臺灣博碩士論文加值系統

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。

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.

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

[1] R.E. Kalman, “Contributions to the theory of optimal control” , Bull.Soc. Math. Mex., vol. 5, pp. 102-119, 1960
[2] G. Zames, ”Feedback and optimal sensitivity: Model reference transformations, multiplicative seminorms, and approximate inverses”,IEEE Trans. on Automatic Control, Vol. 26,pp.301-320, 1981
[3] J. C. Doyle, K. Glover, P. P. Khargonekar and B.A.Francis, “State-Space solutions to standard H2and Hinfinity control problems”, IEEE Trans. on Automatic Control, vol.34 , pp. 831-847, 1989.
[4] S. P. Boyd, L. El Ghaoui, E. Feron and V. Balakrishnan, “Linear Matrix Inequalities in System and Control Theory”, SIAM Studies in Applied Mathematics, 1994
[5] J. C. Doyle, A. Packard and K. Zhou. “Review of LFTs, LMIs, and mu”, in Proc. IEEE Conf. Decision and Control ,pp. 1227-1232, 1991.
[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.