臺灣博碩士論文加值系統

CNC 工具機在加工時，由於工作物件的重量不定，且隨著切削作業而變化，加上切削量與工作物件材質的不同等因素，造成系統的慣性、阻尼與外力干擾等參數的不確定性，使得其控制器必須具備良好的強健性，方能滿足不同作業環境的需求，適應性控制對克服此一問題具有良好的效果。另外為求提高產品精度，改善輪廓誤差亦為一重要課題，交叉耦合控制 (CCC) 理論即是針對該問題而產生的，本研究提出一簡潔有效的輪廓誤差演算法，並簡化交叉耦合控制器的架構，使控制參數的調校更加容易，經實驗驗證本研究所提之演算法僅約為 Koren & Lo演算法的 1/13運算量及 Yeh & Hsu 的1/5，可以有效的減少系統的運算時間。另外再將其成功的與適應性控制結合，提出一交叉耦合適應性控制器 (CCAC)，該控制器具有良好的強健性及誤差改善的優異效果。經實驗結果顯示，在外力干擾下與同條件的 PI 控制器相比較，CCAC 在直線路徑下可將位置誤差 Max 及 Rms 分別減少到 41.44 % 及37.94 %，CCC 則為 98.8 % 及 98.89 %，而 CCAC 在輪廓誤差 Max 及 Rms能分別降低達 42.73 % 及 32.67 %，CCC 則為 70 % 及 59.69 %；在圓形路徑下 CCAC 可將位置誤差 Max 及 Rms 分別減少到 41.42 % 及 37.25 %，CCC 則為 98.32 % 及 97.6 %，而 CCAC 在輪廓誤差 Max 及 Rms 能分別降低達 37.56 % 及 27.42 %，CCC 則為 71.04 % 及 57.79 %。由以上實驗驗證可知 CCAC 的整體性能表現均優於 PI 與 CCC 控制器。

When a CNC machine tool is machining, there are some uncertainties of parameters and disturbances in system’s model due to the weight and material of workpiece and cutting rate are usually variant. Therefore the controller must be robust for such varying conditions. Adaptive control is suitable for that. Besides, to improve the machining precision, it’s essential to improve the contour errors, which is the main goal of the cross-coupling control (CCC). This research proposes a simple and effective contour-error algorithm to reduce the amount of computation to about 1/13 and 1/5 compare with Koren’s and Yeh’s work respectively. In addition to robustness, this research proposes cross-coupling adaptive control (CCAC) by combining above two controllers that could bring a significant improvement of tracking and contour errors. Compare with the PI controller under disturbance, the experimental results show that the CCAC can reduce the maximum and RMS of tracking errors to 41.44 % and 37.94 % respectively, while CCC can only reduce to 98.8 % and 98.89 % in linear contouring. For the maximum and RMS of contour errors, CCAC can reduce to 42.73 % and 32.67 % respectively, while CCC can only reduce to 70 % and 59.69 % in linear contouring. In circle contouring, CCAC can reduce the maximum and RMS of tracking errors to 41.42 % and 37.25 % respectively, while CCC can only reduce to 98.32 % and 97.6 %. For the maximum and RMS of contour errors, CCAC can reduce to about 37.56 % and 27.42 % respectively, while CCC can only reduce to 71.04 % and 57.79 %. The results show the superiority of CCAC.

中文摘要　 ------------------------------------------------------------------------------- i
英文摘要 ------------------------------------------------------------------------------- ii
誌謝 ------------------------------------------------------------------------------- iii
目錄 ------------------------------------------------------------------------------- iv
表目錄 ------------------------------------------------------------------------------- vii
圖目錄 ------------------------------------------------------------------------------- viii
符號說明 ------------------------------------------------------------------------------- xii
一、緒論 -------------------------------------------------------------------------------- 1
1.1 研究動機-------------------------------------------------------------------- 1
1.2 文獻回顧-------------------------------------------------------------------- 3
1.2.1 非耦合控制----------------------------------------------------------------- 3
1.2.1.1 PID控制-------------------------------------------------------------------- 4
1.2.1.2 前饋控制-------------------------------------------------------------------- 4
1.2.1.3 模糊邏輯控制-------------------------------------------------------------- 5
1.2.1.4 適應性控制----------------------------------------------------------------- 5
1.2.1.5 其它-------------------------------------------------------------------------- 6
1.2.2 交叉耦合控制-------------------------------------------------------------- 6
1.3 研究目的-------------------------------------------------------------------- 11
1.4 本文貢獻-------------------------------------------------------------------- 11
1.5 本文大綱-------------------------------------------------------------------- 12
二、交叉耦合適應性控制器設計-------------------------------------------------------- 14
2.1 系統建模-------------------------------------------------------------------- 14
2.1.1 建模實驗設計-------------------------------------------------------------- 15
2.1.2 數學模式的建立----------------------------------------------------------- 16
2.1.3 訊號擷取-------------------------------------------------------------------- 18
2.1.4 系統鑑別-------------------------------------------------------------------- 21
2.2 交叉耦合適應性控制器設計-------------------------------------------- 25
2.2.1 位置迴路控制器設計----------------------------------------------------- 25
2.2.2 交叉耦合控制器設計----------------------------------------------------- 29
2.2.2.1 直線輪廓誤差的演算法----------------------------------------------- 29
2.2.2.2 輪廓誤差的補償----------------------------------------------------------- 31
2.2.2.3 輪廓誤差演算法在曲線路徑的適用性----------------------------- 33
2.2.2.4 交叉耦合控制器設計----------------------------------------------------- 36
2.2.3 適應性控制器設計-------------------------------------------------------- 38
2.2.4 交叉耦合適應性控制器設計-------------------------------------------- 41
2.3 穩定性分析----------------------------------------------------------------- 43
2.3.1 交叉耦合控制器穩定性分析-------------------------------------------- 43
2.3.2 適應性控制器穩定性分析----------------------------------------------- 45
三、控制系統模擬-------------------------------------------------------------------------- 47
3.1 直線路徑模擬-------------------------------------------------------------- 49
3.2 直線路徑模擬數據分析-------------------------------------------------- 55
3.3 圓形路徑模擬-------------------------------------------------------------- 56
3.4 圓形路徑模擬數據分析-------------------------------------------------- 62
四、實驗驗證-------------------------------------------------------------------------------- 65
4.1 實驗系統架構介紹-------------------------------------------------------- 65
4.2 實驗結果與驗證----------------------------------------------------------- 68
4.2.1 輪廓誤差演算法的運算時間-------------------------------------------- 68
4.2.2 直線路徑實驗結果-------------------------------------------------------- 69
4.2.3 直線路徑實驗結果分析-------------------------------------------------- 76
4.2.4 圓形路徑實驗結果-------------------------------------------------------- 80
4.2.5 圓形路徑實驗結果分析-------------------------------------------------- 87
五、結論與未來展望----------------------------------------------------------------------- 92
5.1 結論-------------------------------------------------------------------------- 92
5.1.1 即時系統-------------------------------------------------------------------- 92
5.1.2 輪廓誤差演算法----------------------------------------------------------- 92
5.1.3 交叉耦合控制器架構----------------------------------------------------- 92
5.1.4 交叉耦合適應性控制器對誤差的改善-------------------------------- 93
5.1.5 交叉耦合適應性控制器的強健性-------------------------------------- 93
5.2 未來展望-------------------------------------------------------------------- 93
5.2.1 即時系統-------------------------------------------------------------------- 93
5.2.2 驅動器控制模式----------------------------------------------------------- 94
5.2.3 適應性控制----------------------------------------------------------------- 94
5.2.4 干擾-------------------------------------------------------------------------- 94
5.2.5 回饋系統-------------------------------------------------------------------- 94
參考文獻 -------------------------------------------------------------------------------- 95
附錄 核心程式碼----------------------------------------------------------------- 98

[1]Koren, Y., and Lo, C. C., 1992, “Advanced Controller for Feed Drivers”, Annals of the CIRP, Vol. 41, pp. 689-698.
[2]Tomizuka, M., 1987, “Zero Phase Error Tracking Algorithm for Digital Control”, ASME Transactions, Journal of Dynamic system, Measurement and Control, Vol. 109, pp. 65-68.
[3]Weck, M. and Ye, G., 1990, “Sharp Corner Tracking Using the IKF Control Strategy”, Annals of the CIRP, Vol. 39/1/1990, pp. 437-441.
[4]Larkin, L. I., 1985, “A Fuzzy logic Controller for Aircaft Flight control”, Industrial Applications of Fuzzy Control, M(ed.), pp. 87-103.
[5]Murakami, S., Takemoto, F., Fujimura, H., and Ide, E., 1989 “Weld-line Tracking Control of Arc Welding Robot Using Fuzzy Logic Controller”, Fuzzy Sets and Systems, Vol. 32, No. 2, pp. 221-238.
[6]Li, Y. F. and Lau C. C., 1989, “Development of Fuzzy Algorithms for Servo Systems” , IEEE Control Systems Magazine, Vol. 9, No. 3, pp. 65-72.
[7]Yeh, Z.-M., Tarng, Y. S., Lin, Y. S. , 1997, “Cross-coupled Fuzzy Logic Control for Multiaxis Machine Tools”, Mechatronics, Vol. 7, No. 8, pp. 663-681.
[8]Shin, D.-J., Ryu, H.-S., Huh, U.-Y., 2001 “Fuzzy Logic Control for the Contouring Accuracy of XY Position System”, IEEE International Symposium on Industrial Electronics, Vol. 2, pp. 1248-1252.
[9]Lin, F. J. and Lin, Y. S., 1999, “A Robust PM Synchronous Motor Driver with Adaptive Uncertainty Observer”, IEEE Trans. on Energy Conv., Vol. 14, No. 4, pp. 989-995.
[10]Zhang, H. J. and Landers, R. G., 2007, “Precision Motion Control Methodology for Complex Contours”, ASME Transaction, Journal of Manufacturing Science and Engineering, Vol. 129, pp. 1060-1068.
[11]Koren, Y., 1980, “Cross-coupled Biaxial Computer Control for Manufacturing Syetem”, ASME Transaction, Journal of Dynamic System, Measurement and Control, Vol. 102, No. 4, pp. 265-272.
[12]Kulkarni, P. K. and Srinivasan, K., 1990, “Cross-coupled Control of Biaxial Feed Drive Servomechanisms”, ASME Transactions, Journal of Dynamic systems, Measurement and Control, Vol. 112, No. 2, pp. 225-232.
[13]Koren, Y. and Lo, C. C., 1991, “Variable-gain Cross-coupling Controller for Contouring”, Annals of the CIRP, Vol. 104, pp. 371-374.
[14]Chen, B. C., Tibury, D. M and Ulsoy, S. G., 1998, “Modular Control for Machine Tool: Cross-coupling Control with Friction Compensation”, American Society of Mechanical Engineers, Dynamic Systems and Control Division (Publication) DSC, Vol. 64, pp. 455-462.
[15]Yeh, S. S. and Hsu, P. L., 2000, “A New Approach to Biaxial Cross-coupled Control”, IEEE International Conference on Control App., pp. 168-173.
[16]李文昊，2004，交叉耦合控制在輪廓誤差之改善，國立中山大學，碩士論文。
[17]陳蔚強，2005，基因演算法對工具機軌跡交叉耦合預補償控制法參數之最佳化，國立交通大學，碩士論文。
[18]李宜達，2007，控制系統設計與模擬，五版，全華書局。
[19]俞克維，2004，控制系統分析與設計-使用MATLAB，新文京開發書局。
[20]潘能煌等，2007，Visual C++ 2005，松崗書局。
[21]Natick, 2001, System Identification Toolbox － User’s Guide, Version 4, The MathWorks.
[22]R. Krishnan, 2001, Electric Motor Drivers. Modeling, Analysis and Control, Prentice Hall.
[23]Charles L. Phillips H. Troy Nagle, 1991, Digital Control System Analysis and Design, Version 2, Prentice Hall.
[24]Eronini Umez-Eronini, 1990, System Dynamics and Control, ITP Inc.
[25]Gang Tao, 2003, Adaptive control design and analysis, Wiley-Interscience.