博碩士論文 953203073 詳細資訊


姓名 高聖鎰(Sheng-Yi Gau)  查詢紙本館藏   畢業系所 機械工程學系
論文名稱 奇異攝動耗散模糊控制系統-波雅定理
(dissipative control for singularly perturbed fuzzy systems with Polya theorem)
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摘要(中) 第一部份, Takagi-Sugeno 模糊模型可完整地代表原始的非線性系統, 並且藉由Lyapunov 定理將問題轉為線性矩陣不等式, 此一簡單且兼具數理基礎和系統化步驟的特色成為本篇論文使用的主要原因。如上, 所以我們先建立一具耗散性的模糊化奇異攝動系統, 接著導入耗散性控制, 可藉由選取供應率(supplyrate) 的特點來處理各種性能問題, 之後再設計一分散平行補償控制器(PDC)利用狀態回饋控制來控制系統。
第二部分, 在最近幾年的模糊控制文獻中, 大部分研究主要著重於找出一共同P 矩陣來滿足二次Lyapunov 函數, 此一方法為充分但非必要條件且求解較保守(conservatism)。在此我們使用了波雅定理的代數性質來建立一組線性矩陣不等式, 此組線性矩陣不等式可求得出一二次穩定之不保守解(less conservativesolution), 進而漸進至系統穩定之必要條件, 在數理方面證明雙向的充要條件, 以工程的角度則可設計出使系統性能便好的控制器。
摘要(英) In this thesis, we propose a general quadratic dissipative state feedback control method to solve a stabilization problem for fuzzy singularlyperturbed system. The problem covers the bounded real, positive realand sector-bounded performance as a special case by choosing the corresponding
quadratic supply rate. Moreover, we also prove necessary
and sufficient conditions to state feedback controllers ensuring quadratic stability for Takagi-Sugeno fuzzy systems in theory. But our main objective is to generate a family of linear matrix inequalities based on an extension of P´olya’s theorem(a.k.a Matrix-valued P´olya’s heorem).
The proposed conditions are stated as progressively less conservative sets of linear matrix inequalities, allowing us to obtain a solution for the quadratic stabilizability problem whenever a solution exists.
關鍵字(中) ★ 奇異攝動系統
★ 耗散控制
★ 波雅定理
關鍵字(英) ★ dissipative control
★ Polya theorem
★ singularly perturbed systems
論文目次 論文摘要I
Abstact III
誌謝IV
圖目IX
第一章簡介1
1.1 文獻回顧¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ 1
1.2 研究動機¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ 2
1.3 論文結構¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ 3
1.4 符號標記¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ 4
1.5 預備定理¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ 5
第一部份: 耗散性控制(Dissipative Control) 6
第二章系統架構與穩定條件6
2.1 廣義非線性系統¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ 6
2.2 定義一(耗散系統) ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ 7
2.3 奇異攝動耗散模糊系統的之分析與綜合¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ 8
2.3.1 數學模型¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ 8
2.3.2 備註¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ 10
2.3.3 定理一(連續時間系統) ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ 11
2.3.4 定理二(離散時間系統) ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ 14
第三章狀態回饋控制器設計18
3.1 狀態回饋控制器數學模型¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ 18
3.2 奇異攝動耗散模糊控制系統之分析與綜合¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ 19
3.2.1 數學模型¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ 19
3.2.2 定理三(連續時間系統) ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ 21
3.2.3 定理四(離散時間系統) ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ 22
3.2.4 備註¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ 24
第四章電腦模擬26
4.1 連續控制系統¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ 26
4.1.1 數學模型¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ 26
4.1.2 求解¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ 29
4.1.3 備註(求解結果之討論) ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ 39
4.2 離散控制系統¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ 40
4.2.1 數學模型¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ 40
4.2.2 求解¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ 42
4.2.3 備註(求解結果之討論) ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ 51
第二部份: 波雅定理53
第五章控制系統架構與波雅定理53
5.1 定理五(波雅定理)[54] ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ 53
5.1.1 備註¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ 53
5.2 數學模型¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ 54
5.3 狀態回饋控制器數學模型¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ 55
5.4 定義二(二次穩定) ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ 57
5.5 定理六¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ 58
5.5.1 備註¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ 59
第六章狀態回饋控制器設計61
6.1 連續系統¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ 61
6.1.1 定理七(連續系統穩定充要條件) ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ 62
6.2 離散系統¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ 63
6.2.1 定理八(離散系統穩定充要條件) ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ 64
6.3 範例¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ 65
6.3.1 備註¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ 67
第七章電腦模擬68
7.1 連續控制系統¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ 68
7.1.1 數學模型¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ 68
7.2 離散控制系統¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ 74
7.2.1 數學模型¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ 74
第八章結論與未來方向80
8.1 總結¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ 80
8.2 未來研究方向¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ 81
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指導教授 羅吉昌(Ji-Chang Lo) 審核日期 2008-6-25
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