Rate-Dependent Hysteresis Modeling and Hybrid Inverse Compensation Control for Piezoelectric Actuators
Abstract
Highlights What are the main findings? A seventh-order, frequency-dependent rising/falling branch model is selected using validation error and endpoint-stability criteria. A direct inverse feedforward path is integrated with disturbance-observer-based adaptive sliding-mode feedback and verified on a laboratory piezoelectric stack platform. What are the implications of the main findings? The direct inverse model strongly reduces hysteresis nonlinearity, while the feedback loop compensates residual model errors, bounded disturbances, and unmodeled dynamics. The hybrid architecture improves tracking beyond feedforward-only compensation while smooth tanh switching and projection adaptation suppress chattering and parameter drift. Abstract Piezoelectric ceramic actuators are widely used in precision positioning and sensor-integrated micro-motion systems, but their accuracy is limited by asymmetric, rate-dependent hysteresis and by residual disturbances that remain after feedforward linearization. This study develops a self-contained modeling and control framework that combines an explicit rising/falling branch polynomial model, frequency-dependent coefficient maps, direct inverse feedforward compensation, and disturbance-observer-based adaptive sliding-mode feedback. The actuator is represented as a multilayer piezoelectric stack coupled to an equivalent electrical-mechanical-sensing plant. A branch-state logic resolves the multivalued inverse mapping, and a numerical order-sensitivity study shows that the seventh-order model provides the lowest validation RMSE while avoiding the endpoint growth observed at higher orders. Laboratory measurements at 1, 5, 10, 20, 50, and 100 Hz, together with attenuated, triangular, random-amplitude, step, and 2 Hz sinusoidal tests, are used for validation. The proposed branch model reduces static maximum relative fitting error from 4.50–6.21% for the classical P-I model to 1.28–2.58%. Direct inverse compensation reduces linearity error from 8.56–13.88% to 0.53–1.024%, and the hybrid controller achieves a 1% settling time of 8.6 ms, a maximum tracking error of 0.0051 micrometers, and an RMSE of 0.0012 micrometers. The results demonstrate an embedded-oriented compromise between model accuracy, online computational simplicity, and robust closed-loop precision.