多項式模糊雙線性系統控制器設計—齊次李亞普諾夫法

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姓名

邱价偉(Chieh-wei Chiu) 查詢紙本館藏

畢業系所

機械工程學系

論文名稱

多項式模糊雙線性系統控制器設計—齊次李亞普諾夫法
(Controller Design for Polynomial Fuzzy Bilinear Systems via Homogeneous Lyapunov Methods)

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摘要(中)

本論文主要是研究多項式模糊雙線性系統之狀態回授控制器設計，以泰勒級數建模得出模糊系統，並且使用齊次多項式李亞普諾夫函數(Lyapunov function)及其對時間變化率推導穩定條件，本論文將以兩種方法解決雙線性系統問題，第一種方法我們將雙線性項Nxu與Bu合併成一項，第二種控制方法我們以三角函數來描述。其中在連續系統中利用尤拉齊次多項式解決$V(x)$對時間微分所造成V(x)問題並建立齊次之李亞普諾夫函數，而離散系統中則使用非齊次之李亞普諾夫函數，
其中系統向量x中不受控制力影響的系統狀態集合而成，即需假設系統為可控典型式(canonical controllable form)，此限制才能使後續電腦模擬可行，內文將詳細說明。最後藉由電腦程式以平方和方法(Sum Of Squares)來檢驗模糊系統的穩定條件，並設計狀態回授控制器。

摘要(英)

The main contribution in this thesis is a state feedback controller design for polynomial fuzzy bilinear systems modeled by Taylor series. The stability is proved with homogeneous polynomial Lyapunov function. In this thesis, two methods to tackle the control problem of polynomial fuzzy bilinear systems are proposed. In the first method we combine the bilinear term Nxu into the Bu term. The second method is to describe control input with trigonometric functions. For continuous-time systems, we utilize the Euler′s homogeneous polynomial theorem to solve the V(x) which is created by time derivative of V(x), and build the homogeneous Lyapunov function.In discrete-time systems, the non-homogeneous Lyapunov function
state x is a collection of system states that are unaffected by control. This restriction is to avoid problems when doing simulation. The details will be described in this thesis. Finally in numerical simulations, we test the stability condition of the fuzzy systems via Sum Of Squares, and design the state feedback controllers.

關鍵字(中)

★ 雙線性模糊系統
★ 平方和
★ 狀態回授控制
★ 尤拉齊次多項式定理

關鍵字(英)

★ bilinear fuzzy systems
★ sum of squares
★ state feedback
★ Euler′s Theorem for Homogeneous Function

論文目次

一.背景介紹...................1
1.1研究動機..................1
1.2文獻回顧...................2
1.3論文結構..................3
1.4符號標記..................4
1.5預備定理..................6
二.系統架構與主要定理.........11
2.1雙線線性模糊系統架構簡介..11
2.2狀態回售控制系統.........12
2.3主要定理.................12
2.3.1方法一................13
2.3.2方法二................18
三.模糊建模法及平方和檢驗法...29
3.1泰勒級數模糊法...........29
3.2平方和檢驗法.............32
3.3平方和檢驗法之方法一穩定條件.36
3.4平方和檢驗法之方法二穩定條件.38
四.電腦模擬..................40
4.1例題一..................40
4.1.1方法一...............44
4.1.2方法二...............47
4.2例題二..................50
4.2.1方法一...............51
4.2.2方法二...............54
4.3例題三..................57
4.3.1方法一...............58
4.3.2方法二...............61
4.4例題四..................64
4.4.1方法一...............65
4.4.2方法二...............69
五.結論與未來方向............73
5.1結論....................73
5.2未來方向................74
參考文獻.....................75

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指導教授

羅吉昌(Ji-Chang Lo)

審核日期

2019-7-17

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