本論文的研究目的是設計一利用遞迴式以小波函數為基礎之Elman類神經網路估測器之智慧型互補式滑動模態控制系統，控制X-Y-Ө三軸超音波線性馬達移動平台，以達到具有強健性之精密定位控制。本論文首先說明線型超音達馬達之工作原理，接著介紹線性超音波馬達之數學模型，因為其模型相當複雜，且馬達參數具有非線性且時變特性，易受溫度、負載轉矩及加在定子、轉子的彈簧靜壓力影響，故無法精確獲得。為了使X-Y-Ө三軸線性超音波馬達運動控制系統能在參數變化、摩擦力、外來干擾與多軸系統中交叉耦合干擾的影響下具備強健之控制性能，本論文依序提出Elman類神經網路控制系統、遞迴式以小波函數為基礎之Elman類神經網路控制系統、滑動模態控制系統、互補式滑動模態控制系統和智慧型互補式滑動模態控制系統，配合線上學習法則與滑動模態控制中之迫近控制律，分別控制X-Y-Ө三軸線性超音波馬達運動控制系統，以達到精密定位控制之目的。接著利用非均勻有理B-spline曲線插值法(non-uniform rational B-spline, NURBS)，針對XY軸設計了圓形和蝴蝶形輪廓軌跡命令以及Ө軸設計了弦波和梯形波輪廓軌跡命令，以驗證所發展智慧型控制架構之有效性。最後由不同軌跡追隨之實作結果證明相較於Elman類神經網路控制系統、遞迴式以小波函數為基礎之Elman類神經網路控制系統、滑動模態控制系統與互補式滑動模態控制系統，本論文所提出之智慧型互補式滑動模態控制系統具有最佳的控制性能與強健性。

An intelligent complementary sliding-mode control (ICSMC) system using a recurrent wavelet-based Elman neural network (RWENN) estimator is proposed to control the mover position of a linear ultrasonic motors (LUSMs)-based X-Y-Ө motion control stage and to achieve high precise position control with robustness in this study. First, the structure and operating principles of the LUSM were introduced. Since the motor parameters are highly non-linear and time-varying due to increase in temperature and change in operating conditions, the exact mathematical model of the LUSM is very difficult to obtain. Moreover, the control accuracy of the LUSM is influenced easily by the existence of uncertainties, which usually comprises system parameter variations, external disturbances, cross-coupled interference and friction force. In order to develop high performance and robust position control systems for LUSMs-based X-Y-Ө motion control stage under the occurrence of the uncertainties, five control systems including Elman neural network (ENN) control, recurrent wavelet-based Elman neural network (RWENN) control, sliding-mode control (SMC), complementary sliding-mode control (CSMC), and intelligent complementary sliding-mode control (ICSMC) systems, are proposed. Furethermore, to demonstrate the different control performances of various control systems, the circle, butterfly contours and sinusoid, trapezoid trajectories are designed for X-Y axes and Ө-axis, recepectively, using NURBS curve interpolator. Finally, some experimental results of various contours and trajectories tracking show that the proposed ICSMC owns the best control performance and robustness compared with the ENN, RWENN, SMC and CSMC systems.

[1] 宏惠光電股份有限公司, http://www.unice.com.tw
[2] D. Dalecki, C. H. Raeman, S. Z. Child, and E. L. Carstensen, “Thresholds for intestinal hemorrhage in mice exposed to a piezoelectric lithotripter,” Ultrasound in Medicine & Biology, vol. 21, no. 9, pp. 1239-1246, 1995.
[3] A. Katsuki, H. Onikura, T. Sajima, T. Takei, and D. Thiele, “Development of a high-performance laser-guided deep-hole boring tool: Optimal determination of reference origin for precise guiding,” Precision Engineering, vol. 24, no, 1, pp. 9-14, 2000.
[4] M. A. Paesler and P. J. Moyer, Near-Field Optics: Theory, Instrumentation, and Applications. New York: John Wiley & Sons, 1996.
[5] 謝伯璜，“利用智慧型控制之X-Y-θ三軸線性超音波馬達運動系統”，博士論文，國立東華大學電機工程系，2007。
[6] 江田弘著，杜光宗編譯，”精密定位技術及其設計技術”，建宏出版社，1992。
[7] 江田弘著，杜光宗編譯，”超精密工作機械的製作”，建宏出版社，1995。
[8] E. C. Park, H. Lim, and C. H. Choi, “Position control of X-Y table at velocity reversal using presliding friction characteristics,” IEEE Trans. Control Systems Technology, vol. 11, no. 1, pp. 24-31, 2003.
[9] M. Zhu, “Contact analysis and mathematical modeling of traveling wave ultrasonic motors”, IEEE Transactions on Ultrasonics, Ferroelectrics, Frequency Control, vol. 51, no. 6, pp. 668-679, 2004.
[10] 黃柏凱，“利用智慧型控制之壓電致動器精密定位控制系統”，博士論文，國立東華大學電機工程系，2006。
[11] S. H. Jeong, H. K. Lee, Y. J. Kim, H. H. Kim, and K. J. Lim, ” Vibration analysis of the stator in ultrasonic motor by FEM,” Ultrasonic Symposium, vol. 14, pp. 1091-1094, 1997.
[12] C. Zhao, G. Wang, and L. Jin, “A new type of self-correction ultrasonic motor using standing wave,” Ultrasonic Symposium, vol. 30, pp. 671-674, 1999.
[13] F. J. Lin, R. J. Wai, and M. P. Chen, “Wavelet neural network control for linear ultrasonic motor drive via adaptive sliding-mode technique,” IEEE Trans. Ultrasonics, Ferroelectrics, Frequency Control, vol. 50, no. 6, pp. 686-698, 2003.
[14] F. J. Lin and P. H. Shieh, “Recurrent RBFN-based fuzzy neural network control for X-Y-Theta motion control stage using linear ultrasonic motors,” IEEE Trans. Ultrasonics, Ferroelectrics, Frequency Control, vol. 53, no. 12, pp. 2450-2464, 2006.
[15] L. X. Wang, Adaptive Fuzzy Systems and Control: Design and Stability Analysis. Englewood Cliffs, NJ: Prentice-Hall, 1994.
[16] L. X. Wang, A Course in Fuzzy Systems and Control. NJ: Prentice-Hall, 1997.
[17] O. Omidvar and D. L. Elliott, Neural Systems for Control. New York: Academic, 1997.
[18] W. Y. Wang, T. T. Lee, C. L. Liu, and C. H. Wang, “Function approximation using fuzzy neural networks with robust learning algorithm”, IEEE Transactions on Systems Man and Cybernetics Part B, vol. 27, pp. 740–747, 1997.
[19] Y. H. Kim, F. L. Lewis, and C. T. Abdallah, “A dynamic recurrent neural-network-based adaptive observer for a class of nonlinear systems”, Automatica, vol. 33, no. 8, pp. 1539–1543, 1997.
[20] G. A. Rovithakis and M. A. Christodoulou, “Adaptive control of unknown plants using dynamical neural networks”, IEEE Transactions on Systems Man and Cybernetics, vol. 25, pp. 400–412, 1994.
[21] C. H. Wang, W. Y. Wang, T. T. Lee, and P. S. Tseng, “Fuzzy B-spline membership function and its applications in fuzzy-neural control”, IEEE Transactions on Systems Man and Cybernetics, vol.25, pp. 841–851, 1995.
[22] Y. G. Leu, W. Y. Wang, and T. T. Lee, “Observer-based direct adaptive fuzzy-neural control for nonaffine nonlinear systems”, IEEE Transactions on Neural Networks, vol. 16, no. 4, pp. 853-861, 2005.
[23] C. K. Chui, An introduction to wavelets. San Diego: Academic Press, 1992.
[24] N. Sureshbabu and J. A. Farrell,“Wavelet-based system identification for nonlinear control”, IEEE Transactions on Automatic Control, vol. 44, no. 2, pp. 412-417, 1999.
[25] B. Delyon, A. Juditsky, and A. Benveniste, “Accuracy analysis for wavelet approximations”, IEEE Transactions on Neural Networks,vol. 6, no. 2, pp. 332-348, 1995.
[26] C. F. Chen and C. H. Hsiao, “Wavelet approach to optimising dynamic systems”, IEEE Proceedings Control Theory Appl., vol. 146,no. 2, pp. 213-219, 1999.
[27] T. Lindblad, and J. M. Kinser, “Inherent features of wavelets and pulse coupled networks”, IEEE Transactions on Neural Networks, vol. 10, no. 3, pp. 607-614, 1999.
[28] J. Zhang, G. G. Walter, Y. Miao, and W. N. W. Lee, “Wavelet neural networks for function learning”, IEEE Transactions on Signal Processing, vol. 43, no. 6, pp. 1485-1496, 1995.
[29] J. S. R. Jang, C. T. Sun, and E. Mizutani, Neuro-Fuzzy and Soft Computing: A Computational Approach to Learning and Machine Intelligence. New Jersey: Prentice-Hall, Upper Saddle River, 1997.
[30] 陳瑄易，“利用智慧型滑動模式控制之五軸主動式磁浮軸承控制系統”，博士論文，國立中央大學電機工程系，2010。
[31] 鄧禮濤，“結合智慧型控制與改良粒子群尋優法之風力驅動感應發電機系統”，博士論文，國立東華大學電機工程系，2008。
[32] 林俊良，智慧型控制分析與設計（修訂版），全華圖書股份有限公司，2002。
[33] J. Elman, Finding structure in time. Cognitive Science, no. 14, pp. 179-211, 1990.
[34] X. Li, G. Chen, Z. Chen, and Z. Yuan, “Chaotifying linear Elman networks”, IEEE Transactions on Neural Networks, vol. 13, no. 5, pp. 1193–1199, 2002.
[35] T. Sawaragi, and T. Kudoh, “Self-reflective segmentation of human bodily motions using recurrent neural networks”, IEEE Transactions on Industrial Electronics, vol. 50, no. 5, pp. 903–911, 2003.
[36] M. Wlas, Z. Krzeminski, J. Guzinski, H. Abu-Rub, and H. A. Toliyat, “Artificial-neural-network-based sensorless nonlinear control of induction motors”, IEEE Transactions on Energy Conversion, vol. 20, no. 3, pp. 520–528, 2005.
[37] J. S. R. Jang and C. T. Sun, “Functional equivalence between radial basis function networks and fuzzy inference systems”, IEEE Transactions on Neural Networks, vol. 4, no. 1, pp. 156-159, 1993.
[38] F. J. Lin, C. H. Lin, and C. M. Hong, “Robust control of linear synchronous servo drive using disturbance observer and recurrent neural network compensator”, IEEE Proceedings Electric Power Application, vol. 147, no. 4, pp. 263-272, 2000.
[39] P. Campolucci, A. Uncini, F. Piazza, and B. D. Rao, “On-line learning algorithms for locally recurrent neural networks”, IEEE Transactions on Neural Networks, vol. 10, no. 2, pp. 340-355, 1999.
[40] J. J. E. Slotine and W. Li,Applied Nonlinear Control. Englewood Cliffs, NJ: Prentice-Hall, 1991.
[41] V. I. Utkin,“Sliding mode control design principles and applications to electric drives,” IEEE Trans. Ind. Electron., vol.40, no.1, pp.23-36, 1993.
[42] I. Boiko and L. Fridman, “Analysis of chattering in continuous sliding-mode controllers,” IEEE Trans. Automat. Contr., vol. 50, no. 9, pp. 1442-1446, 2005.
[43] I. Boiko, L. Fridman, and M. I. Castellanos, “Analysis of second-order sliding-mode algorithms in the frequency domain,” IEEE Trans. Automat. Contr., vol. 49, no. 6, pp. 946-950, 2004.
[44] A. J. Koshkouei, K. J. Burnham, and A. S. I. Zinober, “Dynamic sliding mode control design,” IEE Proc. Control Theory Appl., vol. 152, no. 4, pp. 392-396, 2005.
[45] Y. B. Shtessel, “Nonlinear output tracking in conventional and dynamic sliding manifolds,” IEEE Trans. Automat. Contr., vol. 42, no. 9, pp. 1282-1286, 1997.
[46] M. Zribi, H. Sira-Ramirez, and A. Ngai, “Static and dynamic sliding mode control schemes for a permanent magnet stepper motor,” Int. J. Control, vol. 74, no. 2, pp. 103-17, 2001.
[47] Y. Guo and P. Y. Woo, “An adaptive fuzzy sliding mode controller for robotic manipulators,” IEEE Trans. Sys., Man, Cybern. A, Syst. and Humans.,, vol. 33, no. 2, pp. 149-159, 2003.
[48] Y. R. Hwang and M. Tomizuka, “Fuzzy smoothing algorithms for variable structure systems,” IEEE Trans. Fuzzy Syst., vol. 2, pp. 277-284, 1994.
[49] Q. P. Ha, Q. H. Nguyen, D. C. Rye, and H. F. Durrant-Whyte, “Fuzzy sliding-mode controllers with applications,” IEEE Trans. Ind. Electron., vol. 48, no. 1, pp. 38-46, 2001.
[50] Y. Fang, T. W. S. Chow, and X. D. Li, “Use of a recurrent neural network in discrete sliding-mode control,” IEE Proc. Control Theory Appl., vol. 146, no. 1, pp. 84-90, 1999.
[51] A. Karakasoglu and M. K. Sundareshan, “A recurrent neural network-based adaptive variable structure model-following control of robotic manipulators,” Automatica, vol. 31, no. 10, pp. 1495-1507, 1995.
[52] J. P. Su and C. C. Wang, “Complementary sliding control of non-linear systems,” Int. J. Control, vol. 75, no. 5, pp. 360-368, 2002.
[53] C. Y. Liang and J. P. Su, “A new approach to the design of a fuzzy sliding mode controller,” Fuzzy Sets and Systems, vol. 139, no. pp. 111-124, 2003.
[54] Piegl L., and Tiller W.: ‘The NURBS book’ (Springer-Verlag, New York, 1995).
[55] 洪英智，“以FPGA為基礎之類神經網路控制線型波音波馬達驅動系統”，碩士論文，國立東華大學電機工程系，2008。
[56] F. J. Lin, R. J. Wai, and C. C. Lee, “Fuzzy neural network position controller for ultrasonic motor drive using push-pull DC-DC converter”, IEEE Proceedings Control Theory Appl., vol. 146, no. l, pp. 99-107, 1999.
[57] Y. C. Chen and C. C. Teng, “A model reference control structure using a fuzzy neural network”, Fuzzy Sets and Systems, no. 73, pp. 291-312, 1995.
[58] Chui C. K.: ‘An introduction to wavelets’ (San Diego: Academic Press, 1992).
[59] I.Dauberchies,“Orthonaomal bases of compactly supported wavelets, ”Communications on Pure and Applied Mathematics, vol.
41,pp.909-996, 1998.
[60] Sureshbabu N., and Farrell J. A.:‘Wavelet-based system identification for nonlinear control’, IEEE Trans. Automatic Control, vol.44, no. 2, pp. 412-417, 1999.
[61] Zhang J., Walter G. G., Miao Y., and Lee W. N. W.: ‘Wavelet neural networks for function learning’, IEEE Trans. Signal Processing, vol.43, no. 6, pp. 1485-1496, 1995.
[62] 陳永年、張浚林，可變結構控制設計（修訂版），全華圖書股份有限公司，2006。
[63] Y. Tan, J. Chang, and H. Tan, “Adaptive backstepping control and friction compensation for AC servo with inertia and load uncertainties,” IEEE Trans. Ind. Electron., vol. 50, no. 5, pp. 944-952, 2003.
[64] 沈柏宏，“以數位訊號處理器為基礎之智慧型控制雙軸運動控制系統”，博士論文，國立東華大學電機工程系，2006。
[65] J. J. E. Slotine and W. Li,Applied Nonlinear Control. Englewood Cliffs, NJ: Prentice-Hall, 1991.
[66] J. P. Su and C. C. Wang, “Complementary sliding control of non-linear systems,” Int. J. Control, vol. 75, no. 5, pp. 360-368, 2002.