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研究生:林玉婷
研究生(外文):Yu-Ting Lin
論文名稱:強健模糊動態輸出回饋控制-Circle與Popov定理
論文名稱(外文):No
指導教授:羅吉昌
指導教授(外文):J.C. Lo
學位類別:碩士
校院名稱:國立中央大學
系所名稱:機械工程研究所
學門:工程學門
學類:機械工程學類
論文種類:學術論文
論文出版年:2004
畢業學年度:92
語文別:中文
論文頁數:91323091
中文關鍵詞:雙線性矩陣不等式線性矩陣不等式Popov定理圓定理強健控制平行分佈補償器T-S模糊模型
外文關鍵詞:Popov theoremLure-type Lyapunov functionLinear matrix inequality (LMI)Circle theoremParallel distributed compensator (PDC)Bilinear matrix inequality (BMI)Robust controlTakagi-Sugeno (T-S) fuzzy model
相關次數:
  • 被引用被引用:1
  • 點閱點閱:137
  • 評分評分:
  • 下載下載:19
  • 收藏至我的研究室書目清單書目收藏:0
本篇論文主要分為兩部分:

1.經由事先給定非線性系統的動態方程式,將此系統精確的轉換成 Takagi-Sugeno (T-S) 模糊模型。設計動態輸出回授控制器來穩定連續及離散 T-S 模糊模型並滿足圓定理(Circle theorem)的穩定條件。

2.同樣將經由事先給定非線性系統的動態方程式,將此系統精確的轉換成Takagi-Sugeno (T-S) 模糊模型。設計動態輸出回授控制器來穩定連續及離散 T-S 模糊模型並滿足Popov 定理(Popov theorem)的穩定條件。

本篇論文不同於以往的部分在於我們是從時域切入,並且在絕對穩定(Absolute stability)架構中將原為線性系統中的非線性項,改成模糊系統中的非線性項。改變系統架構後,先將非線性系統轉換成T-S 模糊模型,以提供一套系統化的研究方法研究非線性系統的穩定性分析問題。當使用這套方法時,由於控制器是根據 T-S 模糊模型所設計而非直接針對非線性系統做設計,因此若非線性系統與 T-S 模糊模型間誤差為0,則此控制法則可用於非線性系統。

為確保系統與模型之間的誤差為零,本篇論文沿用一個方法將誤差以有界非線性項 (sector-bounded nonlinearities) 來表示,而後,非線性系統即可精確的表達成具有非線性項的 T-S 模糊模型。其中非線性項的限制分別須要滿足Circle或 Popov Criteria,若非線性項分別轉換成不確定參數項後,則可視為強健模糊控制。圓定理與Popov 定理最大不同在於他們的Lyapunov函數不同,前者使採用一般的二次Lyapunov 函數,後者則是使用Lure-type Lyapunov函數來證明穩定度的問題。

針對 T-S 模糊模型,本篇論文根據平行分散式補償器 (PDC) 的概念設計控制器。控制系統中,當系統狀態無法完全獲知時,則必須採用估測器獲得所需的資訊或直接以輸出回授做控制,本篇所討論的即是研究動態輸出回授控制器的設計與分析。

在動態輸出回授控制或觀測器方面,最大的問題在於所推導出的穩定條件並非線性矩陣不等式 (LMI) 而是以雙線性矩陣不等式 (BMI)的形式呈現,而 BMI 無法如同 LMI 一般可輕易經由現有工具程式求解。因此,本篇將此部份的重點放在如何求解 BMI 的問題上,透過蕭氏轉換(Schur complement)及全等轉換(congruence transform)的方法可將控制問題中的 BMI 條件轉換為 LMI 形式求解或者經由求解某些 LMI 的子矩陣來達到求解BMI。最後分別以倒單擺及倒車入庫系統的例子來進行電腦模擬。
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 4
第一部份:圓定理(Circle Theorem) 6
第二章 系統架構與圓定理 6
{2.1}數學模型 6
{2.2}穩定條件 8
第三章 動態輸出回饋控制器設計 12
{3.1}數學模型 12
{3.2}廣義動態輸出回饋控制器 13
{3.3}動態輸出回饋控制器 15
{3.3.1}連續系統 15
{3.3.2}離散系統 18
第四章 電腦模擬 28
{4.1}倒單擺例子 28
{4.1.1}數學架構 28
{4.1.2}求解 30
{4.2}倒車例子 37
{4.2.1}數學架構 37
{4.2.2}求解 39
第二部份:Popov定理 47
第五章 系統架構與Popov定理 47
{5.1}數學模型 47
{5.2}穩定條件 49
第六章 動態輸出回饋控制器設計 55
{6.1}數學模型 55
{6.2}廣義動態輸出回饋控制器 56
{6.3}動態輸出回饋控制器 58
{6.3.1}連續系統 58
{6.3.2}離散系統 62
第七章 電腦模擬 70
{7.1}倒單擺例子 70
{7.1.1}數學架構 70
{7.1.2}求解 71
{7.2}倒車例子 78
{7.2.1}數學架構 78
{7.2.2}求解 79
第八章 總結與未來方向 87
{8.1}總結 87
{8.2}未來研究方向 88
參考文獻 89
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