臺灣博碩士論文加值系統

摘 要
本論文主要探討用強健性之H∞控制器，來控制一個脈寬模組（Pulse Width Modular,PWM）切換式降壓型DC-DC轉換器（Buck DC-DC Converter）的方法，並推導其交流（Alternating Current）小訊號數學模式。本文首先推導出拓撲電路（Topological Circuit）的狀態空間方程式，藉由建立一DC擾動操作點，將系統在操作點線性化，獲得系統之線性化狀態空間方程式。但是此狀態空間方程式，必須再加上PWM轉移函數及切換開關轉移函數形成一個完整的受控體（Plant）。接著，再根據其數學模式設計H∞控制器，使得輸出電壓外在干擾（Disturbance）及負載變動的影響降至最低程度。最後再針對不同的輸入信號，在雜訊（Noise）造成系統參數擾動的情況下，分別驗證本文控制架構的可行性及強健性（Robustness）。

Abstract
An H∞-Control design of the Pulse Width Modulator (PWM) switch buck DC-DC converter is studied in this thesis. The AC small-signal mathematical model for the PWM switch buck DC-DC converter is derived in this research and the state space equation of a topological circuit through a DC perturbation operating point is then established and linearized around the operating point. The composite model to be controlled is then composed of a AC small-signal model , a PWM transfer function and a switch transfer function. To minimize the ill-effects of the noises , disturbances and the parameter variations , the H∞-control methodolody is applied on the composite model to achieve the desired performance. Finally , computer simulations results are made to verify the feasibility and the robustness of the proposed control design under the presence of system parameter uncertainties and noises.

目 錄
中文摘要………………………………………………………………Ⅰ
英文摘要………………………………………………………………Ⅱ
誌謝……………………………………………………………………Ⅲ
目錄……………………………………………………………………Ⅳ
圖目錄…………………………………………………………………Ⅵ
一、緒論…………………………………………………………………1
1－1 研究動機……………………………………………………1
1－2 文獻回顧……………………………………………………3
1－3 本文架構……………………………………………………4
二、切換式降壓型DC-DC轉換器拓撲電路之交流小信號分析……6
2－1 降壓型DC-DC轉換器之簡介與工作原理………………6
2－2 切換開關函數………………………………………………10
2－3 操作模式……………………………………………………12
2－4 狀態空間分析………………………………………………14
2－4－1 狀態變數解析……………………………………14
2－4－2 狀態方程式………………………………………15
2－4－3 狀態平均化法……………………………………18
2－5 脈波寬度調變器……………………………………………22
三、H∞控制概論………………………………………………………26
3－1 H∞控制概論………………………………………………26
3－2 norm的定義………………………………………………27
3－3 H∞控制理論………………………………………………30
3－4 H∞控制問題的求解………………………………………33
3－5 權重函數的選擇…………………………………………36
四、PWM切換式降壓型DC-DC轉換器之H∞控制設計……………39
4－1 基本控制架構………………………………………………39
4－2 受控體之狀態方程式………………………………………42
4－3 H∞控制設計………………………………………………47
4－4 設計流程……………………………………………………52
五、電腦模擬……………………………………………………………54
六、結論與未來發展……………………………………………………69
6－1 結論…………………………………………………………69
6－2 未來發展……………………………………………………70
參考文獻………………………………………………………………72
自述……………………………………………………………………74

參考文獻
[1]Chakrabarty, K.; Poddar, G.; Banerjee, S.;“Bifurcation behavior of the buck converter”Power Electronics, IEEE Transactions onVolume 11, Issue 3, May 1996 Page(s):439–447
[2]Doyle, J.C., K. Glover, P.P. Khar Gonekar and B.A. Francis, “State-Space Solutions to Standard H2 and H∞ Control Problems,” IEEE Trans. Autom. Control, Vol. 34, No. 8, pp. 831-847, 1989.
[3]E. Nordgren, M. A. Franchek, O. D. I. Nwokah, "A Design Procedure for the Exact H( SISO-Robust Performance Problem", International Journal of Robust and Nonlinear Control, Vol. 5, pp.107-118, 1995.
[4]Forsyth, A. J. ; Mollov, S. V. ,”Modelling and control of DC-DC converters,”Volume 12, Issue 5, pp. 229–236, 1998.
[5]Glover, J. Sefton, D.C. McFarlane, "A Tutorial On Loop Shaping Using H-infinity Robust Stabilization", Transaction of the Institute of Measurement and Control, Vol. 14, No. 3, pp.157-168, 1992.
[6]Hwang, C.N., "Formulation of H2 and H∞ Optimal Control Problems - A Variational Approach", Journal of the Chinese Institute of Engineerings, Vol. 16, No. 6, pp.853-866, 1993.
[7]Hwang, C.N., “A Variational Approach to H2 and H∞ Control Problems for Linear Nonautonomous System”, Journal of the Chinese Institute of Engineerings, Vol. 19, No. 5, pp.408-422, 1994.
[8]Kazimierczuk, M.K.; Sathappan, N.; Czarkowski, D.;
“Voltage-mode-controlled PWM buck DC-DC converter with a proportional controller”Aerospace and Electronics Conference, 1993. NAECON 1993., Proceedings of the IEEE 1993 National
24-28 May 1993 Page(s):413 - 419 vol.1
[9]Nazirul, A.S.M.; Shaheen, I.; Pujara, L.R.; Kazimierczuk, M.K.;
“Comparison of the Kharitonov method with others for the robust
stability analysis of a PWM buck converter” Control Applications,
1997., Proceedings of the 1997 IEEE International Conference on 5-7 Oct. 1997 Page(s):779–784
[10]S.S. Sastry and A. Isidori, "Adaptive control of linearizable systems,", IEEE Trans. Automat. Contr., Vol. 34, no. 11,pp.1123-1131, 1989.
[11]Van Dijk, E.; Spruijt, J.N.; O'Sullivan, D.M.; Klaassens, J.B.;
“PWM-switch modeling of DC-DC converters” Power Electronics,
IEEE Transactions on Volume 10, Issue 6, Nov. 1995 Page(s):659-665
[12]Zames, G.; Francis, B.;“On H∞ optimal sensitivity theory for SISO feedback systems”Automatic Control, IEEE Transactions on
Volume 29, Issue 1, Jan 1984 Page(s):9-16
[13]Zamierczuk, M.K.; Cravens, R.C., II; Reatti, A.,“Closed-loop input impedance of PWM buck-derived DC-DC converters;”
IEEE Trans. Volume 6, 30 May-2 June 1994 Page(s):61-64 vol.6
[14]白中和 ,“交換式電源設計入門”, 全華出版社 , 2001。
[15]梁適安 ,“交換式電源供應器之理論與實務設計”, 全華出版社, 1994。
[16]楊憲東 , 葉芳栢 ,“線性與非線性H∞控制理論”, 全華出版社 , 1999。
[17]謝慧蓉 , 廖德祿 ,“可變結構控制法應用於切換式降壓型DC-DC轉換器之控制器設計 與實現”, 國立成功大學工程科學研究所碩士論文 , 1997。