Data-Driven Koopman Learning and Prediction of Piezoelectric Tube Scanner Hysteresis
提出一种基于Koopman算子的数据驱动建模方法，用于分析和预测原子力显微镜中压电管扫描器的交叉耦合迟滞效应，通过Hankel扩展动态模式分解算法实现线性化处理，并在实际AFM上验证了其优于传统模型。
This article presents a data-driven, Koopman operator-based modeling scheme for analyzing and predicting cross-coupling hysteresis effects of the piezoelectric tube scanners (PTSs) used in atomic force microscopes (AFMs). Such cross-coupling hysteresis effects between different PTS axes significantly reduce the positioning precision of AFMs. In contrast to most of the existing methods for PTS hysteresis, which involve complex nonlinear dynamics identification processes, the present study leverages the Koopman operator theory instead to treat the nonlinear hysteresis as a linear system. Therein, a Hankel extended dynamic mode decomposition (H-EDMD) algorithm is proposed to learn the finite-dimensional descriptions of the Koopman operator and the associated Koopman eigenspectrum. Moreover, the proposed H-EDMD even allows sparse sampling on the PTS systems, which is desirable in real industrial applications. Finally, extensive comparison experiments with a mainstream modified Prandtl-Ishlinskii model are conducted on an NTMDT Prima AFM to substantiate the effectiveness and superiority of the proposed H-EDMD method.