多軸馬達系統的循跡運動為現代電腦數值控制之工具機中相當重要的應用，並且廣泛使用於各類型加工機具上。因此，如何降低循跡運動過程之追蹤誤差與輪廓誤差即為提升循跡精度的首要課題。一般而言，於馬達控制器之設計多半採用PID控制器，優點為設計簡單且參數容易調整。然而，在實作上則需要針對實際系統之特性及變化，時常調整其控制器參數，且參數易受外在環境影響。為解決上述問題，本論文選擇使用模型預測控制(Model Predictive Control)，藉由其移動時域(Preceding Horizon)最佳化，即時補償誤差量，並利用受控系統的二階近似模型建立預測模型，再透過參數搜尋法則，如：基因演算法，求其最佳控制參數組合。此外，為解決循跡運動中所產生之週期性干擾，本論文使用反覆學習控制架構修改命令軌跡以減少輪廓誤差指標。實驗結果顯示，本論文透過模型預測控制結合反覆學習控制之控制架構，能夠有效降低循跡運動中產生的追蹤誤差及輪廓誤差。

Multi-axis contour following is one of the most important applications in nowadays CNC machine tools, and is widely seen in various types of industrial machineries. The primary objective of a multi-axis motion controller is to increase the accuracy of contour following by decreasing its tracking error and contour error. In general, most existing commercial motion controllers are designed by using the concept of PID control due to the advantages such as “easy to design” and “easy to adjust parameters”. However, the control parameters are constantly modified because of the characteristic/change in the practical system. Furthermore, the parameters are easily affected by the environment. To solve the problem mentioned above, the thesis uses model predictive control (MPC) to compensate the errors in real time by optimizing the preceding horizon, and uses a second order system model to construct predictive models. In addition, an evolution computation technique -genetic algorithm, is used to find the optimal combination of control parameters. In addition, the thesis employs a command-based iterative learning controller (ILC) to modify tracking commands in order to improve contouring accuracy. The command-based ILC is used to cope with the periodic disturbance encountered during contour following. Experimental results indicate that the combination of MPC and ILC proposed in this thesis can effectively reduce contour error and tracking error of contour following tasks.

[1] Arimoto S, Kawamura S and Miyazaki F, “Bettering operation of robots by learning,”Journal of Robotic Systems., vol.1, no.2, pp.123-140, 1984.
[2] Bristow D.A, Tharayil M and Alleyne A.G., “A survey of iterative learning control,” IEEE Control Systems Magazine, vol.26, no.3, pp.96-114, 2006.
[3] 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, pp. 511-518, 2006.
[4] J.A. Rossiter, Model-based Predictive Control: a Practical Approach, CRC, 2003.
[5] 邱曉惠，基於串級控制的預測控制算法分析與研究，碩士論文，南京信息工程大學電氣工程學系，2007年。
[6] 張日東，非線性預測控制及應用研究，博士論文，浙江大學控制科學與工程學系，2007年。
[7] 盧俊男，模型預測控制設計及於雙線性伺服系統之應用，碩士論文，國立成功大學機械工程學系，2008年。
[8] L. Wang, Model Predictive Control System Design and Implementation Using MATLAB, Springer, 2009.
[9] H.-S. Ahn, Y. Chen, and K. L. Moore, "Iterative learning control: brief survey and categorization," IEEE Transactions on Systems Man and Cybernetics part C Applications and Reviews, vol. 37, pp. 1099-1121, 2007.
[10] D. A. Bristow, M. Tharayil, and A. G. Alleyne, "A survey of iterative learning control," Control Systems, IEEE, vol. 26, pp. 96-114, 2006.
[11] K. H. Su , M. Y. Cheng , H. R. Chen, and Y. C. Chang, "Iterative Learning Control-based Tracking Error and Contour Error Compensations for Biaxial Contouring Control Systems," in Proceedings of the 5th International Conference on Positioning Technology, pp. 107-110, 2012.
[12] R. W. Longman, "Iterative learning control and repetitive control for engineering practice," International Journal of Control, vol. 73, pp. 930-954, 2000.
[13] J. S. Lu, M. Y. Cheng, L. W. Cheng, H. R. Chen, K. H. Su, M. C. Tsai, "Tension Control Improvement in Automatic Stator In-Slot Winding Machines Using Iterative Learning Control," in Proceedings of the International Conference on Information Science, Electronics and Electrical Engineering, vol. 3, pp. 1643-1647, 2014.
[14] L. Piegl, "On NURBS: a survey," IEEE Computer Graphics and Applications, vol. 11, pp. 55-71, 1991.
[15] 陳泓睿，參數式曲線之輪廓誤差估測研究，碩士論文，國立成功大學電機工程學系，2014。
[16] 李政謙，基於改良式切線輪廓誤差之伺服控制器設計與實現，碩士論文，國立成功大學電機工程學系，204。
[17] C. T. Johnson and R. D. Lorenz, "Experimental identification of friction and its compensation in precise, position controlled mechanisms," IEEE Transactions on Industry Applications , vol.28, , pp.1392-1398, 1992
[18] 廖兼賢，以離散位置資訊作速度與加速度估測之研究，碩士論文，國立成功大學電機工程學系，2004。
[19] 劉叡明，伺服馬達低轉速控制改善之研究，碩士論文，國立成功大學電機工程學系，2008。