博碩士論文 102323086 詳細資訊




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姓名 林承緯(Cheng-wei Lin)  查詢紙本館藏   畢業系所 機械工程學系
論文名稱 模糊系統觀測控制器設計─齊次多項式尤拉法
(Observer and Controller Design of Fuzzy Systems via Homogeneous Euler′s Method)
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摘要(中) 本論文主要研究連續模糊系統的非二次穩定(non-quadratic stability)
條件,以泰勒級數建模得出模糊系統,且以非二次的李亞普諾
夫函數(Lyapunov function) 及對時間的變化率作為穩定的條件,對
於決定擴展狀態的高階李亞普諾夫函數,其形式為
V(x,e)=[x e][adj(Q(x)) 0;0 U(e)][x;e]
而使用尤拉齊次多項式可以排除V(x,e)對時間t 微分所產生Q(x) 之
微分項,再以平方和方法(Sum-of-Squares) 來檢驗模糊系統的穩定條
件,並設計出其觀測器及控制器。
由於觀測器與控制器的相依性,分離設計並不容易,本論文將以
限制條件分段解析,並找出有條件下的分離設計方法。
摘要(英) It′s not easy to separate the synthesis of observer and controller
due to their dependability. The main contribution in this thesis is
non-quadratic stability of continuous fuzzy systems, which is modeled
by Taylor series method. And we can solve the inequations derived
from non-quadratic Lyapunov function and its time gradient. The
form of extension from the state dependent Riccati inequalities to
non-quadratic Lyapunov function is
V(x,e)=[x e][adj(Q(x)) 0;0 U(e)][x;e].
To overcome the di erential terms of Q(x) derived from time gradient
of V(x,e), we introduce Euler′s homogeneous polynomial theorem
to derive the SOS condition and solve for the observer and controller
with sum-of-squares approach.
關鍵字(中) ★ 非二次穩定
★ 平方和
★ 參數相依齊次多項式
★ Takagi-Sugeno模糊系 統
★ 尤拉齊次多項式定理
★ 泰勒級數
關鍵字(英) ★ Non-quadratic stability
★ Sum of squares
★ Homogeneous polynomially parameter-dependent (HPPD) functions
★ T-S fuzzy systems
★ Euler′s Theorem for Homogeneous Functions
★ Taylor-Series
論文目次 中文摘要.......................................................................................... v
英文摘要.......................................................................................... vi
謝誌.................................................................................................vii
目錄.................................................................................................viii
圖目錄.............................................................................................. x
一、背景介紹..................................................................... 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
二、系統架構與檢測條件................................................... 7
2.1 系統架構. . . . . . . . . . . . . . . . . . . . . . . 7
2.2 連續系統控制器與觀測器設計. . . . . . . . . . . . 8
2.3 尤拉齊次多項式定理. . . . . . . . . . . . . . . . . 9
2.4 模型簡化及分類. . . . . . . . . . . . . . . . . . . . 12
2.5 類型一系統之穩定度條件. . . . . . . . . . . . . . . 13
2.6 類型二系統之穩定度條件. . . . . . . . . . . . . . . 17
2.7 類型三系統之穩定度條件. . . . . . . . . . . . . . . 21
三、模糊建模方法及平方和檢測法....................................26
3.1 泰勒級數模糊. . . . . . . . . . . . . . . . . . . . . 26
3.2 平方和檢驗法. . . . . . . . . . . . . . . . . . . . . 28
3.3 平方和檢驗法之類型一系統穩定度條件. . . . . . . 32
3.4 平方和檢驗法之類型二系統穩定度條件. . . . . . . 33
3.5 平方和檢驗法之類型三系統穩定度條件. . . . . . . 34
3.6 求解技巧. . . . . . . . . . . . . . . . . . . . . . . 35
四、電腦模擬.....................................................................37
4.1 例題一. . . . . . . . . . . . . . . . . . . . . . . . . 37
4.2 例題二. . . . . . . . . . . . . . . . . . . . . . . . . 52
4.3 例題三. . . . . . . . . . . . . . . . . . . . . . . . . 60
五、結論與未來方向..........................................................68
5.1 結論. . . . . . . . . . . . . . . . . . . . . . . . . . 68
5.2 未來研究方向. . . . . . . . . . . . . . . . . . . . . 69
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指導教授 羅吉昌(Ji-Chang Lo) 審核日期 2015-7-30
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