Random Forest-Enhanced Madelung Model for High-Precision Hysteresis Characterization in Piezoelectric Actuators

Piezoelectric actuators are widely utilized in ultra-precision positioning applications. However, their intrinsic hysteresis nonlinearity significantly degrades positioning accuracy. Although the traditional Madelung model effectively captures history-dependent characteristics through its wiping-out mechanism, it encounters a precision bottleneck regarding the mathematical characterization of the Current Hysteresis Curve (CHC). This paper presents an enhanced Madelung hysteresis modeling approach synergistically integrated with Random Forest (RF). The proposed approach retains the analytical framework and wiping-out mechanism of the Madelung model, facilitating the accurate identification of trajectory turning points and motion directions. To enhance the fidelity of the CHC characterization, the traditional analytical mapping is replaced by a data-driven RF algorithm. By constructing a 13-dimensional feature space, independent regression models for the ascending and descending branches are systematically developed to ensure high-precision performance. Experimental results demonstrate that the RF-Madelung model can precisely reconstruct complex asymmetric hysteresis loops. Furthermore, under variable-amplitude sinusoidal excitations, the proposed model demonstrates superior predictive precision, yielding a relative root-mean-square error of 0.19% compared with 0.38% for the conventional model.