廣義模糊控制-離散系統
線性分式轉換法

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姓名

陳文字(Wen-Tzu Chen) 查詢紙本館藏

畢業系所

機械工程學系

論文名稱

廣義模糊控制-離散系統線性分式轉換法

相關論文

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★ H∞模糊控制－連續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
★ 強健模糊動態輸出回饋控制-Circle 與 Popov 定理	★ 強健模糊觀測狀態回饋控制-Circle與Popov定理
★ H_infinity 取樣模糊系統的觀測型控制	★ H∞取樣模糊系統控制與觀測定理
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★ H∞模糊系統控制-寬鬆變數法	★ 時間延遲 T-S 模糊系統之強健 H2/H(Infinity) 控制與估測
★ 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)

本篇論文提出一種新的模糊模型：線性分式轉換(Linear fractional transformation，LFT)架構的系統，
並分別設計出二階及三階兩種控制器，研究相同受控系統的控制問題。
論文中研究一個含有分式項的模糊控制問題，
以PDC動態輸出回饋控制器來使其達到二次漸進穩定，
並滿足廣義$H_{2}$性能指標的要求。採用全等轉換(congruence transform)
的方法來分析與設計控制器，使控制目標滿足廣義$H_{2}$的性能指標。
因為系統為LFT架構，所以必須考慮LFT架構的比例條件，此限制為求解時重要的條件之一。
在論文中，我們設計了兩種控制器，經過蕭氏轉換(Schur complement)與全等轉換之後，
可以分別得兩組控制器的線性矩陣不等式(LMIs)，
來對原本的控制問題求解。我們也考慮因為線性矩陣不等式數目太多，
易造成求解時的難度增加，
所獲得的解過於侷限等情形提出簡化線性矩陣不等式(LMIs)數目與增加求解裕度的方法。
亦嘗試限制$Delta$滿足二次模(2-norm)的架構，探討如此限制下的求解條件。
最後，使用含有分式項的倒車例子進行電腦的模擬求解。

摘要(英)

關鍵字(中)

★ 模糊控制
★ 線性矩陣不等式
★ 線性分式轉換

關鍵字(英)

★ Fuzzy control
★ LMI
★ LFT

論文目次

第一章緒論
{1.1}文獻回顧
{1.2}研究動機
{1.3}論文架構
{1.4}符號標記
第二章模糊線性分式轉換系統
{2.1}系統的數學模型
{2.2}控制器的數學模型
{2.2.1}二階模糊LFT動態輸出回饋控制器
{2.2.2}三階模糊LFT動態輸出回饋控制器
{2.3}閉迴路系統
{2.3.1}二階閉迴路系統
{2.3.2}三階閉迴路系統
第三章模糊線性分式轉換架構之限制
{3.1}預備定理
{3.2}比例條件
第四章廣義$H_{2}$性能限制
{4.1}廣義$H_{2}$性能
{4.2}LFT架構性能限制
{4.2.1}二階閉迴路系統之性能限制
{4.2.2}三階閉迴路系統之性能限制
第五章寬鬆求解條件
{5.1}二階系統
{5.2}三階系統
第六章電腦模擬倒車例子
{6.1}數學架構
{6.2}模擬結果
第七章特殊情況
{7.1}數學模型
{7.2}控制目標
{7.3}舉例
第八章總結與未來研究方向
{8.1}總結
{8.2}未來研究方向
{參考文獻}
附錄A 附註1說明
附錄B Sijk與Wijk各元素
附錄C 倒車例子
{C.1}推導
{C.2}求解增益矩陣
{C.2.1}二階系統增益矩陣
{C.2.2}三階系統增益矩陣

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指導教授

羅吉昌(Ji-Chang Lo)

審核日期

2003-6-26

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