模糊系統H∞靜態輸出回授控制器設計─齊次多項式尤拉法

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劉鎔維(Jung-Wei Liu) 查詢紙本館藏

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機械工程學系

論文名稱

模糊系統H∞靜態輸出回授控制器設計─齊次多項式尤拉法
(H∞ Static Output Feedback 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之靜態輸出回授控制器設計，使用
非二次李亞普諾夫函數(non-quadratic Lyapunov function) 及其對時間的變化率做為穩定的條件, 並滿足H1 性能指標。本論文分為兩個步驟設計靜態輸出回授控制器，步驟一: 求得狀態回授增益，使用二
次李亞普諾夫函數(quadratic Lyapunov function) ，步驟二: 求解靜態輸出回授增益, 使用非二次李亞普諾夫函數(non-quadratic Lyapunov function)，其中以尤拉齊次多項式定理建立非二次李亞普諾夫函數(non-quadratic Lyapunov function)，其形式為
V (x) = x′P(x)x = 1/(g(g-1))x′∇xxV (x)x。
電腦模擬方面以平方和方法(Sum-of-Squares) 來檢驗模糊系統的
穩定條件，並設計出狀態回授控制器以及靜態輸出回授控制器。

摘要(英)

The main contribution in this thesis is static output feedback controller
design of H1 continuous fuzzy system. And we can solve the inequalities derived from non-quadratic Lyapunov function and its time gradient. It’s a two-step procedure for solving output feedback control gain, step 1: solve for state feedback gain (for common P theorem), step 2: solve for static output feedback gain (for homogeneous polynomial P(x) theorem). A non-quadratic Lyapunov function derived from
Euler’s homogeneous polynomial theorem has following form
V (x) = x′P(x)x = 1/(g(g-1))x′∇xxV (x)x。
In numerical simulation, we solve for state feedback gain first and then solve for static output feedback gain with sum-of-squares approach.

關鍵字(中)

★ 非二次穩定
★ 平方和
★ Takagi-Sugeno模糊系統
★ 尤拉齊次多項式定理
★ H∞狀態回授控制
★ H∞靜態輸出回授控制

關鍵字(英)

★ non-quadratic stability
★ sum of squares
★ T-S fuzzy systems
★ Euler′s Theorem for Homogeneous Function
★ H∞ state feedback control
★ H∞ static output feedback control

論文目次

中文摘要............................................................................................. i
英文摘要............................................................................................. ii
謝誌.................................................................................................... iii
目錄.................................................................................................... iv
圖目錄................................................................................................ vi
1、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
2、系統架構與檢測條件...................................................... 7
2.1 模糊系統架構簡介. . . . . . . . . . . . . . . . . . . 7
2.2 尤拉齊次多項式定理. . . . . . . . . . . . . . . . . 8
2.3 H1 狀態/靜態輸出迴授控制系統. . . . . . . . . . . 12
2.4 主要定理. . . . . . . . . . . . . . . . . . . . . . . . 17
3、模糊建模方法及平方和檢測法........................................ 24
3.1 泰勒級數模糊. . . . . . . . . . . . . . . . . . . . . 24
3.2 平方和檢驗法. . . . . . . . . . . . . . . . . . . . . 26
3.3 平方和檢驗法之定理2.1 穩定度條件. . . . . . . . . 30
3.4 平方和檢驗法之定理2.2 穩定度條件. . . . . . . . . 31
4、電腦模擬......................................................................... 34
4.1 例題一. . . . . . . . . . . . . . . . . . . . . . . . . 34
4.2 例題二. . . . . . . . . . . . . . . . . . . . . . . . . 42
4.3 例題三. . . . . . . . . . . . . . . . . . . . . . . . . 47
4.4 例題四. . . . . . . . . . . . . . . . . . . . . . . . . 53
5、結論與未來方向.............................................................. 59
5.1 結論. . . . . . . . . . . . . . . . . . . . . . . . . . 59
5.2 未來研究方向. . . . . . . . . . . . . . . . . . . . . 61
文獻.................................................................................................... 62

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指導教授

羅吉昌(Ji-Chang Lo)

審核日期

2016-7-28

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