A Canonical Polyadic Decomposition Based Dynamical Model for Piezo-Actuated Nanopositioning Stage and its Experimental Validation

Piezo-actuated nanopositioning stages (piezo-stages) are widely employed in high-precision positioning. However, the hysteresis nonlinearity of piezo-stages exhibits complex characteristics, including but not limited to frequency and state dependency. In this paper, a canonical polyadic decomposition (CPD) based dynamical model is proposed to accurately describe the dynamics of piezo-stages. The model consists of a linear submodel and a nonlinear submodel, connected in parallel. Based on the identification of the linear submodel, we first construct the input variables for the nonlinear submodel using its states and control inputs, and model the hysteresis in the form of multivariate polynomials from all input variables. Subsequently, the CPD is employed to transform the multivariate polynomials into several univariate nonlinear branches. Finally, the proposed model is implemented experimentally on a piezo-stage, demonstrating its advantages compared to traditional Prandtl-Ishlinskii and Bouc-Wen models.