本論文的目的為使用linear quadratic Regulator(LQR)設計法設計一個最佳化的回授控制器，去設計及實現主動式消除噪音耳機。這控制器將音源訊號和經由耳機上的一個很小的麥克風偵測到的測試訊號做比較，並且試圖去產生一個控制訊號到耳機產生一個消音的區域，不受環境噪音干涉。
論文中實現的噪音消除耳機控制頻帶為100Hz到600Hz，這控制器設計強調藉由權重函數的選擇在不同的頻率下形成這控制器增益，以便在控制頻帶內取得最大的噪音消除，以及控制頻帶外的低噪音放大。經由實際量測在控制頻帶內噪音消除最好可達25dB，控制頻帶外高頻噪音增長最大為6dB，低頻噪音增長為4.5dB。

The purpose of this thesis is to design and implement an active noise cancellation headphone (ANC) with a feedback controller optimally designed using the linear quadratic regulator (LQR) design approach. The controller compares the audio input signal with the measured signal from a mini microphone in the headphone, and attempts to generate a control signal so that the headphone may reproduce a clean, low noise audio sound, without being interfered by the environmental noise.
The control bandwidth of the ANC headphone is 100~600Hz. The controller design emphasizes the choice of a weighting function in shaping the controller gain at different frequencies, so as to achieve maximum in-band noise cancellation and low noise amplification outside the bandwidth. The experimental result shows achievable noise cancellation of maximum 25dB within the control bandwidth and a barely noticeable slight noise amplification of maximum 6dB at high frequencies and 4.5dB at inaudible low frequencies.

第1章 緒論 1
1.1 主動式噪音控制史簡介 2
1.2 研究動機 5
1.3 章節內容 7
第2章 系統簡介 8
2.1 類比式主動控制 8
2.2 回授控制架構 9
2.3 控制器設計限制 11
第3章 回授控制器設計與分析 13
3.1 受控體分析 13
3.1.1 耳機的比較與選取 14
3.1.2 系統鑑別 16
3.2 頻率塑型Linear Quadratic Regulator概念與分析 18
第4章 設計與模擬 24
4.1 權重函數的選取 25
4.1.1 權重函數 的選取 26
4.1.2 常數權重R的選取 28
4.2 控制器設計 30
4.2.1 控制器 設計 30
4.2.2 控制器 設計 33
4.2.3 模擬結果 39
第5章 電路實現與性能量測 42
5.1 實作電路 42
5.1.1 受控體電路 42
5.1.2 控制器電路 44
5.2 實測結果 47
5.3 其它設計法性能比較 48
第6章 結論 50
參考文獻 52

[1] M. O. Tokhi and R. R. Leitch, Active Noise Control, Clarendon Press, 1992.
[2] P. Lueg, “Process of silencing sound oscillations,” U. S. Patent 2043416, 1936.
[3] H. F. Olson and E. G. May, “Electronic sound absorber,” Journal of the Acoustical Society of America, vol. 25, pp. 1130-1136, 1953.
[4] H. F. Olson, Acoustic Engineering, Princeton, N.J.: Van Nostrand, 1957.
[5] S. J. Elliott and P. A. Nelson, “Active noise control,” IEEE Signal Processing Magazine, vol. 14, pp. 12-35, 1993.
[6] J. F. Abbott, “Acoustical design criteria for active noise control systems,” IEEE International Conference on Acoustics, Speech, and Signal Processing, vol. 5, pp. 630-633, 1993.
[7] J. C. Doyle, B. A. Francis, and A. R. Tannenbaum, Feedback Control Theory, New York: Macmillan Publishing Company, 1992.
[8] V. R. Sule and V. V. Athani, “Directional sensitivity tradeoffs in multivariable feedback system,” Automatica, vol. 27, no. 5, pp. 869-872, 1991.
[9] J. Freudenberg and D. P. Looze, “Right half plane poles and zeros and design tradeoffs in feedback system,” IEEE Trans. Automat. Control, vol. AC-30, no. 6, pp. 555-565, 1985.
[10] J. G. Truxal, Automatic Feedback Control System Synthesis, New York: McGraw-Hill, 1955.
[11] P. Dorato, Analytic Feedback System Design: An Interpolation Approach, Brook/Cole, 2000.
[12] S. H. Yu and J. S. Hu, “Controller design for active noise cancellation headphones using experimental raw data,” IEEE/ASME Transactions on Mechatronics, vol. 6, no. 4, pp. 483-490, Dec. 2001.
[13] B. Rafaely and S. J. Elliott, “ Active control of sound in a headrest: design and implementation,” IEEE Transactions on Control Systems Technology, vol. 7, no. 1, pp. 79-84, 2000.
[14] M. O'Brien and P. Pratt, “Active noise control using robust feedback techniques,” IEEE International Conference on Acoustics, Speech, and Signal Processing, vol. 5, pp. 3209-3212, 2001.
[15] J. C. Burgess, “Active adaptive sound control in a duct: a computer simulation,” Journal of the Acoustical Society of America, vol. 70, pp. 715-726, 1981.
[16] M. Winberg, S. Johansson, and I. Claesson, “An active headset based on hybrid active noise control technology,” Proceedings of the Inter-noise, pp. 557-562, 2001.
[17] K. Su, Analog Filters, Kluwer Academic Publishers, 2002.
[18] S. H. Yu and M. H. Tseng, “Modulation and control of a three-level class-D audio power amplifier,” IEEE International Conference on Power Electronics and Drive Systems, pp. 1447-1450, 2005.
[19] 黃怡智, 主動式消音耳機系統之回授控制器設計與實現, 國立交通大學電機與控制工程研究所碩士論文, 1997.
[20] 吳俊德, 基於DSP之主動式噪音消除耳機控制器設計與實現, 國立交通學電機與控制工程研究所碩士論文, 2004.
[21] B. D. O. Anderson and J. B. Moore, Optimal Control: Linear Quadratic Methods, Prentice-Hall, Inc., 1990.
[22] A. Saberi, P. Sannuti, and B. M. Chen, Optimal Control, Prentice-Hall International Limited, 1995.
[23] N. K. Gupta, “Frequency-shaped cost functionals: extension of linear- quadratic-Gaussian design methods,” Journal of Guidance, Control, and dynamics, vol. 3, no. 6, pp. 529-535, 1980.