H∞模糊控制－連續系統  線性分式轉換法

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任中華(Jung-Hua Ren) 查詢紙本館藏

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機械工程學系

論文名稱

H∞模糊控制－連續系統線性分式轉換法

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★ 廣義模糊控制-離散系統線性分式轉換法	★ H∞模糊控制—離散系統線性分式轉換法
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★ 寬鬆耗散性模糊控制-波雅定理	★ 耗散性估測器-波雅定理

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摘要(中)

本篇論文共分為三大部分來進行討論，其第一部分為數學式子的推導，在這一部分中推導出的矩陣不等式為含有μ(激發強度)的非線性矩陣不等式。另外，本篇論文中的模糊模型與模糊控制器都是線性分式轉換(LFT)架構。第二部分為三次參數化動態平行分佈控制器(DPDC)的討論而第三部分則是二次參數化動態平行分佈控制器的探討。
在第一部分中，我們推導出二條矩陣不等式，第一條是根據李亞普諾夫(Lyapunov)定理而推導出來，第二條則是因為系統的架構而產生。在第二部分中，我們將上一部分所推導出的矩陣不等式提出μ，經由推導得到線性矩陣不等式(LMI)並歸納出一個定理。為了求解上的問題，我們也提出較寬鬆的方法並推導出另一個衍生定理。
第三部分與第二部分大同小異，只是控制器設計上的不。最後我們探討三次參數化動態平行分佈控制器的特殊情，目的是不須經由重覆推導，只須要將之前推導出的通式做一些調整與改變即可得到特殊情況下的線性矩陣不等式。在例子方面，我們採用了三個例子來驗證定理的可行性，分別為旋轉平移制動器、球桿系統與質簧系統。將這三個例子做電腦的模擬與分析，其中第一個例子與第二個例子都分別用三次參數化與二次參數化做動態平行分佈控制，第三個例子則用狀態回授平行分佈控制。

摘要(英)

關鍵字(中)

★ π轉換
★ 線性分式轉換
★ 模糊
★ 蕭氏轉換
★ 線性矩陣不等式

關鍵字(英)

★ LFT
★ Lyapunov
★ DPDC
★ LMI
★ H∞

論文目次

論文摘要.............................Ⅰ
誌謝.................................Ⅱ
圖目.................................Ⅵ
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
第二章數學模型與H∞性能指標 5
2.1 數學模型..........................5
2.2 H∞性能指標.......................8
2.3 預備定理..........................8
第三章 LFT模糊控制器設計(三次參數化) 9
3.1 通式..............................9
3.2 三次參數化.......................17
3.3 寬鬆方法.........................23
第四章 LFT模糊控制器設計(二次參數化) 28
4.1 二次參數化.......................28
4.2 寬鬆方法.........................33
第五章特殊情況 36
第六章電腦模擬 41
6.1 旋轉平移制動器...................41
6.1.1 數學架構推導...................41
6.1.2 求解...........................46
6.2 球桿系統.........................56
6.2.1 數學架構推導...................56
6.2.2 求解...........................58
6.3 質簧系統.........................67
6.3.1 數學架構推導...................67
6.3.2 求解...........................69
第七章總結與未來研究方向 72
7.1 總結.............................72
7.2 未來研究方向.....................72
參考文獻 74
附錄 77

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指導教授

羅吉昌(Ji-Chang Lo)

審核日期

2003-6-30

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