臺灣博碩士論文加值系統

本論文針對一具有未知時變參數並且持續受到外在環境干擾之磁浮系統，提出一適應控制器，其係利用函數近似法(Function Approximation Technique, FAT)將系統之未知時變參數以有限項的正規直交函數近似，並配合Lyapunov法則來證明系統的穩定性，以改善傳統適應控制必須假設未知參數為常數及強健控制需確切知道系統未知項邊界值的限制。此外，經由實驗結果與PID控制器的比較，可得到良好的追蹤性能。

In this paper, a function approximation based adaptive controller is designed to a magnetic levitation system. The system dynamics is assumed to be with time-varying uncertainties so that traditional adaptive controllers fail. The proposed controller uses function approximation technique to represent those uncertainties as finite combinations of the basis functions. A Lyapunov function candidate is then designed to find update laws to the coefficients of the approximating series. Experimental results are performed to test its feasibility, and good results are obtained.

中文摘要……………………………………………………………………………………Ⅰ
英文摘要……………………………………………………………………………………Ⅱ
誌謝…………………………………………………………………………………………Ⅲ
目錄…………………………………………………………………………………………Ⅳ
圖表索引……………………………………………………………………………………Ⅴ

第一章 緒論………………………………………………………………………………1
第二章 一維磁浮系統之數學模型建立…………………………………………………3
2.1 電磁力之推導……………………………………………………………………3
2.2 一維磁浮系統之動態方程式推導………………………………………………7
第三章 控制器設計………………………………………………………………………9
3.1 適應多面滑動控制器之設計……………………………………………………9
3.2 適應律設計及穩定度分析………………………………………………………13
第四章 實驗設備…………………………………………………………………………17
4.1 實驗架構及實驗設備的詳細資料………………………………………………17
4.2 磁浮定子之設計…………………………………………………………………20
第五章 實驗結果…………………………………………………………………………21
第六章 結論………………………………………………………………………………33
參考文獻………………………………………………………………………………………34
作者簡介………………………………………………………………………………………37

[1] A. Charara, J. D. Miras and B. Caron, “Nonlinear Control of a Magnetic Levitation System without premagnetization,” IEEE Trans. On Control Systems Technology, pp. 513-523, 1996.

[2] P. K. Sinha, A. N. Pechev, “Model Reference Adaptive Control of a Maglev System with Stable Maximum Descent Criterion,” Automatica , Vol. 35, pp. 1457-1465, 1999.

[3] Z.-J. Yang, K. Miyazaki, S. Kanae and K. Wada, “Robust Position Control of a Magnetic Levitation System via Dynamic Surface Control Technique,” IEEE Trans. On Industrial Electronics, Vol. 51, No. 1, 2004.

[4] S. Mittal and C.-H. Menq, “Precision Motion Control of a Magnetic Suspension Actuator Using a Robust Nonlinear Compensation Scheme,”IEEE/ASME Trans. On Mechatronics, Vol. 2, No. 4, 1997.

[5] P. K. Sinha and A.N. Pechev, “Nonlinear Controllers for Electromagnetic Suspension Systems,”IEEE Trans. On Automatic Control, Vol. 49, No. 4, 2004.

[6] M. S. de Queiroz and D. M. Dawson, “Nonlinear Control of Active Magnetic Bearings：A Backstepping Approach,”IEEE Trans. On Control Systems Technology, Vol. 4, No. 5, 1996.

[7] J. D. Lindlau and C. R. Knospe, “Feedback Linearization of an Active Magnetic Bearing With Voltage Control,”IEEE Trans. On Control Systems Technology, Vol. 10, No. 1, 2002.

[8] G. D. Buckner, “Intelligent Bounds on Modeling Uncertainty：Applications to Sliding Mode Control,”IEEE Trans. On System, Man and Cybernetics-Part C：Applications and Reviews, Vol. 32, No. 2, 2002.

[9] D. L. Trumper, S. M. Olson and P. K. Subrahmanyan, “Linearizing Control of Magnetic Suspension Systems,” IEEE Trans. On Control Systems Technology, Vol. 5, pp. 427-438, 1997.

[10] A. C. Huang and Y. C. Chen,“Adaptive Sliding Control for Single-Link Flexible-Joint Robot with Mismatched Uncertainties,”IEEE Trans. On Control Systems Technology, Vol. 12, No. 5, 2004.

[11] S. Joo and J. H. Seo, “Design and Analysis of the Nonlinear Feedback Linearizing Control for an Electromagnetic Suspension System,”IEEE Trans. On Control Systems Technology, Vol. 5, No. 1, 1997.

[12] M. Fujita, T. Namerikawa, F. Matsumura and K. Uchida, “ -synthesis of an Electromagnetic Suspension Systems,” IEEE Trans. On Automatic Control, Vol. 40, No. 3, pp. 530-536, 1995.

[13] 郭有順,“不確定時變系統之適應控制研究”, 國立台灣科技大學機械工程技術研究所, 博士學位論文, 2002.

[14] 黃安橋,“適應性控制理論” 上課筆記, 2003.

[15] J. J. E. Slotine and W. Li, Applied Nonlinear Control, Prentice Hall, pp. 122-125, 1991.

[16] 洪紹剛, “智慧型磁浮模組之設計與特性研究” , 國立臺灣大學機械工程學研究所 , 碩士學位論文 , 2000
[17] 涂文超,“磁浮系統之製作分析與強健控制器之設計” , 國立成功大學 ,碩士學位論文 ,1996
[18] P. Poramate, R. Vanchai, “Nonlinear Backstepping Control Design Applied to Magnetic Ball Control,” TENCON 2000. Proceedings. Vol 3, 24-27 , pp 304 - 307, 2000.
[19]A. E. Fitzgerald, C. Kingsley, Jr., S. D. Umans, Electric Machinery, 5th ed , NewYork：McGraw-Hill , 1990.
[20]M. Won and J. K. Hedrick, “Multiple-surface sliding control of a class of uncertain nonlinear systems,” Int. J. of Control, vol.64, No. 4, pp. 693-706, 1996
[21]Hajjaji and Ouladsine, “Modeling and Nonlinear Control of Magnetic Levitation Systems,” IEEE Trans. On Industronics, Vol. 48, No. 4, 2001.

[22]C.Y. Kim and K.H. Kim, “Gain scheduled control of magnetic suspension systems,” in proc. IEEE CCA , pp. 3127-3131, 1994
[23]Lairi and G. Bloch, “Neural control of Maglev systems,” in Proc. MCEA’s98, Sept. 1998, pp 472-475, 1999
[24] D. G. Fink and H. W. Beaty , Standard Handbook for Electrical Engineers, 12ed, McGraw-Hill, pp. 4-74