臺灣博碩士論文加值系統

傳統系統鑑別的方法，大多是在時域或頻域裡，對於量測訊號之分析而進一步作系統鑑別。 近幾年來，發展出許多使用時-頻域技巧：小波分析於系統鑑別領域的技術。 本論文旨在提出一利用Daubechies小波函數展開之系統鑑別理論，來鑑別出主動式四極磁浮軸承系統運動方程式之參數。 鑑別過程則是利用Daubechies小波基底展開系統運動方程式，並且在對應之子空間利用最小誤差平方觀念求解，同時與特徵系統實現運算法作一比較。 本文所提出之鑑別法則，藉由數值模擬與實際之系統，驗證其可行性。 本研究所使用之測試設備是以dSPACE DS-1104為主體所建立並且搭配MATLAB/Simulink程式語言。 由數值模擬及實驗結果可知：本論文所提出之小波鑑別理論具有較佳之收斂性及準確性。

Most traditional methods in system identification are based on the analysis of measured signal in either time or frequency domain. In recent years, some technologies in time-frequency domain which utilize wavelet analysis in the context of system identification were developed. The purpose of this thesis is to develop an algorithm based upon Daubechies wavelet expansions to identify unknown system parameters of the 4-pole active magnetic bearing systems (AMBs). The procedure stems from the equation of motion obtained by Daubechies wavelet and means of Least Squared Method. The wavelet identification method is compared with another populary-used method: Eigensysem Realization Algorithm (ERA). The proposed algorithms were examined by numerical simulations and experiments. The test rig is equipped with dSPACE DS-1104 and MATLAB/Simulink. The results of numerical simulations and experiments verify that the Wavelets System Identification Method has better efficacy in convergence and accuracy.

中文摘要 I
英文摘要 II
致謝 III
目錄 IV
表目錄 VII
圖目錄 VIII

第一章 緒論 1

第二章 鑑別理論介紹 6
2.1 特徵系統實現運算法 6
2.1.1 系統馬可夫參數 7
2.1.2 特徵系統實現 8
2.2 小波理論概述 13
2.2.1 多尺度解析 13
2.2.2 Daubechies尺度函數 19
2.2.3 Daubechies尺度函數及小波函數之導函數 23
2.2.4 Daubechies尺度函數之動量值 25
2.2.5 Daubechies小波之聯結係數 28

第三章 主動式兩軸磁浮軸承之系統鑑別 32
3.1 磁浮軸承系統之運動方程式 33
3.2 磁浮軸承系統之參數鑑別 38
3.2.1 磁浮軸承系統之迴授 39
3.2.2 閉迴路磁浮軸承系統之系統鑑別 42
3.3 電腦模擬與分析 46
3.3.1 控制器與估測器之設計 46
3.3.2 特徵系統實現運算法之電腦模擬 48
3.3.3 小波函數鑑別理論之電腦模擬 49
3.3.4 雜訊影響下的系統鑑別 50

第四章 實驗與驗證 66
4.1 磁浮軸承系統硬體裝置 66
4.1.1 渦電流型間隙感測器校正 70
4.1.2 功率放大器輸入與輸出之關係 72
4.2 控制器設計與實驗結果討論 74
4.2.1 控制器設計與實現 74
4.2.2 實驗結果 75

第五章 結論與展望 88
5.1 結論 88
5.2 未來發展與建議 88

參考文獻 90

附錄A. 四極磁浮軸承系統磁力推導 93
A.1 電磁鐵之磁束(Flux)表示式 93
A.2 永久磁鐵之磁束(Flux)表示式 98
A.3 磁極之磁力表示式 100

自述 104

[1] 黃忠良，磁懸浮與磁力軸承，復漢出版社，1994。

[2] T. Söderström, P. Stoica, System Identification, Prentice Hall, New
York, 1988

[3] L. Ljung, System Identification : Theory for the User, Prentice-Hall,
Englewood Cliffs, New Jersey, 1987.

[4] S. Srinivasan, Y. M. Cho, “Modeling and System Identification of Active
Magnetic Bearing Systems”, Proceedings of the 1995 IEEE Conference on
Control Applications, 252-260, 1995.

[5] V. O. Peter, D. M. Bart, “N4SID : Subspace Algorithms for the
Identification of Combined Deterministic-Stochastic Systems”, Automatica,
Vol. 30, No. 1, 75-93, 1994.

[6] S. J. Kim, C. W. Lee, “On-Line Identification of Current and Position
Stiffnesses by LMS Algorithm in Active Magnetic Bearing System Equipped
with Force Transducers”, Mechanical Systems and Signal Processing, Vol.
13, No. 5, 681-690, 1999.

[7] V. Jayanth, H. Choi, G. Buckner, “ Identification and control of a
flexible rotor supported on active magnetic bearings”, Proceedings of the
IEEE SoutheastCon, 273-278, 2002.

[8] T. N. Shiau, M. S. Tsai, C. H. Chang, “State Space Identification of
Nonlinear Hydro Dynamic Bearing by Eigensystem Realization Algorithm
(ERA)”, International Gas Turbine Institute ASME TURBO EXPO, Vol. 4, 551-
560, 2003.

[9] R. Mohd-Mokhtar, L. Wang, L. Qin, T. Barry, “Continuous Time System
Identification of Magnetic Bearing Systems Using Frequency Response
Data”, Proceedings of the 5th Asian Control Conference, Vol. 3, 2066-
2072, 2004.

[10] C. K. Chui, Wavelet : A Tutorial in Theory and Applications, Academic
Press, 1992.

[11] I. Daubechies, Ten Lectures on Wavelet, Society for Industrial and
Applied Mathematics, Philadelphia, Pa, 1992.

[12] R. D. Priebe, G. R. Wilson, “Wavelet Applications to Structural
Analysis”, Proceedings of the IEEE International Conference on
Acoustics, Speech and Signal Processing, Vol. 3, 205-208, 1994.

[13] D. E. Newland, “Wavelet Analysis of Vibration, Part 1: Theory”, Journal
of Vibration and Acoustics, Transactions of the ASME, Vol. 116, No. 4,
409-416, 1994.

[14] D. E. Newland, “Wavelet Analysis of Vibration, Part 2: Wavelet Maps”,
Journal of Vibration and Acoustics, Transactions of the ASME, Vol. 116,
No. 4, 417-425, 1994.

[15] M. Ruzzene, A. Fasana, L. Garibaldi, B. Piombo, “Natural Frequencies and
Dampings Identification Using Wavelet Transform: Application to Real
Data”, Journal of Mechanical Systems and Signal Processing, Vol. 11, No.
2, 207-218, 1997.

[16] W. J. Staszewski, “Identification of Damping in MDOF Systems Using Time-
Scale Decomposition”, Journal of Sound and Vibration, Vol. 203, No. 2,
283-305, 1997.

[17] A. N. Robertson, K. C. Park, K. F. Alvin, “Extraction of Impulse
Response Data via Wavelet Transform for Structural System
Identification”, Journal of Vibration and Acoustics, Transactions of the
ASME, Vol. 120, No. 1, 252-260, 1998.

[18] A. N. Robertson, K. C. Park, K. F. Alvin, “Identification of Structural
Dynamics Models Using Wavelet-Generated Impulse Response Data”, Journal
of Vibration and Acoustics, Transactions of the ASME, Vol. 120, No. 1,
261-266, 1998.

[19] R. Ghanem, F. Romeo, “A Wavelet-Based Approach for the Identification of
Linear Time-Varying Dynamical Systems”, Journal of Sound and Vibration,
Vol. 234, No. 4, 555-576, 2000.

[20] R. Ghanem, F. Romeo, “A Wavelet-Based Approach for Model and Parameter
Identification of Non-linear Systems”, International Journal of Non-
Linear Mechanics, Vol. 36, No. 5, 835-859, 2001.

[21] J. N. Juang, R. S. Pappa, “An Eigensystem Realization Algorithm for
Modal Parameter Identification and Model Reduction”, Journal of
Guidance, Control, and Dynamics, Vol. 8, No. 5, 620–627, 1985.

[22] J. N. Juang, Applied System Identification, Prentice Hall PTR, New
Jersey, 1994.

[23] 單維彰，1998，”凌波初步”，全華圖書公司。

[24] I. Daubechies, “Wavelet Transforms and Orthonormal Wavelet Bases”,
Proceedings of Symposia in Applied Mathematics, Vol. 47, Different
Perspectives on Wavelets, 1993.

[25] G. Strang, “Wavelets and Dilation Equation : A Brief Introduction”,
SIAM Review , Vol. 31, 614-627, 1989.

[26] M.Q. Chen, C. Hwang, Y.P. Shih, “Computation of Wavelet-Galerkin
Approximation on a Bounded Interval”, International Journal for
Numerical Methods in Engineering, Vol. 39, No. 17, 2921-2944, 1996.

[27] A.C. Lee, F.Z. Hsiao, D. Ko “Analysis and Testing of Magnetic Bearing
with Permanent Magnets for Bias”, JSME International Journal, Vol. 37,
No. 4, 774-782, 1994.