Distributed Hammerstein Modeling for Cross-Coupling Effect of Multiaxis Piezoelectric Micropositioning Stages

Hysteresis modeling is interesting yet challenging for piezoelectric actuated systems, which are often used in micro/nano scale measurement and manufacturing equipments. However, due to its complexity, few efforts have been devoted to characterizing cross-coupling hysteresis effect of multiaxis piezoelectric micropositioning stages. To this end, a distributed Hammerstein model, composed of a cascaded connection of a static nonlinearity and a dynamic linearity, is proposed in this paper to approximate the nonlinear spatial/temporal cross-coupling effect. This model outperforms conventional piezo models, such as the Preisach model. Meanwhile, theoretical analysis is provided to guarantee the convergence of the proposed Hammerstein model. Finally, extensive experiments are conducted to verify the superiority of the proposed modeling method.