowest RMSE and MAE in every case. A computation-time assessment is also reported to clarify the present implementation scope.