Rate-Dependent Hysteresis Modeling and Hybrid Inverse Compensation Control for Piezoelectric Actuators

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.