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中文論文名稱 權重靈敏度函數最小化問題之降階控制器設計
英文論文名稱 Design of Reduced-order Controllers for Weighted Sensitivity Minimization Problem
校院名稱 淡江大學
系所名稱(中) 電機工程學系碩士班
系所名稱(英) Department of Electrical Engineering
學年度 94
學期 2
出版年 95
研究生中文姓名 褚永誠
研究生英文姓名 Yong-Cheng Chu
學號 693380189
學位類別 碩士
語文別 中文
第二語文別 中文
口試日期 2006-05-30
論文頁數 76頁
口試委員 指導教授-周永山
委員-翁慶昌
委員-王和盛
中文關鍵字 降階控制器  Hinfinity  H2  線性矩陣不等式  遞迴法線性矩陣不等式 
英文關鍵字 reduced-order  Hinfinity  H2  Linear Matrix Inequality(LMI)  Iterative Linear Matrix Inequality (ILMI) 
學科別分類 學科別應用科學電機及電子
中文摘要 控制器的階數越高,硬體實現的成本及複雜度就越高,所以,長久以來,研究人員不斷尋求較低階控制器的設計方法,但目前仍缺乏有效的方法。我們改良Souza等人的想法,提出新型的 暨 降階輸出迴授動態控制器以及追踨控制器之設計。首先將原動態控制器的設計問題轉換為靜態輸出迴授增益的設計問題,再藉由控制靜態輸出迴授增益向量的個數以達到降階的目的。我們利用類似的技巧推導得到降階控制器存在的充要以及充分條件。另外,我們也提出植基於等價條件的疊代式演算法,將可以得到性能更佳的降階控制器。我們推導得到的條件皆為線性矩陣不等式(Linear Matrix Inequality,LMI)的形式,因此可以用現有軟體Matlab所提供的LMI Control Toolbox有效求解。
英文摘要 As the order of a controller becomes higher, the complexity of its hardware implementation becomes higher and the cost is more expensive. Therefore, much work has been done for the design of low-order controllers. However, it still lacks an efficient way to solve the problem in practice. We extend the idea of Souza et al to propose a novel design of the reduced-order Hinfinity or H2 output feedback controllers and tracking controllers. First, we convert the problem of designing dynamic controllers into the problem of designing static output feedback gain. Necessary and sufficient conditions for the existence of the reduced-order controllers are derived in a unified manner. Then we reach the goal of obtaining lower order controllers via controlling the number of variables of the feedback gain vector. Only sufficient conditions are obtained. In addition, we also present two iterative algorithms which can yield reduced-order controllers with better performance. The conditions we obtained are all in LMI form which can be efficiently solved via the LMI Control Toolbox in Matlab.
論文目次 章節目錄
第一章 緒論 ...........................................1
1.1文獻回顧與研究動機................................1
1.2 論文架構.........................................2
第二章 背景知識與問題敘述...................................4
2.1 範數.............................................4
2.1.1訊號的範數..................................4
2.1.2系統的範數..................................5
2.2 Hinfinity和H2性能分析............................6
2.2.1 Hinfinity性能分析..........................7
2.2.2 H2性能分析.................................7
2.3 線性矩陣不等式...................................8
第三章 全階及降階控制器之設計..............................10
3.1 全階控制器設計-Scherer等人的做法................10
3.2 降階控制器設計-Souza等人的做法..................17
第四章 新型降階控制器之設計................................22
4.1 問題描述與轉換..................................22
4.2 Hinfinity降階控制器之設計.......................31
4.2.1降階控制器之設計...........................31
4.2.2低階控制器之設計...........................34
4.2.3低階控制器之分析與應用ILMI求解.............38
4.3 H2降階控制器之設計..............................45
4.3.1降階控制器之設計...........................46
4.3.2低階控制器之設計...........................47
4.3.3低階控制器之分析與應用ILMI求解.............49
4.4 數值模擬........................................57
4.5 推廣應用:追踨控制器.............................65
第五章 結論與未來研究方向..................................73
第六章 參考文獻............................................74

圖目錄
圖2.1 線性非時變穩定系統....................................5
圖2.2 單輸入單輸出系統的波德增益圖..........................6
圖3.1 G-K架構..............................................10
圖4.1 迴授控制系統.........................................22
圖4.2 等價迴授控制系統.....................................24
圖4.3 S-|p|與Sc兩集合交集情況..............................26
圖4.4 靜態狀態迴授增益系統.................................28
圖4.5 靜態輸出迴授增益系統.................................35
圖4.6 情況2應用演算法1於3階控制器之r值最小化...............62
圖4.7 情況2應用演算法2於3階控制器之r值最小化...............62
圖4.8 誤差訊號圖(一).......................................71
圖4.9 誤差訊號圖(二).......................................72

表目錄
表4.1 求解降階控制器之最佳化問題...........................57
表4.2 情況1的Hinfinity性能.................................59
表4.3 情況1的H2性能........................................60
表4.4 情況2的Hinfinity性能.................................61
表4.5 情況2的H2性能........................................63
表4.6 情況3的Hinfinity性能.................................64
表4.7 情況3的H2性能........................................65
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[6] C. Scherer, P. Gahinet, and M. Chilali, “Multiobjective Output- feedback Control via LMI
Optimization”, IEEE Trans on Automatic Control, vol.42, pp. 896-911, 1997.
[7] P. Gahinet, A. Nemirovski, A. J. Laub, and M. Chilali, Manual of LMI Control Toolbox, the Math Works, Inc, 1995.
[8] T. Iwasaki and R. E. Skelton “All fixed-order Hinfinity controllers:observer- based structure and covariance bounds”, IEEE Trans. on Automatic Control,vol. 40, pp. 512-516, 1999.
[9] P. Gahinet and A. Ignat, “Low-order Hinfinity Synthesis via LMIs”, in Proc. American Control Conference, pp. 1499-1500, 1994.
[10] P. Gahinet and P. Apkarian, “A Linear matrix inequality approach to Hinfinity control ”, Int. J. Robust Nonlinear Control, vol.4, pp. 421-448, 1994.
[11] P. Gahinet and P. Apkarian, “An LMI-based Parameterization of all Hinfinity Controllers with Applications”, in Proc. IEEE Conf. Decision and Control , San Antonio, Texas, pp. 656-661, 1993.
[12] K. M. Grigoriadis and R. E. Skelton, “Fixed-order Control Design for LMI Control Problems Using Alternating Projection Methods”, in Proc. IEEE Conf. Decision and Control, pp. 2003-2008, 1994.
[13] C. E. de Souza and U. Shaked , “An LMI Method for Output-feedback Hinfinity Control Design for System with Real Parameter Uncertainty”, in Proc. IEEE Conf. Decision and Control, Tampa, Florida USA, pp. 1777-1779, 1998.
[14] Y. S. Chou, K.C. Hsieh and C.M. Chuang, “Fixed-order Hinfinity Controller Design for LTI SISO Systems” International Conference on Informatics, Cybernetics, and Systems, pp. 1724-1729, Dec 2003
[15] 謝坤志,降階輸出迴授控制器之設計,淡江大學電機工程研究所碩士論文,民93年。
[16] Y.S. Chou, Y.C. Chu and C.C. Ho, “Design of Reduced-order Hinfinity Controllers for Weighted Sensitivity Minimization Problem” CACS Automatic Control Conference, Nov 2005
[17] Y. S. Chou, K. C. Hsieh, Y. C. Chu, C. C. Ho and T. H. Li, A Unified Approach to Reduced-Order H2 Output Feedback Controller Design, to appear in Tamkang Journal of Science and Engineering, 2006
[18] K. Zhou and J. C. Doyle, Essentials of Robust Control, Prentice Hall, 1998.
[19] 楊憲東和葉芳栢,線性與非線性Hinfinity控制理論,全華科技圖書股份有限公司,民86年
[20] C. A. R. Crusius and A. Trofino, “Sufficient LMI Conditions for Output Feedback Control Problems”, IEEE Trans. on Automatic Control, pp. 1053-1057, 1999.
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