System identification of a novel 6-DOF precision positioning table

Abstract The purpose of this study is to identify a novel 6-DOF precision positioning table, which is assembled by two different 3-DOF precision positioning tables: a plane-type 3-DOF (X, Y, θz) precision positioning table and a cylinder-type 3-DOF (θx, θy, Z) one. According to the dynamics of a mechanical mass-spring system, we establish simple mathematical equations that contain linear mass (inertia), viscous friction, and spring stiffness associated with cross-coupling effects due to mechanical bending. In system identification, we identify parameters of this 6-DOF and two 3-DOF precision positioning tables driven by piezoelectric actuators with hysteresis phenomenon, which is described by Bouc–Wen model. The identification method based on the real-coded genetic algorithm (RGA) has the advantages to identify all the parameters of the table and the hysteresis model simultaneously. From experimental results and numerical simulations, it is found that the numerically identified parameters are almost the same as those of the real system. In comparison of the identified results between the integral and individual tables, it is found that the integral table has better performance than those from the individual table.

[1]  S H Chang,et al.  An ultra-precision XYtheta(Z) piezo-micropositioner. I. Design and analysis. , 1999, IEEE transactions on ultrasonics, ferroelectrics, and frequency control.

[2]  John H. Holland,et al.  Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control, and Artificial Intelligence , 1992 .

[3]  Ilya V. Kolmanovsky,et al.  Predictive energy management of a power-split hybrid electric vehicle , 2009, 2009 American Control Conference.

[4]  Wang Xiaoyue,et al.  A method identifying the parameters of Bounc-Wen hysteretic nonlinear model based on genetic algorithm , 1997, 1997 IEEE International Conference on Intelligent Processing Systems (Cat. No.97TH8335).

[5]  Ying-Shieh Kung,et al.  A comparison of fitness functions for the identification of a piezoelectric hysteretic actuator based on the real-coded genetic algorithm , 2006 .

[6]  Won-jong Kim,et al.  Design and control of a 6-DOF high-precision integrated positioner , 2004, Proceedings of the 2004 American Control Conference.

[7]  Y. Wen.  Method for Random Vibration of Hysteretic Systems , 1976 .

[8]  Sam Kwong,et al.  Genetic algorithms: concepts and applications [in engineering design] , 1996, IEEE Trans. Ind. Electron..

[9]  T. Low,et al.  Modeling of a three-layer piezoelectric bimorph beam with hysteresis , 1995 .

[10]  Xianmin Zhang,et al.  Input coupling analysis and optimal design of a 3-DOF compliant micro-positioning stage , 2008 .

[11]  D. E. Goldberg,et al.  Genetic Algorithms in Search , 1989 .

[12]  Adeike A. Adewuya.  New methods in genetic search with real-valued chromosomes , 1996 .

[13]  Rong-Fong Fung,et al.  Optimization of an impact drive mechanism based on real-coded genetic algorithm , 2005 .

[14]  Shuo-Hung Chang,et al.  An ultra-precision XY/spl Theta//sub Z/ piezo-micropositioner. II. Experiment and performance , 1999 .

[15]  Yung Ting,et al.  Error compensation and feedforward controller design for a 6-dof micro-positioning platform , 2005, 2005 IEEE/RSJ International Conference on Intelligent Robots and Systems.

[16]  Sam Kwong,et al.  Genetic algorithms: concepts and applications [in engineering design] , 1996, IEEE Trans. Ind. Electron..

[17]  D. E. Goldberg,et al.  Optimization and Machine Learning , 2022 .

[18]  Yanling Tian,et al.  Investigation of a 3-DOF micro-positioning table for surface grinding , 2006 .