隨著電子產品的小型化與產品產量的要求，以致對加工速度有越來越快，而加工精度越來越精密的趨勢，所以在進給速度向上提高的過程中 同時提升追蹤過程之輪廓誤差精度已為現今刻不容緩的課題。
本論文內容可分為提高單軸追蹤精度與雙軸輪廓精度兩部分。在提高單軸追蹤精度上，提出以建摩擦力矩模型的方式補償摩擦力矩產生之干擾，再以適應性強健控制器消除系統其他干擾，並增加系統強健性與穩定性，最後以速度前餽控制器增加系統動態響應的速度，消除時間延遲效應，如此得到了單軸上最適當之控制器組合，可直接提升單軸追蹤精度，而間接提高輪廓精度。在提高輪廓精度上，以交叉耦合控制器的補償運算，來增加各軸之協調性，以降低輪廓誤差，並在如此控制器之組合下，提出以設計方式來設計交叉耦合控制器之參數，代替傳統以試誤法求取控制器參數的方法，可使輪廓精度再提高。
關於上述方法，在論文中除了以電腦模擬確定其可行性外，更以實驗證實其正確性。

As the electronic products are gotten smaller and the quantity of output is to be requested, the trend of the needs for speed and accuracy is more precise. Therefore, upgrading the speed and the accuracy of contour error on tracking control has become an important point.
This research is focus on the improvement of tracking error and contour error. In tracking error, we propose that the compensation of friction disturbance is by building friction model. And then adaptive robust controller is used to eliminate other disturbance. Finally, velocity feedforward controller is used to improve system dynamic response and to remove the effect of time delay. The combination of such controllers can improve tracking error directly and contour error indirectly. In contour error, we use cross-coupled controller to coordinate the motors and to reform contour error. On the association of such controllers, we propose the design method of cross-coupled controller, to replace the traditional way of try-and-error, and improving contour error again.
Finally, the above improving strategies are verified by the simulation and experimental results.

第一章 緒論 1
1.1 前言 1
1.2 動機 2
1.3 目的 3
第二章 文獻回顧 5
2.1 誤差定義 5
2.2 軌跡追蹤控制器 6
2.2.1 干擾與模型誤差控制器 7
2.2.2 時間延遲效應控制器 15
2.2.3 各軸間協調控制器 18
第三章 研究方法 20
3.1 系統分析 20
3.2 摩擦力矩補償器 24
3.3 適應性強健控制 29
3.4 前餽控制 36
3.5 交叉耦合控制 38
3.5.1 交叉耦合理論 38
3.5.2 交叉耦合控制架構 41
3.5.3 交叉耦合控制器之設計 42
第四章 模擬與實驗結果 48
4.1 實驗設備介紹 48
4.2 系統模型及參數量測 49
4.3 各控制器的參數值 50
4.4 軌跡追蹤模擬與實驗結果 53
第五章 結論 63
5.1 貢獻 63
5.2 未來研究方向 64
參考文獻 65

1.Armstrong H. B. and Dupont P. and Canudas D. W. C., “A Survey of Models, Analysis Tools and Compensation Methods for The Control of Machines with Friction”, Automatica, Vol. 30, No. 7, pp1083-1138
2.Astrom K. J. and Wittenmark B., Adaptive Control, second edition
3.Choi B. K. and Choi C. H. and Lim H., “Model-Based Disturbance Attenuation for CNC Machining Centers in Cutting Process”, IEEE/ASME Transactions on Mechatronics, Vol. 4 , No.2,1999, pp 157-168
4.Chuang H. Y. and Liu C. H., “Cross-Coupled Adaptive Feedrate Control for Multiaxis Machine Tools”, Journal of Dynamic Systems, Measurement, and Control-Transactions of the ASME, Vol. 113,1991, pp 451-457
5.Chuang H. Y. and Liu C. H., “A Model-Referenced Adaptive Control Strategy for Improving Contour Accuracy of Multiaxis Machine Tools”, IEEE Transactions on Industry Application, Vol. 28,1992, pp 221-227
6.Endo S. and Tomizuka M. and Hori Y., “Robust Digital Tracking Controller Design for High-speed Positioning System”, Proceedings of the American Control Conference, San Francisco, California, June 1993, pp 2494-2498
7.Funahashi Y. and Yamada M., “Zero Phase Error Tracking Controllers With Optimal Gain Characteristics”, Journal of Dynamic Systems, Measurement, and Control-Transactions of the ASME, Vol. 115,1993, pp 311-318
8.Guo L. and Tomizuka M., “High-Speed and High-Precision Motion Control with an Optimal Hybrid Feedforward Controller”, IEEE/ASME Transactions on Mechatronics, Vol. 02,1997, pp 110-122
9.Haack B. and Tomizuka M., “The Effect of Adding Zeroes to Feedforward Controllers”, Journal of Dynamic Systems, Measurement, and Control-Transactions of the ASME, Vol. 113,1991, pp 6-10
10.Lee H. S. and Tomizuka M., “Robust Motion Controller Design for High-Accuracy Positioning Systems”, IEEE Transactions on Industrial Electronics, Vol. 43, NO. 1, 1996, pp 48-55
11.Koren Y. and Lo Ch.-Ch. , “Variable-Gain Cross-Coupling Controller for Contouring”, Annals of the Crip, Vol. 40,1991, pp 371-374
12.Koren Y., “Cross-Coupled Biaxial Computer Control for Manufacturing Systems”, Journal of Dynamic Systems, Measurement, and Control-Transactions of the ASME, Vol. 102,1980, pp 265-272
13.Koren Y., “Control of Machine Tools”, Journal of Manufacturing Science and Engineering, Vol. 119, 1997, pp749-755
14.Koren Y., “Design of Computer Control for Manufactoring Systems”, Journal of Engineering For Industry, Vol. 101, 1979, pp326-331
15.Maosory O., “Improve Contouring Accuracy of NC/CNC System with additional Velocity Feed Forward Loop”, Trans. of the ASME Journal of Engineering for Industry, Vol. 108,1986, pp 227-230
16.Ohishi K. and Nakamura Y., “Robust Speed Servo System for Wide Speed Range Based on Instantaneous Speed Observer and Disturbance Observer”, AMC,96-MIE, 1996, pp 326-331
17.Slotine J. J. E. and Li W., Applied Nonlinear Control
18.Srinivasan K. and Tsao T. C., “Machine Tool Feed drives and Their Control-A Survey of the State of the Art”, Journal of Manufacturing Science and Engineering, Vol. 119, 1997, pp743-748
19.Srinivasan K. and Kulkarni P. K., “Cross-Coupled Control of Biaxial Feed Drive Servomechanisms”, Journal of Dynamic Systems, Measurement, and Control-Transactions of the ASME, Vol. 112,1990, pp 225-232
20.Suzuki A. and Tomizuka M., “Design and Implementation of Digital Servo Control for High Speed Machine Tools”, Proceeding of the 1991 American Control Conference, MA , pp. 1246-1251
21.Tomizuka M., “Zero Phase Error Tracking Algorithm for Digital Control”, Journal of Dynamic Systems, Measurement, and Control-Transactions of the ASME, Vol. 109,1987, pp 65-68
22.Tsao T. C. and Tomizuka M., “Adaptive Zero Phase Error Tracking Algorithm for Digital Control”, Journal of Dynamic Systems, Measurement, and Control-Transactions of the ASME, Vol. 109,1987, pp 349-354
23.Umeno T. and Hori Y., “Robust Speed Control of DC Servomotors Using Modern Two Degrees-of Freedom Controller Design”, IEEE Transactions on Industrial Electronics, Vol. 38, NO. 5, 1991, pp 363-368
24.Yamada K. and Komada S. and Ishida M. and Hori T., “Analysis of Servo System Realized by Disturbance Observer”, AMC,96-MIE, 1996, pp 338-343
25.Yao B., “High Performance Adaptive Robust Control of Nonlinear Systems: A General Framework and New Schemes”, Proceedings of the 36TH Conference On Decision & Control, 1997, pp 2489-2494
26.Yao B. and Al-Majed M. and Tomizuka M., “High-Performance Robust Motion Control of Machine Tools: An Adaptive Robust Control Approach and Comparative Experiments”, IEEE/ASME Transactions on Mechatronics, Vol. 2, NO. 2, 1997, pp 63-76
27.Yao B. and Tomizuka M., “Smooth Robust Adaptive Sliding Mode Control of Manipulators With Guaranteed Transient Performance”, Journal of Dynamic Systems, Measurement, and Control-Transactions of the ASME, Vol. 118,1996, pp 764-775
28.Yeh S. S. and Hsu P. L., “Theory and Applications of the Robust Cross-Coupled Control Design”, Journal of Dynamic Systems, Measurement, and Control-Transactions of the ASME, Vol. 121,1999, pp 524-529
29.高華隆, “DSP應用於兩軸伺服機構之交叉耦合路徑控制”, 碩士論文, 國立成功大學機械工程研究所, 民國八十三年
30.張志平, “兩軸進給驅動伺服機構用交叉耦合控制器的研製”, 碩士論文, 私立淡江大學機械工程研究所, 民國八十五年
31.張樹銘, ”高速軌跡追蹤控制實作”, 碩士論文, 國立中山大學機械工程研究所, 民國八十九年
32.郭一政, “交互型控制器在多軸路徑追蹤的應用”, 碩士論文, 國立成功大學機械工程研究所, 民國八十五年
33.陳金聖, “高速CNC工具機循徑運動控制的軌跡精度改進策略”, 博士論文, 國立交通大學機械工程研究所, 民國八十八年
34.葉賜旭, “改善CNC工具機運動輪廓精度的控制器設計策略”, 碩士論文, 國立交通大學控制工程研究所, 民國八十五年
35.劉瑞弘, “High Speed and Precision Position Control of a X-Y Table”, 碩士論文, 國立中山大學機械工程研究所, 民國八十八年