有效降低追蹤誤差與輪廓誤差是多軸運動平台輪廓循跡應用中所追求的目標。然而多軸平台運動時卻常受到系統外部干擾與非線性現象所影響，導致循跡精度欠佳。為克服上述缺點，本論文提出三種基於不同類型學習控制方法之多軸運動控制架構，期能有效提升循跡運動精度，這些學習控制方法包含反覆學習控制、小腦模型控制及增強式學習等。本論文所提出之第一種運動控制架構利用反覆學習控制演算法結合小腦模型前饋控制器用以抑制重覆性外擾與摩擦力之影響。在本論文所提出之第二種運動控制架構中，引入交叉耦合控制架構結合基於參數之輪廓誤差估測法以消除雙軸運動平台之各軸動態不匹配所造成之不良影響。此外，為了克服傳統反覆學習控制架構因學習率固定導致學習不良之缺點，在本論文所提出之基於模糊控制之增強式反覆學習控制器中，其學習率可根據系統之即時追蹤誤差值調整。本論文所提出之第三種運動控制架構使用具可調學習率功能之增強式Q-學習並結合反覆學習控演算法，根據即時追蹤誤差值，調整多軸運動平台進行輪廓循跡之進給率，以降低追蹤誤差。多軸運動平台循跡實驗結果顯示，本論文所提之三種運動控制架構皆能有效提升循跡運動精度。

Reducing tracking error and contour error is crucial for contour following applications of a multi-axis motion stage. This is because contour following accuracy is most likely to be affected by factors such as external disturbances and nonlinearities. In order to cope with this problem, this dissertation proposes three new motion control schemes that exploit the paradigms of learning control approaches such as Iterative Learning Control (ILC), Cerebellar Model Articulation Control (CMAC) and Reinforcement Learning (RL). In the first motion control scheme proposed in this dissertation, the ILC combined with CMAC is employed to suppress adverse effects due to nonlinearity and periodic external disturbance. In the second motion control scheme proposed in this dissertation, the cross-coupled control scheme with a parameter-based contour error estimation algorithm is employed to cope with modeling uncertainty and dynamics incompatibility among different axes. Moreover, to further reduce tracking error, the learning rate of the fuzzy-logic-based reinforcement ILC also employed in the second motion control scheme can be self-tuned based on the tracking error information. In the third motion control scheme proposed in this dissertation, a reinforcement Q-learning combined with ILC is employed to adjust the contour following feedrate so as to reduce tracking error. Experimental results of several contour following experiments conducted on a biaxial motion stage are used to assess the effectiveness of the proposed motion control schemes.

[1] J. S. Albus, “A new approach to manipulator control: The cerebellar model articulation controller (CMAC),” ASME Journal of Dynamic Systems, Measurement, and Control, vol. 97, no. 3, pp. 220-227, 1975.
[2] J. S. Albus, “Data storage in the cerebellar model articulation controller (CMAC),” ASME Journal of Dynamic Systems, Measurement, and Control, vol. 97, no. 3, pp. 228-233, 1975.
[3] K. L. Barton and A. G. Alleyne, “A cross-coupled iterative learning control design for precision motion control,” IEEE Transactions on Control Systems Technology, vol. 16, no. 6, pp. 1218-1231, 2008.
[4] D. A. Bristow, M. Tharayil, and A. G. Alleyne, “A survey of iterative learning control,” IEEE Control Systems Magazine, vol. 26, no. 3, pp. 96-114, 2006.
[5] C. K. Chen and J. Hwang, “Iterative learning control for position tracking of a pneumatic actuated x-y table,” Control Engineering Practice, vol. 13, issue 12, pp. 1455-1461, 2005.
[6] C. K. Chen, C. J. Lin, J. Hwang, and C. W. Hung, “The iterative learning control of a Stewart platform system,” Journal of Chinese Society of Mechanical Engineers, vol. 34, no. 1, pp. 21-30, 2013.
[7] C. L. Chen and K. S. Li, “Observer-based robust AILC for robotic system tracking problem,” Journal of Chinese Society of Mechanical Engineers, vol. 30, no. 6, pp. 483-491, 2009.
[8] C. Y. Chen and M. Y. Cheng, “Velocity field control and adaptive virtual plant disturbance compensation for planar contour following tasks,” IEE Proceedings - Control Theory and Applications, vol. 6, no. 9, pp. 1182-1191, 2012.
[9] F. C. Chen and C. H. Chang, “Practical stability issues in CMAC neural network control systems,” IEEE Transactions on Control Systems Technology, vol. 4, no. 1, pp. 86-91, 1996.
[10] H. R. Chen, M. Y. Cheng, C. H. Wu, and K. H. Su, “Real time parameter based contour error estimation algorithms for free form contour following,” International Journal of Machine Tools & Manufacture, vol. 102, pp.1-8, 2016.
[11] C. W. Cheng and M. C. Tsai, “Real-time variable feed rate NURBS curve interpolator for CNC machining,” The International Journal of Advanced Manufacturing Technology, vol. 23, pp. 865-873, 2004.
[12] G. Cheng, K. Peng, B. M. Chen, and T. H. Lee, “Improving transient performance in tracking general references using composite nonlinear feedback control and its application to high-speed xy-table positioning mechanism,” IEEE Transactions on Industrial Electronics, vol. 54, no. 2, pp. 1039-1051, 2007.
[13] M. Y. Cheng and C. C. Lee, “Motion controller design for contour-following tasks based on real-time contour error estimation,” IEEE Transactions on Industrial Electronics, vol. 54, pp. 1686-1695, 2007.
[14] M. Y. Cheng and K. H. Su, “Contouring accuracy improvement using a tangential contouring controller with a fuzzy logic-based feedrate regulator,” The International Journal of Advanced Manufacturing Technology, vol. 41, pp. 75-85, 2009.
[15] M. Y. Cheng, M. C. Tsai, and J. C. Kuo, “Real-time NURBS command generators for CNC servo controllers,” International Journal of Machine Tools and Manufacture, vol. 42, pp. 801-813, 2002.
[16] M. Y. Cheng and Y. H. Wang, “Velocity field construction for contour following tasks represented in NURBS form,” IEEE Transactions on Automatic Control, vol. 54, pp. 2405-2410, 2009.
[17] G. T. C. Chiu and M. Tomizuka, “Coordinated position control of multi-axis mechanical systems,” ASME Journal of Dynamic Systems, Measurement, and Control, vol. 120, pp. 389-393, 1998.
[18] A. Elfizy, G. Bone, and M. Elbestawi, “Model-based controller design for machine tool direct feed drives,” International Journal of Machine Tools and Manufacture, vol. 44, pp. 465-477, 2004.
[19] K. Erkorkmaz and Y. Altintas, “High speed CNC system design. Part III: high speed tracking and contouring control of feed drives,” International Journal of Machine Tools and Manufacture, vol. 41, issue 11, pp. 1637-1658, 2001.
[20] C. T. Freeman, A. M. Hughes, J. H. Burridge, P. H. Chappell, P. L. Lewin, and E. Rogers, “Iterative learning control of FES applied to the upper extremity for rehabilitation,” Control Engineering Practice, vol. 17, issue 3, pp. 368-381, 2009.
[21] L. Freidovich, A. Robertsson, A. Shiriaev, and R. Johansson, “LuGre-model-based friction compensation,” IEEE Transactions on Control Systems Technology. vol. 18, pp. 194-200, 2010.
[22] N. Fujii and K. Okinaga, “X-Y linear synchronous motors without force ripple and core loss for precision two-dimensional drives,” IEEE Transactions on Magnetics, vol. 38, no. 5, pp. 3273-3275, 2002.
[23] H. Fujimoto and T. Takemura, “High-precision control of ball-screw-driven stage based on repetitive control using N-times learning filter,” IEEE Transactions on Industrial Electronics, vol. 61, no. 7, pp. 3694-3703, 2014.
[24] E. Golubovic, E. A. Baran, and A. Sabanovic, “Contouring controller for precise motion control systems,” Automatika, vol. 54, pp. 19-27, 2013.
[25] C. Hu, B. Yao, Z. Chen, and Q. Wang, “Adaptive robust repetitive control of an industrial biaxial precision gantry for contouring tasks,” IEEE Transactions on Control Systems Technology, vol. 19, no. 6, pp. 1559-1568, 2011.
[26] D. Huang, J. X. Xu, V. Venkataramanan, and T.C.T. Huynh, “High-performance tracking of piezoelectric positioning stage using current-cycle iterative learning control with gain scheduling,” IEEE Transactions on Industrial Electronics, vol. 61, no. 2, pp. 1085-1098, 2014.
[27] J. Jahanpour, M. C. Tsai, and M. Y. Cheng, “High-speed contouring control with NURBS-based C2 PH spline curves,” The International Journal of Advanced Manufacturing Technology, vol. 49, pp. 663-674, 2010.
[28] J. O. Jang, “Deadzone compensation of an xy-positioning table using fuzzy logic,” IEEE Transactions on Industrial Electronics, vol. 52, no. 6, pp. 1696-1701, 2005.
[29] K. Jezernik and M. Rodic, “High precision motion control of servo drives,” IEEE Transactions on Industrial Electronics, vol. 56, pp. 3810-3816, 2009
[30] D. Kim and S. Sungkwun, “An iterative learning control method with application for CNC machine tools,” IEEE Transactions on Industry Applications, vol. 32, no. 1, pp. 66-72, 1996.
[31] Y. Koren, “Cross-coupled biaxial computer control for manufacturing systems,” ASME Journal of Dynamic Systems, Measurement, and Control, vol. 102, pp. 265-272, 1980.
[32] S. S. Ku, U. Pinsopon, S. Cetinkunt, and S. Nakjima, “Design, fabrication, and real-time neural network of a three-degrees-of freedom nanopositioner,” IEEE Transactions on Mechatronics, vol. 5, no. 3, pp. 273-280, 2000.
[33] C. C. Lee, “Fuzzy logic in control system: fuzzy logic controller—Part II,” IEEE Transactions on Systems, Man, and Cybernetics, vol. 20, pp. 419-435, 1990.
[34] C. H. Lee, F. Y. Chang, and C. M. Lin, “An efficient interval type-2 fuzzy CMAC for chaos time-series prediction and synchronization,” IEEE Transactions on Cybernetics, vol. 44, no. 3, pp. 329-341, 2014.
[35] H. S. Lee and M. Tomizuka, “Robust motion controller design for high-accuracy positioning systems,” IEEE Transactions on Industrial Electronics, vol. 43, pp. 48-55, 1996.
[36] S. C. Lee and C. L. Shih, “Optimal single input PID-type fuzzy logic controller,” Journal of the Chinese Institute of Engineers, vol. 35, no. 4, pp. 413-420, 2012.
[37] S. Levine, P. Pastor, A. Krizhevsky, and D. Quillen, “Learning hand-eye coordination for robotic grasping with deep learning and large-scale data collection,” unpublished.
[38] P. Y. Li, “Coordinated contour following control for machining operations-a survey,” in Proceedings of the 1999 American Control Conference (99ACC), San Diego, CA, USA, 1999, pp. 4543-4547.
[39] P. Y. Li and R. Horowitz, “Passive velocity field control of mechanical manipulators,” IEEE Transactions on Robotics and Automation, vol. 15, pp. 751-763, 1999.
[40] Y. Li and Q. Xu, “Design and robust repetitive control of a new parallel-kinematic xy piezostage for micro/nanomanipulation,” IEEE Transactions on Mechatronics, vol. 17, no. 6, pp. 1120-1132, 2012.
[41] C. M. Lin and C. S. Hsueh, “Adaptive EKF-CMAC-based multisensor data fusion for maneuvering target,” IEEE Transactions on Instrumentation and Measurement, vol. 62, no. 7, pp. 2058-2066, 2013.
[42] C. M. Lin and H. Y. Li, “Adaptive dynamic sliding-mode fuzzy CMAC for voice coil motor using asymmetric gaussian membership function,” IEEE Transactions on Industrial Electronics, vol. 61, no. 10, pp. 5662-5671, 2014.
[43] C. M. Lin and H. Y. Li, “Intelligent control using the wavelet fuzzy CMAC backstepping control system for two-axis linear piezoelectric ceramic motor drive systems,” IEEE Transactions on Fuzzy systems, vol. 22, no.4, pp. 791-802, 2014.
[44] C. S. Lin and C. T. Chiang, “Learning convergence of CMAC technique,” IEEE Transactions on Neural Network, vol. 8, no. 6, pp. 1281-1292, 1997.
[45] M. T. Lin, C. L. Yen, M. S. Tsai, and H. T. Yau, “Application of robust iterative learning algorithm in motion control system,” Mechatronics, vol. 23, issue 5, pp. 530-540, 2013.
[46] Z. Z. Liu, F. L. Luo, and M. Azizur Rahman, “Robust and precision motion control system of linear-motor direct drive for high-speed x-y table positioning mechanism,” IEEE Transactions on Industrial Electronics, vol. 52, no. 5, pp. 1357-1363, 2005.
[47] C. C. Lo and C. Y. Chung, “Tangential-contouring controller for biaxial motion control,” ASME Journal of Dynamic Systems, Measurement, and Control, vol. 121, pp. 126-129, 1999.
[48] R. W. Longman, “Iterative learning control and repetitive control for engineering practice,” International Journal of Control, vol. 73, no. 10, pp. 930-954, 2000.
[49] L. Lu, Z. Chen, B. Yao, and Q. Wang, “Desired compensation adaptive robust control of a linear-motor-driven precision industrial gantry with improved cogging force compensation,” IEEE Transactions on Mechatronics, vol. 13, no. 6, pp. 617-624, 2008.
[50] W. Maebashi, K. Ito, and M. Iwasaki, “Practical feedback controller design for micro-displacement positioning in table drive systems,” Automatika, vol. 54, pp. 9-18, 2013.
[51] F. Marcassa and R. Oboe, “Disturbance rejection in hard disk drives with multi-rate estimated state feedback,” Control Engineering Practice, vol. 12, no. 11, pp. 1409-1421, 2004.
[52] W. T. Miller, F. H. Glanz, and L. G. Kraft, “Application of a general learning algorithm to the control of robotic manipulators,” The International Journal of Robotics Research, vol. 6, no. 2, pp. 84-98, 1987.
[53] K. Ohnishi, M. Shibata, and T. Murakami, “Motion control for advanced mechatronics,” IEEE Transactions on Mechatronics, vol. 1, pp. 56-67, 1996.
[54] H. Olsson, K. J. Åström, C. Canudas de Wit, M. Gäfvert, and P. Lischinsky, “Friction models and friction compensation,” European Journal of Control, vol. 4, pp. 176-195, 1998.
[55] E. C. Park, H. Lim, and C.H. Choi, “Position control of x-y table at velocity reversal using presliding friction characteristics,” IEEE Transactions on Control Systems Technology, vol. 11, no. 1, pp. 24-31, 2003.
[56] G. L. Shi and W. B. Shen, “Hybrid control of a parallel platform based on pneumatic artificial muscles combining sliding mode controller and adaptive fuzzy CMAC,” Control Engineering Practice, vol. 21, issue 1, pp. 76-86, 2013.
[57] D. Silver, A. Huang, C. J. Maddison, A. Guez, L. Sifre, G. V. D. Driessche, J. Schrittwieser, et al. “Mastering the game of Go with deep neural networks and tree search,” Nature, vol. 529, pp. 484-489, 2016.
[58] K. H. Su and M. Y. Cheng, “Contouring accuracy improvement using cross-coupled control and position error compensator,” International Journal of Machine Tools and Manufacture, vol. 48, pp. 1444-1453, 2008.
[59] R. S. Sutton and A. G. Barto, Reinforcement Learning: An Introduction: Springer Science & Business Media, 2012.
[60] M. Tomizuka, “Zero phase error tracking algorithm for digital control,” ASME Journal of Dynamic Systems, Measurement, and Control, vol. 109, pp. 68-68, 1987.
[61] M. C. Tsai, I. F. Chiu, and M. Y. Cheng, “Design and implementation of command and friction feedforward control for CNC motion controllers,” IEE Proceedings - Control Theory and Applications, vol. 151, no. 1, pp. 13-20, 2004.
[62] M. S. Tsai, M. T. Lin, and H. T. Yau, “Development of command-based iterative learning control algorithm with consideration of friction, disturbance, and noise effects,” IEEE Transactions on Control Systems Technology, vol. 14, no. 3, pp. 511-518, 2006.
[63] M. S. Tsai, C. L. Yen, and H. T. Yau, “Integration of an empirical mode decomposition algorithm with iterative learning control for high-precision machining,” IEEE Transactions on Mechatronics, vol. 18, no. 3, pp. 878-886, 2013.
[64] X. Wang, N. Liu, and M. Wang, “Research and implementation of high-precision biaxial tracking control system based on NURBS interpolator,” The International Journal of Advanced Manufacturing Technology, vol. 52, pp. 255-262, 2011.
[65] C. Wei, Z. Zhang, W. Qiao, and L. Qu, “Reinforcement-learning-based intelligent maximum power point tracking control for wind energy conversion systems,” IEEE Transactions on Industrial Electronics, vol. 62, no. 10, pp. 6360-6370, 2015.
[66] C. M. Wen and M. Y. Cheng, “Contouring accuracy improvement of a piezo-actuated micro motion stage based on fuzzy cerebellar model articulation controller,” Control Engineering Practice, vol. 20, issue 11, pp. 1195-1205, 2012.
[67] C. M. Wen and M. Y. Cheng, “Development of a recurrent fuzzy CMAC with adjustable input space quantization and self-tuning learning rate for control of a dual-axis piezoelectric actuated micromotion stage,” IEEE Transactions on Industrial Electronics, vol. 60, no. 11, pp. 5105-5115, 2013.
[68] M. Wiering and M. V. Otterlo, Reinforcement Learning: State-of-the-Art: Springer-Verlag Berlin Heidelberg, 2012.
[69] C. Canudas de Wit, H. Olsson, K. J. Astrom, and P. Lischinsky, “A new model for control of systems with friction,” IEEE Transactions on Automatic Control, vol. 40, pp. 419-425, 1995.
[70] W. K. Xu, B. Chu and E. Rogers, “Iterative learning control for robotic-assisted upper limb stroke rehabilitation in the presence of muscle fatigue,” Control Engineering Practice, vol. 31, pp. 63-72, 2014.
[71] M. T. Yan and Y. J. Shiu, “Theory and application of a combined feedback-feedforward control and disturbance observer in linear motor drive wire-EDM machines,” International Journal of Machine Tools and Manufacture, vol. 48, pp. 388-401, 2008.
[72] K. C. Yang and C. Hsieh, “Nanometer positioning of a dual-drive gantry table with precise yaw motion control,” Journal of Chinese Society of Mechanical Engineers, Vol. 36, No. 2, pp. 107-117, 2015.
[73] B. Yao, C. Hu, and Q. Wang, “An Orthogonal Global Task Coordinate Frame for Contouring Control of Biaxial Systems,” IEEE Transactions on Mechatronics, vol. 17, no. 4, pp. 1-13, 2011.
[74] M. F. Yeh and C. H. Tsai, “Standalone CMAC control system with online learning ability,” IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics, vol. 40, no. 1, pp. 43-53, 2010.
[75] S. S. Yeh and P. L. Hsu, “Estimation of the contouring error vector for the cross-coupled control design,” IEEE Transactions on Mechatronics, vol. 7, pp. 44-51, 2002.
[76] S. S. Yeh and P. L. Hsu, “Analysis and design of integrated control for multi-axis motion systems,” IEEE Transactions on Control Systems Technology, vol. 11, pp. 375-382, 2003.
[77] S. Zhao and Z. Gao, “An active disturbance rejection based approach to vibration suppression in two-inertia systems,” in Proceedings of American Control Conference (ACC), Cleveland, OH, June 30-July 2, 2010, pp. 1520-1525.
[78] Y. Zhao and S. Jayasuriya, “Feedforward controllers and tracking accuracy in the presence of plant uncertainties,” ASME Journal of Dynamic Systems, Measurement, and Control, vol. 117, pp. 490-495, 1995.
[79] J. M. Zurada, Introduction to Artificial Neural Systems: Singapore, 1992.