本論文針對一維管道聲場的特性進行分類，並推導相對應之適應控制。其中先以時間延遲之存在與否，區分為兩大類。在這兩大類之中，再以增益參數、噪音訊號是否為已知，分別推導控制策略。對於時間延遲為未知的情形，本文提出以Padé近似法來處理，再藉由函數近似法設計適應控制器。控制器之推導皆以嚴格的數學證明其穩定性，並確保內部訊號為有界。每一狀況皆進行電腦模擬，以驗證控制器之性能與可行性，並針對具有時間延遲之系統進行實驗驗證。

In this paper, we focus on the active noise reduction of a one dimensional acoustic field in a duct which can be considered in two types by existence of the time delay. Adaptive controllers are constructed for these two types respectively based on the knowledge of the gain parameter and noise signal. For the case when the time delay to be unavailable, the Padé approximation is used to represent the unknown time delay under the support of the function approximation based adaptive control strategies. Rigorous mathematical justifications are given for the proof of closed loop stability as well as the boundedness of the internal signals. Computer simulation and experiment results are presented to test the efficacy of the proposed schemes.

[1] P. Lueg, “Process of Silencing Sound and Oscillations,” U.S. Patent, no 2043416, 1936.

[2] 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.

[3] J. C. Burgess, “Active Adaptive Sound Control in a Duct: A Computer Simulation,” Journal of Acoust. Soc. Amer., Vol. 27, No. 3, pp. 715-725, 1981.

[4] 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 Transaction on Acoustics, Speech, and Signal Processing, Vol. ASSP-35, No. 4, pp. 433-437, April. 1987.

[5] B. Huang, Y. Xiao, J. Sun, G. Wei, “A Variable Step Size FxLMS Algorithm for Narrowband Active Noise Control,” IEEE Transaction on Audio, Speech, and Language Processing, Vol. 21, No. 2, pp. 301-312, February. 2013.

[6] R. Pal, M. K. Sharma, S. Thangjam, “Ambulance Siren Noise Reduction Using Virtual Sensor Based Feedforward ANC System,” Second International Conference on Advances in Computing and Communication Engineering, Dehradun, India, May 1-2. 2015.

[7] A. Zeb, A. Mirza, S. A. Sheikh, “Filtered-x RLS Algorithm Based Active Noise Control of Impulsive Noise,” 7th International Conference on Modeling, Identification and Control, Sousse, Tunisia, December 18-20. 2015.

[8] T. Zhao, “A New FXLMS Algorithm With Offline and Online Secondary-Path Modeling Scheme for Active Noise Control of Power Transformers,” IEEE Transactions on Industrial Electronics, Vol. 64, Issue: 8, August. 2017.

[9] C. K. Chen, “Active Cancellation System of Acoustic Noise in MR Imaging,” IEEE Transactions on Biomedical Engineering, Vol. 46, No. 2, February 1999.

[10] P. J. Gawthrop and M. T. Nihtila, “Identification of Time Delays Using a Polynomial Identification Method,” Systems & Control Letters, Vol. 5, pp. 267-271, February 1985.

[11] J. Na, X. Ren, and Y. Xia, “Adaptive Parameter Identification of Linear SISO Systems with Unknown Time-delay,” Systems & Control Letters, Vol. 66, pp. 43-50, April 2014.

[12] B. Widrow and S. D. Stearns, Adaptive Signal Processing. Cliffs, NJ: Prentice-Hall, 1985.

[13] S. J. Elliott, Signal Processing for Active Control, New York: Academic, 2001.

[14] K. A. Chen, Active Noise Control, China: National Defense Industry Press, 2014.

[15] G. A. Baker, Jr. and P. Graves-Morris, Padé Approximants, New York: Cambridge, 1996

[16] G. M. Phillips, and P. J. Taylor, Theory and Applications of Numerical Analysis, San Diego: Academic, 1996.

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

[18] M. Vajta, “Some Remarks on Padé-approximations,” Proceedings of 3rd TEMPUS-INTCOM Symposium, pp. 53-58, September 9-14, 2000.

[19] 白明憲，「聲學理論與應用-主動式噪音控制」，全華出版社，1999。

[20] 黃安橋，「適應控制理論」，上課講義，2003。

[21] 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。