中 文 摘 要

近幾年來，高性能數控工具機（CNC）的發展一直受到工業界的重視，主要訴求是其運動控制器要能夠實現高精密度與高速度的加工方式。有鑑於此，本論文提出摩擦力前饋補償器及命令前饋控制器，以期達成高加工速度與高加工精度之目標。本研究首先針對由滾珠螺桿所組成之實驗平台進行摩擦力鑑別實驗，並採用Karnopp模型近似。再根據所求得之近似摩擦力模型，提出摩擦力前饋補償器，以消除因摩擦力所導致之加工誤差。此外本研究使用前加減速規劃與速度命令前饋控制器，用以降低輪廓誤差及因伺服落後所產生之循跡誤差。本研究之所有實驗皆以DSP運動控制卡作即時實現。實驗結果顯示，在同一實驗平台且高速進給時，本論文所提之控制架構比一般控制架構能獲得更高之精密度。

ABSTRACT
Recently, the developments of high-performance CNC machines have attracted much attention from the industry. The main concern is that the motion controllers of CNC machine tools must be capable of achieving high speed and highly accurate machining. Hence, the aim of this thesis is to develop appropriate servo control structures such that the goal of high speed and highly accurate machining can be achieved. In this study, an experiment is first conducted to identify the friction disturbance model of a two-axis ball-screw table, in which the Karnopp model is used to approximate the actual friction disturbance. Then, based on the approximate friction model, a friction disturbance feed-forward compensator is proposed to reduce the machining error due to friction disturbance. In addition, “motion planning before interpolation” and a command feed-forward controller are employed to reduce the contouring error and the tracking error resulting from the servo lag. All the experiments conducted in this study are implemented using DSP-based motion card. According to the experimental results, it is found that the proposed servo control structure exhibits better performance than the conventional ones.

參考文獻

[1] C. D. Walrath, “Adaptive Bearing Friction Compensation based on Recent Knowledge of Dynamic Friction,” Automatica, Vol. 20, No. 6, pp. 717-727, 1984.
[2] D. Karnopp, “Computer Simulation of Slip-Stick Friction in Mechanical Dynamic Systems,” ASME Journal of Dynamic Systems, Measurement and Control, Vol. 107, pp. 100-103, 1985.
[3] B. Armstrong, “Friction：Experimental, Modeling and Compensation,” IEEE International Conference on Robotics and Automation, Philadelphia, PA, pp. 1422-1427, 1988.
[4] D. Haessig and B. Friedland, “On the Modeling and Simulation of Friction,” Amer. Contr. Conf., San Diego, CA, pp. 1256-1261, 1990.
[5] C. Canudas de Wit, H. Olsson, K. J. Åström, and P. Lischinsky, “A new Model for Control of Systems with Friction,” IEEE Transactions on Automatic Control, Vol. 40, No. 3, pp. 419-425, 1995.
[6] B. Armstrong-Hélouvry, P. Dupont, and C. Canudas de Wit, “A Survey of Models, Analysis Tools and Compensation Methods for Control of Machines with Friction,” Elserver Science Ltd. Survey paper of Automatica, Vol. 30, No. 7, pp. 1083-1138, 1994.
[7] M. Gafvert, “Comparisons of Two Dynamic Friction Models,” Proc. of the 1997 IEEE International Conf. On Control Applications, pp. 386-391, 1997.
[8] R. Kelly and J. Liamas, “Determination of Viscous and Coulomb Friction by Using Velocity Responses to Torque Ramp Inputs,” Proc. Of the 1999 IEEE International Conf. Of Robotics and Automation, pp. 1740-1745, 1999.
[9] A. Suzuki and M. Tomizuka, “Design and Implementation of Design Servo Controller for High Speed Machine Tools,” Proc. 1991 American Control Conference, pp. 1246-1251, 1991.
[10] B. Li, D. Hullender, and M. Direnzo, “Nonlinear Induced Disturbance Rejection in Inertial Stablization Systems,” IEEE Transactions On Control Systems Technology, Vol. 6, No. 3, 1998.
[11] H. Du and S. S. Nair, “Identification of Friction at Low Velocities Using Wavelet Basis Function Network,” Proc. 1998 American Control Conference, Philadelphia, Pennsylvanis, pp. 1918-1922, 1998.
[12] H. Du and S. S. Nair, “Modeling and Compensation of Low-Velocity Friction with Bounds,” IEEE Transactions On Control Systems Technology, Vol. 7, No. 1, pp.110-121, 1999.
[13] 陳國禎，精密線性馬達定位台之導軌摩擦力補償，碩士論文，國立中正大學機械工程系，2000年。
[14] S. Cong, “Two Adaptive Friction Compensations for DC Servomotors,” IEEE International Conference on Industrial Technology, pp. 113-117, 1996.
[15] S. W. Lee and J. H. Kim, “Robust Adaptive Stick-Slip Friction Compensation,” IEEE Transactions on Industrial Electronics, Vol. 42, No. 5, pp. 474-479, 1995.
[16] P. Yang and J. S. Chu, “Adaptive Velocity Control of DC motor with Colomb Friction Identification,” Journal of Dynamic Systems, Measurement and Control, Vol. 115, 1993.
[17] Y. S. Tarng and H. E. Cheng, “An Investigation of Stick-Slip Friction on the Contouring Accuracy of CNC Machine Tools,” Int. J. Mach. Tools Manufact. , Vol. 35, No. 4, pp. 565-576, 1995.
[18] S. Yang and M. Tomizuka, “Adaptive Pulse Width Control for Precise Positioning under the Influence of Stiction and Coulomb Friction,” Transactions of the ASME Journal of Dynamic Systems, Measurement and Control, Vol. 110, pp. 221-227, 1988.
[19] S. Lee and M. Tomizuka, “Robust Motion Controller designed for High-Accuracy Position System,” IEEE Transactions on Industrial Electronics, Vol. 43, No. 1, pp. 48-55, 1996.
[20] J. Li, L. Alvarez, and R. Horowitz, “Adaptive Emergency Braking Control With Underestimation of Friction Coefficient,” IEEE Transactions on Control Systems Technology, Vol. 10, No. 3, pp. 381-392, 2002.
[21] E. D. Tung, G. Answar, and M. Tomizuka, “Low Velocity Friction Compensation and Feedforward Solution Based on Reptitive Control,” ASME Journal of Dynamic Systems, Measurement and Control, Vol. 115, pp. 279-284, 1993.
[22] M. Tomizuka, T. C. Tsao, and K. K. Chew, “Analysis and Sythesis of Discrete-Time Reptitive Controllers,” ASME Journal of Dynamic Systems, Measurement and Control, Vol. 111, pp. 353-358, 1989.
[23] M. Tomizuka, “Zero Phase Error Tracking Algorithm for Digital,” Journal of Dynamics System Measurements and Control, Vol. 109, pp.65-68, 1987.
[24] M. Weck and G. Ye, “Sharp Corner Tracking Using the IKF Control Strategy,” CIRP Annals, Vol.39, No.1, pp. 437-441, 1990.
[25] O. Masory, “Improving Contouring Accuracy of NC/CNC Systems with Additional Velocity Feedforward Loop,” Trans. Of ASME journal of Engineering for Industry, Vol. 108, pp. 227-230, 1986.
[26] C. S. Chen and A. C. Lee, “New Direct Velocity and Acceleration Feedforward Tracking Control in a Retrofitted Milling Machine,” Int. J. Japan Soc. Prec. Eng., Vol. 33, No. 3, pp.178-184, 1999.
[27] A. Tustin, “The Effects of Backlash and of Speed-Dependent Friction on the Stability of Closed-Cycle Control Systems,” J. of the Institution of Electrical Engineers, Vol. 94, No. 2, pp. 143-51, 1947.
[28] 胡景文，五軸同動之動態輪廓誤差模型建立與分析，碩士論文，國立中正大學機械工程系，2000年。
[29] C. Canudas de Wit and V. Seront, “Robust Adaptive Friction Compensation,” IEEE International Conference on Robotics and Automation, Cincinnati, OH, Vol. 2, pp. 1383-1388, 1990.
[30] C. Canudas de Wit, P. Noel, A. Aubin, B. Brogliato, and P. Drevet, “Adaptive Friction Compensation In Robot Manipulators：Low-Velocities,” IEEE International Conference on Robotics and Automation, Scottsdale, Arizona, U.S.A., pp. 1352-1357, 1989.
[31] 林恆安，運動控制系統之摩擦力即時補償，碩士論文，國立中華大學電機工程學系，1999年。
[32] 黃基育，應用自我調整之適應控制於運動控制系統之摩擦力補償之研究，碩士論文，國立中華大學電機工程學系，2001年。
[33] R. H. Brown, S. C. Schneider, and M. G. Mulliden, “Analysis of Algorithms for Velocity Estimation from Discrete Position Versus Time Data,” IEEE Trans. On Industrial Electronics, Vol.39, No.1, 1992.
[34] B. C. Kuo, Automatic Control Systems, Prentice Hall International, 1991.
[35] 高智賢，PC-Based自調式多軸伺服系統之研發，碩士論文，國立成功大學機械工程學系，1996年。
[36] 胡國清，機電控制工程理論與應用基礎，機電工業出版社，1997年。
[37] P. C. Parks and V. Hahn, Stability Theory, Prentice Hall International, 1993.
[38] M. V. Kothare, P. J. Campo, M. Morari, and C. N. Nett, “A Unified Framework for the Study of Anti-Windup Designs,” Automatica, 30, pp. 1869-1883, 1994.
[39] 洪明諒，高速高精度CNC工具機之前饋控制，碩士論文，國立清華大學動力機械系，2000年。
[40] R. Hanus, M. Kinnaert, and J. L. Henrotte, “Conditioning Technique, a General Anti-windup and Bumpless Transfer Method,” Automatica, 23, pp. 729-739, 1987.
[41] I. Horowitz, “A Synthesis theory for a Class of Saturating Systems,” Int. J. Control, Vol. 38, No. 1, pp. 169-187, 1983.
[42] W. Wu and S. Jayasuriya, “Controller Design for a Nonovershooting Step Response With Saturating Nonlinearities,” Proceedings of American Control Conference, San Diego, California, pp. 3046-3050, 1999.
[43] 莊宏祥，伺服控制系統之強健設計與實現，博士論文，國立成功大學機械工程學系，2001年。
[44] 郭倫毓,陳正裕,張永峰 “控制器的新架構及性能改善研究” 機械工業雜誌, pp. 149-162, 2000年。
[45] 孫金柱，張昭琳〝CNC控制器的加減速法則〞機械工業雜誌，p.131~144，1999年。
[46] J. S. PARK, “Motion Profile Planning of Repetivite Point-to-Point Control for Maximun Energy Conversion Efficiency Under Acceleration Conditions,” Mechatronics Vol.6, No.6, pp. 649~663, 1996.
[47] D. I. Kim, J. I. Song and S. Kim, “Dependence of Maching Accuracy on Acc/Dec and Interpolation Methods in CNC Machine Tools,” IEEE-ISA Annual Meeting, vol.3, pp.1898-1905, 1994.
[48] D. I. Kim, “Study on Interpolation Algorithms of CNC Machine Tools,” IEEE-ISA Annual Meeting, vol.3, pp. 1930-1937, 1995.
[49] C. S. Chen and A. C. Li, “Design of acceleration/deceleration profiles in motion control based on digital FIR filters,” International Journal of Machine Tools and Manufacture, pp. 799-825, 1998.
[50] 郭洲成，CNC伺服控制器之NURBS即時插值器設計與實現，碩士論文，國立成功大學機械工程系，2000年。
[51] FAUNC Corp., FANUC AC Servo Amplifier-Maintenance Manual, 6th edition, 1991.