摘要
CNC工具機要達到高速、高精度切削的目的，必須同時在切削方法、機構剛性、刀具、主軸轉速、進給速度以及運動控制等各方面，皆有性能上的突破。而傳統之間接機構，在進給速度上欲大幅提高極為不易，因此CNC工具機進給速度之提升已成為研發上極具關鍵性的問題。線性馬達以直接驅動方式作直線運動，由於沒有如齒輪、齒條、滾珠螺桿、聯軸器等傳動機構，因而可有效消除機構傳動所造成的定位控制問題，大幅度地提高其伺服性能。本論文研究重點，將由輕載、高速、高精度的線性馬達直接驅動應用場合切入，發展適用之線性伺服系統，並進行分析討論。概為兩大主題，一為針對週期性運動所進行之一系列重複控制理論推導及控制器設計；另一為多軸線性馬達之高速加工實驗台機之建構與同步運動控制系統建立。
在許多加工應用中，常需於有限行程中作連續性的週期運動。本論文首先針對線性馬達之週期運動特性，發展一具實用性之插入型 (plug-in type) 重覆控制理論，以減少系統穩態追蹤誤差。為提高控制器實用性，透過特定穩定度及追蹤性能要求，建立一套控制器參數設計流程。從模擬及實驗結果得知，當系統輸入一特定週期訊號，穩態追蹤誤差於第二週期收斂，收斂速度相當快。此外，亦藉由已設計之重覆控制系統的響應規格及輸入訊號的傅立葉頻譜分析，來估測穩態追蹤誤差的大小值及收斂速度。
在凸輪研磨加工應用中，為符合特定加工條件，凸輪需被操作在變轉速條件，這將使得輸入訊號變成所謂之時變週期訊號，即是位置或角度的週期訊號。因此，為降低時變週期訊號的追蹤誤差，本論文延伸前述的重覆控制理論，發展一新型重覆控制器，此控制器具線性時變特性，故稱為適應性的重覆控制器。
為驗證理論推導之正確性，本研究實際建構一多軸線性馬達之高速加工實驗機台，此龍門式結構的加工機，包括一雙平行之線性馬達系統 (Y軸)，及一橫跨於Y軸上之線性馬達的X軸。為符合高速高精密度追蹤要求，本系統採用一同步運動控制架構，針對平行線性馬達伺服系統，提出一同步運動控制架構，並應用於所建構之高速加工機，進行實測驗證。

ABSTRACT
One crucial component for high-speed machining applications is the development of machine tool feed drives and motion controls that are capable of fast and precise motion. Direct drive actuators, e.g., linear motors, possess advantages such as elimination of gear train problems and faster transient response and better tracking capabilities than conventional lead screw drives. Nevertheless, inefficient attention has been paid to this topic despite the above-mentioned benefits.
Therefore, this research investigates some control aspects of linear motors applied to machine tools in view of their great potential for the next generation machine tool feed drives. To construct a linear servo system, several control strategies of varying complexity are considered, which can be grouped into two major topics, i.e., the repetitive control and the synchronous control. The repetitive control is derived and employed particularly for occasions where periodic movement is applied, for example, the applications in manufacturing processes of semiconductor components or cam machining. A plug-in type repetitive controller is first derived, where tracking error analyses and time-varying periodic inputs are also considered. The synchronous control is considered as a novel technique herewith high-speed machine tools with two parallel linear servo drives can be achieved.
Experimental studies are conducted on a linear servo system to verify the performances of the control strategies, where the real-time control algorithms are implemented using a floating-point digital signal processor (DSP). The results show that the derived repetitive controllers effectively eliminate the steady-state tracking errors within few cycles. For the synchronous control, the results also confirm the performance of the parallel linear servo control system.

References
[1] M. Albert, “Reinventing the machine tool”, Modern Machine Shop, pp. 100-107, November 1994.
[2] D. M. Alter and T. C. Tsao, “Implementation of a direct drive linear motor actuator for dynamic control of the turning process,” Proceedings of American Automatic Control Conference, San Francisco, CA., June 1993.
[3] R. B. Aronson, “Attack of the linear motor,” Manufacturing Engineering, pp. 60-71, May 1997.
[4] P. Braembussche, J. Swevers, H. V. Brussel, and P. Vanherck, “Accurate tracking control of linear synchronous motor machine tool axes,” Mechatronics, vol. 6, no. 5, pp. 507-521, 1996.
[5] H. L. Broberg and R. G. Molyet, ”A new approach to phase cancellation in repetitive control,” Proceedings of the 29th IEEE IAS, pp. 1766-1770, 1994.
[6] Z. Cao and G. Ledwich, “Tracking variable periodic signals with fixed sampling rate,” Proceedings of the 40th IEEE Conference on Decision & Control, Orlando, Florida USA, December 2001.
[7] H. David, “Linear motors provide precise positioning,” Mechanical Engineering, pp. 70-74, Nov. 1988.
[8] H. Dotsch and H. Smakman, “Adaptive repetitive control of a compact disc mechanism,” Proceedings of the 34th Conference on Decision & Control, New Orleans, LA USA, December 1995.
[9] L. Feng, Y. Koren, and J. Broenstein, “Cross-coupling motion controller for mobile robots,” IEEE Transactions on Control Systems, pp. 35-43, December 1993.
[10] B. A. Francis and W. M. Wonham, ”The internal model principle for linear multivariable regulators,” Appl. Math. Opt., vol. 2, pp. 170-194, 1975.
[11] B. A. Francis, “A course in control theory,” Lecture Notes Control and Information Sciences, vol. 88, Springer Verlag Berlin, 1987.
[12] H. Haack and M. Tomizuka, “Zero phase error tracking algorithm for digital control,” ASME Journal of Dynamic Systems, Measurement, and Control, 113, pp. 6-10, 1991.
[13] S. Hara, Y. Yamammoto, T. Omata, and M. Nakano, ”Repetitive control system: a new type servo system for periodic exogenous signals,” IEEE Transactions on Automatic Control, vol. 33, no. 7, pp. 659-666, 1988.
[14] G. Hillerstrom, “On repetitive control,” PhD thesis, Control Engineering Group, Lulea University of Technology, Sweden, 1994.
[15] G. Hillerstrom and J. Sternby, ”Application of repetitive control to a peristaltic pump,” Proceedings of the Automatic Control Conference, pp. 136-140, 1993.
[16] T. Inoue, “Practical repetitive control system design,” Proceedings of the 29th Conference on Decision and Control, vol. 3, pp. 1673-1678, 1990.
[17] M. Ishida, S. Higuchi, and T. Hori, ”Reduction control of mechanical vibration of an induction motor with fluctuated torque load using repetitive controller,” Proceedings of IEEE International Conference on Industrial Technology, pp. 533-537, 1994.
[18] W. C. Johnson, K. Srinivasan, and P. Kulkarni, “Digital control algorithms for electromechanical machine tool feed drives,” Proceedings of the 12th North American Manufacturing Research Conference, Houghton, Michigan, pp. 447-453, 1984.
[19] T. Jolly, T. C. Tsao and J. Bentsman, ”Rejection of unknown periodic load disturbances in continuous steel casting process using learning repetitive control approach,” Proceedings of IEEE International Symposium on Intelligent Control, pp. 36-41, 1993.
[20] K. Kanzaki and N. Kobayashi, “Output of cam motion curve by DC servo motor (1st report) – application of inverse systems,” Journal of the Japan Society for Precision Engineering, vol.55, no.12, pp.2215-2221, Dec. 1989.
[21] K. Kanzaki and N. Kobayashi, “Output of cam motion curve by DC servo motor (2nd report) – residual vibrating characteristics of motor load,” Journal of the Japan Society for Precision Engineering, vol.57, no.11, pp.2023-2029, Nov. 1991.
[22] K. Kanzaki and N. Kobayashi, ”Output of cam motion curve by DC servo motor (3rd report)- position by poly-dyne motion curve,” Journal of the Japan Society for Precision Engineering, vol. 59, no. 1, pp. 107-112, 1993.
[23] C. Kempf, W. Messner, M. Tomizuka, and R. Horowitz, “A comparison of four discrete-time repetitive control algorithms,” Proceedings of the American Control Conference, Chicago, IL, June, vol. 4, pp. 2700-2704, 1992.
[24] F. Kobayashi, S. Hara, and H. Tanaka, ”Reduction of motor speed fluctuation using repetitive control,” Proceedings of the 29th CDC, pp. 1697-1702, 1990.
[25] Y. Koren, “Cross-coupled biaxial computer controls for manufacturing systems,” ASME Journal of Dynamic Systems, Measurement, and Control, vol. 102, pp. 265-272, 1980.
[26] P. K. Kulkarni and K. Srinivasan, “ Cross-coupled control of bi-axial feed drive servomechanism,” ASME Journal of Dynamic Systems, Measurement, and Control, vol.112, no. 2, 1990.
[27] M. Labarre and B. Schneider, “Electronic cams boost machine flexibility, productivity”, Power Transmission Design, vol.37, iss.3, pp.35-38, 1995.
[28] G. M. Lammers, “Linears lead in ultrasmooth motion,” Machine Design, pp.60-64, September 1994.
[29] H. C. Lee and G. J. Jeon, “A neuro-controller for synchronization of two motion axes,” International Journal of Intelligent Systems, vol. 13, pp. 571-586, 1998.
[30] Z. H. Luo and B. Mahawan, “Repetitive control of tracking systems with time-varying periodic references,” Proceedings of the 37th IEEE Conference on Decision & Control, Tampa, Florida, USA, Dec. 1998.
[31] G. W. McLean, “Review of recent progress in linear motors,” IEE Proceedings, Part. B, vol. 135, no. 6, pp. 380-416, Nov. 1988.
[32] A. E. Middleditch and F. W. Paul, “Dynamic performance of a computer numerical control system for multi-axis contouring machine tools,” ASME Winter Annual Meeting, Detroit, Mich., Paper no. 73-WA/Aut-13, 1973.
[33] A. N. Poo, J. G. Bollinger, and G. W. Younkin, “Dynamic errors in type-1 contouring systems,” IEEE Transactions on Industry Applications, vol. 1A-8, no. 4, pp. 471-484, 1972
[34] F. A. Rothbart, Cams-design, dynamics and accuracy, John Wiley and Sons, New York, 1956.
[35] P. Sarachik and J. R. Ragazzini, “A 2-dimensional feedback control system,” Transactions of the AIEE, vol. 76, part II, pp. 55-61, 1957.
[36] J. H. She and M. Nakano, “Elimination of position-dependent disturbances in constant-speed-rotation control systems,” Proceedings of the 35th Conference on Decision & Control, Kobe, Japan, December 1996.
[37] K. Srinivasan and F. R. Shaw, ”Analysis and design of repetitive control systems using the regeneration spectrum,” Transactions ASME, vol. 113, pp.113-217, 1991.
[38] D. Sun, H. N. Dong, and S. K. Tso, “Tracking stabilization of differential mobile robots using adaptive synchronization control,” Proceedings of IEEE International Conference on Robotics and Automation, 2002.
[39] D. Tesar and G. K. Matthew, The Dynamics Synthesis, Analysis, and Design of Modeled Cam Systems, Lexington Books, 1976.
[40] M. Tomizuka, J. S. Hu, and T. C. Chiu, “Synchronization of two motion control axes under adaptive feedforward control,” ASME Journal of Dynamic Systems, Measurement, and Control, vol. 114, no. 6, pp. 196-689, 1992.
[41] M. Tomizuka, T. C. Tsao, and K. K. Chew, ”Discrete-time domain analysis and synthesis of repetitive controllers,” Proceedings of the American Control Conference, vol. 2, Atlanta, Ga., pp. 860-886, June, 1988.
[42] M. Tomizuka, “Design of digital tracking controller for manufacturing applications,” Proceedings of the Symposium on Control Methods for Manufacturing Processes, ASME Winter Annual Meeting, Chicago, III, DSC vol. 9, pp. 71-78, 1988.
[43] M. C. Tsai and W. S. Yao, “Design of a plug-in type repetitive controller for periodic inputs“, IEEE Transactions On Control Systems Technology, vol. 10, no. 4, pp. 1-9, July 2002.
[44] M. C. Tsai and W. S. Yao, “Repetitive control design for linear servo systems,” Proceedings of the American Control Conference, San Diego, California, pp. 3728-3732, June 1999.
[45] M. C. Tsai and Y. H. Lee, “Tracking control of a software cam machining system”, ASME Journal of Dynamic System, Measurements and Control, vol.121, no.1, pp.729-7735, 1999.
[46] T. C. Tsao and M. Tomizuka, ”Adaptive and repetitive digital control algorithms for noncircular machining,” Proceedings of the American Control Conference, vol. 1, Atlanta, Ga., pp. 115-120, June, 1988.
[47] T. C. Tsao and Y. X. Qian, “An adaptive repetitive control scheme for tracking periodic signals with unknown period,” Proceedings of the American Control Conference, San Francisco, California, vol. 2, pp. 1736-1740, 1993.
[48] L. F. Yang and W. H. Chang, “ Synchronization of two-gyro precession under cross-coupled adaptive feedforward control,” Journal of Guidance, Control, and Dynamics, vol. 19, no. 3, pp. 534-539, 1996.