Identification of Dynamic Model for Ultra-Precision Positioning System

Abstract:

Abstract: In order to improve the control precision of the piezoceramic actuator in precision position system, a dynamic modeling of Ultra-precision Positioning System is proposed. A two-step identification strategy is adopted in this paper. Step 1: The linear model was identified based on step input response by least square method. Step 2: According to the step.1 result, the designed nonlinear observer was applied to estimate the output of hysteresis by Fast Tracking Differentiator. The polynomials are used consistently approximate continuous functions of f(.) and g(.) in the Duhem modeling based on the theorem of the Weierstrass polynomial approximation theory. Recursive least square methods are developed to identify α and the coefficients of the polynomials in Duhem model. At last , the simulation results show applicability, rapid convergence velocity and high calculation accuracy of the algorithm.

• Periodical: Applied Mechanics and Materials (Volumes 190-191)
• Pages: 97-100
• DOI: https://doi.org/10.4028/www.scientific.net/AMM.190-191.97
• Online since: July 2012
• Authors: Hui Chen, Xing Peng Zhou, Yong Hong Tan, Ru Qiong Li, Ya Hong Zhang, Rui Li Dong
• Keywords: Duhem Model, Dynamic Hysteresis Modeling, Fast Tracking Differentiator, Recursive Least Square, Weierstrass Polynomial Approximation

References

[1] SANGJOOK, WANKC,YOUNGILY. On the coarse/fine dual-stage manipulators with perturbation compensator [C].Proceedingsofthe2001IEEE International Conference on Robotic and Automation .Seoul, Korea May, 2001, pp.121-126.

[2] H. T. Banks and R. C. Smith, Hysteresis Modeling in Smart MaterialSystems, J. Appl. Mech. Eng, vol. 5, pp.31-45, 2000.

[3] Ying Feng, Camille Alain Rabbath, Tianyou Chai, Chun-Yi Su ,Robust Adaptive Control of Systems with Hysteretic nonlinearities:A Duhem Hysteresis Modelling Approach, IEEE AFRICOM 2009 pp.1-6.

DOI: 10.1109/afrcon.2009.5308329

[4] L. Xu and B. Yao, "Output feedback adaptive robust precision motion control of linear motors," Automatica, vol. 37, no. 7, pp.1029-039, 2001.

DOI: 10.1016/s0005-1098(01)00052-8

[5] K. K. Tan, T. H. Lee, and H. X. Zhou, "Micro-position of linear-piezoelectric motors based on a learning nonlinear PID controller," IEEE/ASME Trans. Mechatron., vol. 6, no. 4, pp.428-36, Dec. 2001.

DOI: 10.1109/3516.974856

[6] F. Janabi-Sharifi, V. Hayward, and C.-S. J. Chen, "Discrete-time adaptive windowing for velocity estimation," IEEE Trans. Contr. Syst. Technol., vol. 8, no. 6, pp.1003-1009, Nov. 2000.

DOI: 10.1109/87.880606

[7] J. Q. Han, W. Wang, "Nonlinear tracking differentiator," J. Sys. Sci & Math. Sci. vol.14, no.1, pp.177-183, 1994. (In Chinese).

[8] JinHyoung Oh and Dennis S. Bemstein Identification of Rate-Dependent Hysteresis Using the Semilinear Duhem Model, Proceeding of the 2004 American Control Conference,4776-4781[11] H. T. banks and R. C. Smith, "Hysteresis Modeling in Smart MaterialSystems," J. Appl. Mech. Eng, vol. 5, pp.31-45, 2000.

DOI: 10.23919/acc.2004.1384068

[9] J. Oh and D. S. Bernstein, Semilinear Duhem model for rate-independent and rate-dependent hysteresis, IEEE Trans. Autom. Control, vol.50, no. 5, p.631–645, May 2005.

DOI: 10.1109/tac.2005.847035

[10] Chen hui TanYong-hong, Zhou Xingpeng Identification and control of dynamic modeling for piezoceramic actuatorGuangxue Jingmi Gongcheng/Optics and Precision Engineering, v 20, n 1, pp.88-95, January 2012 (In Chinese).

[11] J. Q. Han, W. Wang, Nonlinear tracking differentiator, J. Sys. Sci & Math. Sci. vol.14, no.1, pp.177-183, 1994. (In Chinese).

[12] Songsheng, Approximation of Functions [M]. Publishing House of Beijing Normal University, Beijing. 1989.3