反覆式學習控制(Iterative Learning Control, ILC)，是一經由反覆的控制系統過程中記錄系統所輸入、輸出的資訊，以作為下次控制力修正的參考，且反覆學習控制能達到在有限的學習次數中，將系統的跟隨誤差收斂到一有限的範圍內。本文中設計一應用小波轉換於反覆學習控制律之控制器，且以實驗來實際驗證加上小波轉換的反覆學習控制律後之速度追蹤性能。
　　本文將市售的噴墨印表機改裝成撓性傳動機構之實驗平台，將控制器模組、訊號處理模組及馬達驅動電路模組以硬體描述語言(VHDL)及C語言應用在複雜型可程式邏輯元件(CPLD)與數位訊號處理器(DSP)中。本文介紹反覆學習控制法則與小波轉換理論以及加上小波轉換的反覆學習控制律，並將應用此控制方法在撓性傳動機構所帶動的從動件速度控制上，以進一步驗證此方法的優越性。本文所使用的反覆學習控制律原型為回授式反覆學習控制(Current Cycle Error type ILC)，而再利用小波轉換以處理不可學習之動態，以達到增進學習的收斂速度及降低反覆學習控制的最終誤差。實驗結果並進一步驗證其有效性。

The Iterative Learning Control (ILC) scheme is using the information in repetitive operation and progressive improving the tracking performance. The tracking error can be convergent to a small range within a finite time of learning. This thesis aims to perform the speed-tracking control of a flexible transport mechanism. An iterative learning control (ILC) scheme using wavelet transformation to enhance the learning process is presented in this thesis. The learning law updates the control profile through calculating the previous learning control profile, previous cycle error and current cycle error. After the output of control system is fedback, a wavelet-transform process is utilized in suppressing the un-learnable system dynamics. Because of the wavelet transformation process, the iterative learning scheme will exhibit better learning performance in the speed tracking of a flexible transport mechanism. Here, we setup a flexible transport mechanism through the modification of an Inkjet printer. A DSP-based control module with peripheral circuits was devised to perform several experiments. Both C-language and VHDL (VHSIC Hardware Description Language) were utilized to provide programmability. Experimental results further validate its efficacy.

[1] M. Vetteri and C. Herley, ” Wavelets and filter banks: theory and design,” IEEE Transactions on Signal Processing, vol. 40, no. 9, pp. 2207-2232, 1992.
[2] G. Strang and T. Nguyen, Wavelets and filter banks. USA: Wellesley-Cambridge Press, 1996.
[3] Ingrid Daubechies, Ten Lectures on Wavelets. Philadelphia, Pennsylvania: SIAM, 1992.
[4] Ingrid Daubechies, “Where do wavelets come from? A personal point of view,” Proceedings of the IEEE, vol. 84, no. 4, pp. 510-513, 1996.
[5] R. Balan, I. Daubechies, and V. Vaishampayan, “The analysis and design of windowed Fourier frame based multiple description source coding schemes,” Information Theory, IEEE Transactions on, vol.46, no. 7, pp. 2491-2536, 2000.
[6] Ingrid Daubechies, "The wavelet transform, time-frequency localization and signal analysis," Information Theory, IEEE Transactions on, vol. 36, no. 5, pp. 961-1005, 1990.
[7] Ingrid Daubechies, "Wavelets: an overview, with recent applications," In the 1995 proceedings of Information Theory, IEEE Int. Symposium on, pp. 5-10, 1995.
[8] Ingrid Daubechies, "Wavelets: a tool for time-frequency analysis," In Multidimensional Signal Processing Workshop, the Sixth IEEE Int. Conf, pp. 98-101, 1989.
[9] 單維彰, First concept of wavelets. 台北市: 全華科技圖書, 1998.
[10] Charles K. Chui, Wavelets: A Mathematical Tool for Signal Processing. Philadelphia, Pennsylvania: SIAM Press, 1997.
[11] M. Uchiyama, "Formulation of high-speed motion pattern of a mechanical arm by trial", Trans. Soc. Instrum. Control Eng., vol. 14, no. 1, pp. 706-712, 1978.
[12] S. Arimoto, S. Kawamura, and F. Miyazaki, “Bettering operation of robots by learning,” J. of Robotic Systems, vol. 1, pp. 123-140, 1984.
[13] S. Arimoto, T. Naniwa, and H. Suzuki, “Robustness of P-type learning control with a forgetting factor for robotic motions,” In Proc. 29th IEEE Conf. Decision and Control, Dec. 5-7, vol. 5, pp. 2640-2645, 1990.
[14] Z. Bien and K. M. Huh, “High-order iterative learning control algorithm,” Proc. Inst. Elec. Eng. Control Theory and Applications, vol. 136, no. 3, pt. D, pp. 105-112, 1989.
[15] T. J. Jang, C. H. Cho, and H. S. Ahn, “Iterative learning control in feedback system,” J. of Automatica, vol. 31, no. 2, pp. 243-248, 1995.
[16] L. Cai and W. Huang, “Fourier base learning control and application to position table,” Robotics and Autonomous System, vol. 32, pp. 89-100, 2000.
[17] D. Huang and Y. Jin, “The application of wavelet neural networks to nonlinear predictive control,” IEEE International Conference on Neural Networks, vol. 2, pp. 724-727, 1997.
[18] J. X. Xu, R. Yan, and Z. H. Guan, “Direct learning control design for a class of linear time-varying switched systems,” IEEE Transactions on Circuits and Systems, vol.50, No. 8, pp. 1116 -1120, 2003.
[19] ADSP TS101S TigerSHARC DSP Microcomputer Data Sheet, Revision 0. Norwood, MA: Analog Devices, Inc, 2002.
[20] ADSP TS101S EZ-KIT LITE evaluation system manual, First Edition. Norwood, MA: Analog Devices, Inc, October 2002.
[21] ADSP TS101S Hardware Specification, Revision 1.0.2. Norwood, MA: Analog Devices, Inc, March 2002.
[22] 劉昭恕, 反覆學習之控制器設計, 國立清華大學動力機械工程學系博士論文, 1998
[23] 俞銘九, 噴墨式列印頭伺服控制器之FPGA控制晶片設計與實作, 國立清華大學動力機械工程學系碩士論文, 1997.
[24] 張家榮, 噴墨列印頭伺服控制器之參數最佳化, 國立清華大學動力機械工程學系碩士論文, 2000.
[25] 張浥塵, 噴墨印表機伺服系統之整合測試與監控, 國立清華大學動力機械工程學系碩士論文, 2001.
[26] 郭及文, 噴墨印表機噴墨伺服晶片之設計與實作, 國立清華大學動力機械工程學系碩士論文, 2002.
[27] 曾達欽, 以小波轉換為基礎之反覆學習控制律設計, 國立清華大學動力機械工程學系碩士論文, 2004.
[28] Misiti, M., et al., Wavelet Toolbox User's Guide. Natick, MA: The Mathworks Inc., 1996.
[29] Michel Misiti, Yves Misiti, Georges Oppenheim, Jean-Michel Poggi, Wavelet Toolbox User’s Guide, Version 3. Natick, MA: The MathWorks Inc., 2004.
[30] Wavelet Toolbox Getting Started. Natick, MA: The MathWorks Inc., 2004.
[31] Catalog of RS-385PH. Japan: Mabuchi Motor Co., 2004.
[32] Datasheet of PBL3717A. Italy: STMicroelectronics, 2003
[33] John G. Proakis and Dimitris G. Manolakis, Digital Signal Processing. New Jersey: Prentice Hall, 1996.
[34] Alan V. Oppenheim and Ronald W. Schafer, Discrete-time Signal Processing. New Jersey: Prentice Hall, 1999.
[35] 張智星, Matlab程式設計與應用. 新竹市: 清蔚科技, 2000.
[36] 李宜達, 控制系統設計與模擬使用MATLAB. 台北市: 全華, 1997.
[37] Duane C. Hanselman, Mastering MATLAB 6. Upper Saddle River, N.J.: Prentice Hall, 2001.
[38] 曾坤祥, 基於小波之反覆學習控制器設計及應用, 國立清華大學動力機械工程學系博士論文, 2005.