由於無刷直流馬達具有未知干擾之非匹配式不確定性的系統，所以傳統強健控制無法使用，如滑動控制(Sliding mode control)、PID。故本文提出一個多層滑動面控制器，並使用多層滑動面控制之概念來解決非匹配式不確定性的問題，以改善傳統強健控制之限制。首先，利用多層滑動控制器以改善未知干擾項對無刷直流馬達之影響。接著利用軌跡規劃之設計，使馬達達到期望之軌跡。本文透過多層滑動控制器與軌跡規劃之設計，並且加入不同之範例，以驗證控制器之強健性。由電腦模擬的結果顯示，本文所提出之控制法則對於無刷直流馬達的控制具有優良的工作性能表現。

In this paper, we consider the stabilization of a brushless DC motor subject to a time-varying payload which enters the system in a mismatched fashion. A multiple-surface sliding controller is proposed to deal with the uncertain payload so that good performance can be ensured. The Lyapunov stability method is employed to justify the closed loop stability. Simulation cases are given with satisfactory results.

[1]B. K. Bose, Modern Power Electronics and AC Drives,
Prentice Hall, NJ, 2002.
[2]T. Kenjo, Electric Motors and Their Controls, Oxford
Press, New York, 1991.
[3]D. W. Novotny and T. A. Lipo, Vector Control and
Dynamics of AC Drives, Oxford Press, 1996.
[4]H. Tajima and Y. Hori, “Speed sensorless field-
orientation control of the induction machine,” IEEE Transactions on Industry Applications, vol. 29, no. 1,
Jan. 1993.
[5]K. Y. Cheng, S. Y. Lin and Y. Y. Tzou, ”On-line auto-tuning of a DSP controlled BLDC servo drive,” IEEE Power Electronics Specialists Conference, vol. 3, 2001.
[6]H. K. Khalil, Nonlinear Systems, Prentice Hall, NJ, 1996.
[7]J.-J. E. Slotine and W. Li, Applied Nonlinear Control, Prentice Hall, NJ, 1991.
[8]K. H. Kim, I. C. Baik, S. K. Chung and M. J. Youn, “Robust speed control of brushless dc motors using adaptive input-output linearisation technique,” IEE Proceedings Electric Power Applications, vol. 144, no. 6,
Nov. 1997.
[9]J. S. Ko, Y. S. Jung, S. K. Kim and M. J. Youn, “MRAC load torque observer for position control of brushless dc motors,” International Journal of Electronics, vol. 80, 1996.
[10]J. S. Ko, “Asymptotically stable adaptive load torque observer for precision position control of BLDC motors,” IEE Proceedings Electric Power Applications, vol. 145, no. 4, July 1998.
[11]B. Terzic and M. Jadric, “Design and implementation of the extended Kalman filter for the speed and rotor position estimation of brushless dc motors,” IEEE Transactions on Industrial Electronics, vol. 48, no. 6,
Dec. 2001.
[12]C. Xia, J. Liu, W. Yu and Z. Li, “Variable structure control of BLDCM based on extended state observer,” IEEE International Conference on Mechatronics and Automation, 2005.
[13]H. Lin, W. Yan, J. Wang, Y. Yao and B. Gao, “Robust nonlinear speed control for a brushless dc motor using model reference adaptive backstepping approach,” IEEE Proceedings of International Conference on Mechatronics and Automation, Aug. 2009.
[14]T. L. Chern, J. Chang and G. K. Chang, “DSP-based integral variable structure model following control for brushless dc motor drivers,” IEEE Transactions on Power Electronics, vol. 12, no. 1, Jan. 1997.
[15]H. Fakham, M. Djemai and K. Busawon, “Design and practical implementation of a back-emf sliding-mode observer for a brushless dc motor,” IET Electric Power Application, vol. 2, no. 6, pp. 353-361, 2008.
[16]Z. Chen, M. Tomita, S. Doki and S. Okuma, “New adaptive sliding observers for position and velocity-sensorless controls of brushless dc motors,” IEEE Transactions on Industrial Electronics, vol. 47, no. 3, June 2000.
[17]G. Cai, K Qian, B Li and X. Pang, “Robust PID controller in brushless dc motor applications,” IEEE International Conference on Control and Automation, May 2007.
[18]K. K. Shyu, C. K. Lai, Y. W. Tsai and D. I. Yang, ”A newly robust controller design for the position control of permanent-magnet synchronous motors,” IEEE Transactions on Industrial Electronics, vol. 49, Jun. 2002.
[19]S. K. Chung, J. H. Lee, J. S. Ko and M. J. Youn, “Robust control of brushless direct-drive motor using integral variable structure control,” Proceedings of IEE Electric Power Applications, vol. 142, Nov. 1995.
[20]H. Hashimoto, H. Yamamoto, S. Yanagisawa and F. Harashima, “Brushless servo motor control using variable structure approach,” IEEE Transactions on Industry Applications, vol. 24, no. 1, Jan. 1988.
[21]A. Sabanovic and F. Bilalovic, “Sliding mode control of ac drives,” IEEE Transactions on Industry Applications, vol. 25, Jan. 1989.
[22]M. Won and J. K. Hedrick, “Multiple-surface sliding control of a class of uncertain nonlinear systems,” International Journal of Control, vol. 64, no. 4, pp. 693-706, 1996.
[23]黃仲欽，｢電機機械理論｣，課程講義，2010。
[24]B. K. Bose, Power Electronics and AC Drives, Prentice Hall, NJ, 1986.
[25]B. K. Bose, Power Electronics and Variable Frequency Drives, IEEE press, New York, 1997.
[26]R. Krishnan and P. Pillay, “Modeling, simulation, and analysis of permanent-magnet motor drives. Ⅱ. The brushless dc motor drive,” IEEE Transactions on Industry Applications, vol. 25., no. 2., April 1989.
[27]P. C. Krause, O. Wasynczuk, and S. D. Sudhoff, Analysis of Electric Machinery and Drive Systems, Wiley-Interscience, 2002.
[28]C. M. Ong, Dynamic Simulation of Electric Machinery, Prentice Hall, NJ, 1998.
[29]R. Krishnan and P. Pillay, “Modeling, simulation, and analysis of permanent-magnet motor drives. Ⅱ. The brushless dc motor drive,” IEEE Transactions on Industry Applications, vol. 25., no. 2., April 1989.
[30]P. C. Krause, Analysis of Electric Machinery, McGraw Hill, 1986.
[31]R. H. Park, “Two-reaction theory of synchronous machines-Ⅱ,” Transactions of American Institute of Electrical Engineers, vol. 52, June 1933.
[32]R. H. Park, “Two-reaction theory of synchronous machines- generalized Method of analysis- Part Ⅰ,” Transactions of American Institute of Electrical Engineers, vol. 48, June 1929.
[33]V. I. Utkin, Sliding Modes and Their Application in Variable Structure Systems, MIR Publisher, Moscow, 1978.
[34]R. A. Decarlo, S. H. Zak and G.. P. Matthews, “Variable structure control of nonlinear multivariable systems: a tutorial,” IEEE Proceedings, vol. 76, no. 3, pp. 212-232, 1988.
[35]J. Y. Hung, W. B. Gao and J. C. Hung, “Variable structure control: a survey,” IEEE Transactions on Industry Electronics, vol. 40, no. 1, pp. 1-22, 1993.
[36]黃安橋，｢適應性控制理論｣，課程講義， 2008。
[37]黃安橋，｢非線性控制系統｣，課程講義，2009。
[38]J. J. Craig, Introduction to Robotics Mechanics and Control, Prentice Hall, 2005.
[39]dsPICDEMTM MCLV Development Board User‘s Guide, Microchip Technology Inc., 2008.