中文摘要

本論文針對一維管道聲場系統，引用一以函數近似法(Function Approximation Technique, FAT)設計出之適應性控制器，在假設控制喇叭至誤差麥克風的延遲時間為已知條件時，利用Lyapunov法則求得適應率並確保閉迴路系統的穩定收斂。在控制器設計方面，也探討了近似誤差、已知近似誤差之邊界與參數漂移(parameter drift)對FAT適應性控制器之影響。最後由實驗結果證明FAT適應性控制器不管在單頻噪音與雙主頻噪音之抑制效能上，皆比LMS與FXLMS適應性演算法有較好的性能表現。

Abstract

In this paper, we use an adaptive controller based on the function approximation technique for the active noise cancellation in a duct. If the delay time in the secondary path is known, the update laws for the weighting vectors can be selected using Lyapunov-like design so that asymptotic convergence of the output error can be proved. We also discuss the effect of the approximation error on the system performance and some modifications are proposed to robustify the design. Experimental results for reduction in the single-frequency noise and dual-frequency noise cases show that the proposed controller can give consistently better performance compared with the LMS and FXLMS strategies.

Keyword：Active noise control, Function Approximation Technique, LMS algorithm, FXLMS algorithm.

參考文獻
[1] Q. F. Fan, N. Kenzo and N. Mistuo, “Active noise control of exhaust duct using two-degree-of-freedom control system with model matching”, JSME International Journal, Series C, Vol.40, No.2, pp.203-208,1997.

[2] O. A. Abdel Alim, O. A. Sebakhy, H. A. Yousef and O. A. Jolaha, “Feedfoward controller design using model matching techniques for active noise systems”, Twentieth National Radio Science Conference, March 18-20, 2003.

[3] B. Widrow, “Adaptive filters”, in Aspects of Network and Systems Theory, R. E. Kalman and N. DeClaris, eds., New York: Holt, Rinehart and Winston, pp.563-587, 1970.

[4] D. R. Morgan, “An analysis of multiple correlation cancellation loops with a filter in the auxiliary path”, IEEE Trans. Acoust., Speech, Signal Processing, ASSP-28, 454-467, Aug. 1980.

[5] B. Widrow, D. Shur, and S. Shaffer, “On adaptive inverse control”, in Proc. 15th Asilomar Conf., pp.185-189, 1981.

[6] L. J. Eriksson, M. C. Allie, and R. A. Greiner, “ The selection and application of an IIR adaptive filter for use in active sound attenuation”, IEEE Trans. Acoust., Speech, Signal Processing ASSP-35, 433-437, Apr. 1987.

[7] A. J. Hull, C. J. Radcliffe and S. C. Southward, “Global active noise control of a one dimensional acoustic duct using a feedback controller”, ASME Journal of Dynamic Systems, Measurement, and Control, Vol.115, pp.488-494, Sep. 1993.

[8] J. S. Hu, “Active sound attenuation in finite-length ducts using close-form transfer function models”, ASME Journal of Dynamic Systems, Measurement, and Control, Vol.117, pp143-153, June. 1995.

[9] J. S. Hu, “Active noise cancellation in ducts using internal model-based control algorithms”, IEEE Transactions on Control Systems Technology, Vol.4, No.2, March. 1996.

[10] 陳名裕, 管道聲場之主動噪音控制, 國立台灣科技大學機械工程研究所, 碩士學位論文, 2004.

[11] L. E. Kinsler, A. R. Frey, A. B. Coppens and J. V. Sanders, Fundamentals of Acoustics, John Wiley & Sons, Inc. 1982.

[12] 蔡國隆、王光賢、涂聰賢, 聲學原理與噪音量測控制, 全華出版社, 2005.

[13] P. A. Nelson, S. J. Elliott, Active Control of Sound, Academic Press, Inc. 1992.

[14] 周俊宏, 管道聲場之類神經網路控制, 國立台灣大學工程科學與海洋工程學系,碩士學位論文, 2003.

[15] 白明憲, 聲學理論與應用-主動式噪音控制, 全華出版社, 2001.

[16] S. M. Kuo and D. R. Morgan, Active Noise Control Systems, John Wiley & Sons, Inc. 1996.

[17] 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.

[18] 黃安橋, “適應控制理論”, 國立台灣科技大學機械工程研究所, 上課講義, 2005.

[19] J-J. E. Slotine and W. Li, Applied Nonlinear Control, Prentice Hall, Upper Saddle River, New Jersey, 1991.

[20] S. S. Ge, T. H. Lee and C. J. Harris, Adaptive Neural Network Control of Robotic Manipulators(World Scientific Publishing, Singapore, 1998).

[21] M. B. Menhaj and M. Roubani, “A novel neuro-based model reference adaptive control for a two link robot arm”, Proc. IEEE International Joint Conference on Neural Network, Vol.1, pp.47-52, 2002.

[22] A. V. Oppenheim, E. Weinstein, K. C. Zangi, M. Feder and D. Gauger, “Single-Sensor Active Noise Cancellation”, IEEE Transcations on Speech and Audio Processing, Vol.2, No.2 , pp.285-290, April. 1994.