Online Koopman Operator Learning to Identify Cross-Coupling Effect of Piezoelectric Tube Scanners in Atomic Force Microscopes

作     者：Huang, Xiang Zhou, Wei Li, Xiuting Zhu, LiMin Zhang, Hai-Tao 

作者机构：Huazhong Univ Sci & Technol Sch Artificial Intelligence & Automat Key Lab Image Proc & Intelligent Control Wuhan 430074 Peoples R China Huazhong Univ Sci & Technol State Key Lab Digital Mfg Equipment & Technol Wuhan 430074 Peoples R China Huazhong Agr Univ Coll Sci Wuhan 430070 Peoples R China Shanghai Jiao Tong Univ Sch Mech Engn State Key Lab Mech Syst & Vibrat Shanghai 200240 Peoples R China Shanghai Key Lab Networked Mfg & Enterprise Infor Shanghai Peoples R China 

出 版 物：《IEEE TRANSACTIONS ON INDUSTRIAL INFORMATICS》 (IEEE产业信息学汇刊)

年 卷 期：2022年第18卷第2期

页      面：1111-1120页

核心收录：

学科分类：1201[管理学-管理科学与工程(可授管理学、工学学位)] 0808[工学-电气工程] 08[工学] 0811[工学-控制科学与工程] 0812[工学-计算机科学与技术（可授工学、理学学位）] 

基　　金：National Natural Science Foundation of China [51729501, U1713203, U2013211, 61903148, 61803168] Natural Science Foundation of Hubei Province [2019CFA005] Fundamental Research Fund for the Central Universities [2019KFYXMBZ032, TII-21-1520] 

主　　题：Hysteresis Heuristic algorithms Couplings Nanoscale devices Dynamics Approximation algorithms Force Atomic force microscope (AFM) cross coupling modeling nonlinearity piezoelectric tube scanner (PTS) 

摘      要：As one of the most significant applications of nanopositioning technology, the tremendous development of atomic force microscopes (AFMs) has been witnessed these years. Essentially, the scanning motions of AFMs are generally driven by piezoelectric tube scanners (PTSs), whose cross-coupling effect hinders their high speed and high-precision positioning. Therefore, it becomes an urgent yet challenging mission to establish a niche model for the nonlinear cross-coupling dynamics of the PTS. As an emergent pure data-driven learning approach, the Koopman operator sheds some light on the PTS modeling methodology, which is thus adopted in this article to approximate the nonlinear cross-coupling dynamics of PTSs in an infinite-dimensional space. Moreover, an online high-order extended dynamic mode decomposition algorithm is proposed for the finite-dimensional approximation of the Koopman operator online. The merit of the present model lies in updating the identified cross coupling upon the arrival of new data in an incremental way. Finally, experiments are conducted to approximate the X-Y axes cross coupling of PTSs of an NTMDT Prima AFM, which verifies the effectiveness and superiority of the proposed modeling algorithm. This article is expected to pave the way from the Koopman operator learning theory to real applications in dynamics modeling of abundant nanoscale measurement systems.