The Application of Precision Positioning Table with Filtered Sliding Mode Control 李昶毅、林志哲
E-mail: [email protected]
ABSTRACT
This study is focused on the design problem for precision positioning system. For experimental requirements, the XY table system with the ball-screw driven mechanism was implemented for investigations. The PC-based control architecture, due to their open and flexible architecture, is applied to implement and validate the proposed control algorithm. Friction is one of the most significant sources of nonlinear disturbance for the motion control which caused by the relative motion of different contact surface at very low velocity. The nonlinear component of friction such as static friction and Coulomb friction should be overcome so that the tracking error will be eliminated. The experiments are divided into two parts. The first focuses on the precision positioning tasks and the second is the contour tracking tasks. The precision position experiments utilize the disturbance observer and sliding mode controller to achieve the precision positioning without feedforward compensation with friction model. The tracking problems are compensated by using the friction model combined with the high-gain observer to estimate velocity, which resists unnecessary disturbances by adding disturbance observer and filtered sliding mode controller.
Keywords : Precision position、Friction、Disturbance observer、 Sliding mode controller、High-gain observer Table of Contents
第一章 緒論...1 1.1 前言...1 1.2 文獻回顧...3 1.3 本文內容...5 第二章 精密定位平台建構...6 2.1 滾珠導螺桿所構成的機械系 統...6 2.2 卡氏機械臂...8 2.3 定位系統架構...11 2.3.1 雷射光學 尺...12 2.3.2 dSPACE控制器...13 2.3.3 驅動器硬體設備...15 2.3.4 保護 裝置之設計 ...15 第三章 系統模型與摩擦力分析 ...17 3.1 系統模型建立與鑑別方法
...17 3.2 摩擦力種類與分析 ...18 3.3 系統模型鑑別 ...21 3.4 摩擦力模 型鑑別 ...26 第四章 控制器設計與穩定性分析 ...31 4.1 半閉迴路與全閉迴路控制
...31 4.2 高增益觀測器(High-gain observer) ...33 4.3 干擾觀測器(disturbance observer) ...35 4.4 順滑模態控制器(sliding mode controller) ...38 4.5 具濾波型順滑模態控制器 ...42 第五章 實驗結果 ...44 5.1 單軸定位實驗 ...44 5.2 雙軸循圓實驗 ...59 第六章 結論 ...71 6.1 控制器優缺點 ...71 6.2 結論與未來研究方向
...73 參考文獻 ...74 REFERENCES
[1] Armstrong-Helouvry , B., Dupont, P. and Canudas de Wit ,C.. “A Survey of Models, Analysis Tools and Compensation Methods for the Control of Machines with Friction,” Elserver Science Ltd. survey paper of Automatic, Vol. 30, No. 7,pp. 1083-1138, 1994.
[2] Armstrong-Helouvry, B., Control of Machines with Friction, Kluwer Academic Publishers, Norwell, MAY,1991.
[3] Canudas de wit, C., Olsson, H., Astrom, K. J., and Lischinsky, P., “A New Model for Control of Systems with Friction,” IEEE Transactions on Automatic Control, Vol. 40, No. 3, March 1995.
[4] Haessig, D.A., Friedland , Jr.B. “On the Modeling and Simulation of Friction,” Transactions of the ASME, Vol. 113, pp. 354~362, September 1991.
[5] Armstrong-Helouvry, B., “Stick Slip and Control in Low-Speed Motion,” IEEE Transactions on Automatic Control, Vol. 38, No. 10, pp.
1483-1496, October 1993.
[6] Suzuki, A., Tomizuka, M., “Design and Implementation of Digital Servo Controller for High Speed Machine Tools”,Proc. American Control Conference(ACC),pp. 1246-1251,1991.
[7] Lee , H. S. and Tomizuka ,M.. “Robust Motion Controller Design for High-Accuracy Positioning Systems,” IEEE Transactions on Industrial Electronics, Vol. 43, No. 1, pp.48-55, 1996.
[8] 劉志文，雙軸馬達驅動機砲砲臺之強健性穩定伺服控制，台灣大學電機工程研究所碩士論文，民國八十五??月。
[9] 邱亦範，命令及摩擦力前饋控制於工具機之研究，國立成功大學機械工程研究所碩士論文，民國九十一?七月。
[10]張香鈜，扭力驅動模式下之運動控制研究，國立清華大學動力機械所碩士論文，民國九十年七月。
[11]林銘湧，精密伺服控制系統之摩擦力分析及補償研究，私立逢甲大學自動控制工程學系碩士班碩士?文，民國九十一?七月。
[12]黃百毅，智慧型精密定位控制系統設計，國立台灣大學電機學院研究所博士論文，民國八十九年十月。
[13]Tomei, Patrizio “Robust Adaptive Friction Compensation for Tracking Control of Robots,” Proc. IEEE International Conference on Control Applications,pp.875-880,1999.
[14]Canudas de Wit, C. and Seronf, V. “Robust Adaptive Friction Compensation,” Proc. IEEE International Conference on Robotics and Automation, Cincinnati, OH, pp. 1383-1388, 1990 [15]Umeno, T. and Hori,Y. “ Robust Speed Control of DC Servo- motors Using Modern Two Degrees-of-Freedom Controller Design,” IEEE Transactions on Industrial Electronics, Vol. 38, No. 5, pp. 363-368, 1991.
[16]Jiang, L., Wu, Q.H “Nonlinear adaptive control via sliding-mode state and perturbation observer applications ” , Vol.149 , Issue: 4.
pp.269-277,2002 [17]Xiong ,Yi., Saif, M. “Sliding mode observer for nonlinear uncertain systems, ” IEEE Transactions on Automatic Control , Vol. 46 , Issue: 12 , pp.2012 - 2017, 2001 [18]Korondi, P., Young, D.; Hashimoto, H. “Sliding Mode Based Disturbance Observer For Motion Control, ” IEEE Proc. Conference on Decision and Control, Vol. 2 , pp.1926-1927 ,1998 [19]Endo, S., Kobayashi, H.,Kempf ,C.J.,Kobayashi,S., Tomizuka,M. and Hori ,Y. “Robust Digital Tracking Controller Design for High-Speed Positioning Systems,” PERGAMON Control
Engineering Practice, Vol. 4, No. 4, pp.527-536,1996.
[20]Lee, H. S. and Tomizuka ,M.. “Robust Motion Controller Design for High-Accuracy Positioning Systems,” IEEE Transactions on Industrial Electronics, Vol. 43, No. 1, pp.48-55, 1996.
[21]Burton, J. A. and Zinober, A. S. I. “Continuous approximation of variable structure control”, Int. J. of Systems Science, Vol.17, pp.876-885, 1986 [22]Slotine, J. J. E. and Sastry, S.S. “Tracking control of nonlinear systems using sliding surfaces with application to robot manipulators”, Int. J. Control, Vol.38, pp.465-492, 1983 [23]Edwards, C. and Spurgeon, S.K., Sliding Mode Control: Theory and Applications,, Taylor &
Francis, 1998 [24]Fliess,M., “Generalized Controller Canonical Forms for Linear and Nonlinear Dynamics”, IEEE Trans. On Automatic Control,Vol.AC-35,pp.994-1001, 1990 [25]Hebertt, S.R., “On the Sliding Mode Control of Nonlinear systems”, International Journal of Control, Vol.57, No.5 , pp.1039-1061,1993 [26]Lee, J.J. and Xu, Y., “A New Method of Switching Surface Design for Multivariable Variable Structure Systems”, IEEE Trans. On Automatic Control, Vol.AC-39,pp.414-419, 1994 [27]Utkin, V. and Shi, J., “Integral Sliding Mode in Systems Operating under Uncertainty Conditions”, Proceedings of the 35th Conference on Decision and Control,pp.4591-4596, 1996
[28]Lin,Chih-Jer, “Variable Structure Model Following Control of Robot Manipulators with High-Gain Observer”, JSME International Journal , Vol.47,No 2, 2004 [29]Tung, E. D., Answar ,G. and Tomizuka ,M.. “Low Velocity Friction Compensation and Feedforward Solution Based on Repetitive Control,” ASME J. of Dynamic Systems, Measurement, and Control, Vol. 115, pp. 279-284,1993 [30]Tung, E. D., Urushisaki ,Y. and Tomizuka ,M.. “Low Velocity Friction Compensation for Machine Tool Feed Drives,” Proc. 1993 American Control Conference (ACC), San Francisco, California, pp. 1932-1936, 1993 [31]李凱笙，機械手臂之動態順滑控制，私立大葉大學機械工程所碩士論文，民國九十二年六月 [32]Brain ,A. H., PIERRE, D., CARLOS, C. D. W. “A survey of models, analysis tools and compensation methods for the control of machines with friction,”Automatica, Vol. 30, No.7, pp.1083-1138, 1994.
[33]Nicosia, S., Tornambe ,A. and Valigi,P. “Experimental Results in State Estimation of Industrial Robots”, Proceedings of the 29th
Conference on Decision and Control, 1990 [34]Heredia, J. A. and Yu,W. “A High-Gain Observer-Based PD Control for Robot Manipulator”, Proceedings of the American Control Conference Chicago, pp.2518-2522, 2000 [35]Yu, W. and Li ,X., “PD Control of Robot with Velocity Estimation and Uncertainties Compensation”, Proceedings of the 40th IEEE Conference on Decision and Control, 2001
