臺灣博碩士論文加值系統

相較於一般系統，奇異系統之控制問題將更為複雜，因為涉及較多的運算矩陣( 與 )及奇異系統存在無限大極點。在這篇論文，我們分解奇異系統來解決這些困難，如此方便系統的分析與設計。首先，因為系統的等效轉換，我們可以保留：(1)系統的轉移矩陣 (2)系統的極點與零點以及 (3)系統的特徵多項式。所以我們使用奇異值分解的方法去分解奇異系統，奇異系統分解和轉換之後，我們可以得到簡單的奇異系統結構方塊圖。我們也提供兩種方法去獲得狀態回授增益，一種是直接的方法；另一種方法是時刻轉換的方法。比較這兩種方法得知，第二種方法比第一種方法容易獲得狀態回授增益。最後，針對具狀態回授之奇異系統，我們利用模糊控制器設計來完成奇異系統之輸出追蹤。

In comparing with general system, the control problems of singular systems are more complicated because more operating matrices (E and A) are involved and infinite poles exist in the singular system. In this thesis, we solve these difficulties by decomposing the singular system in simplified structure. This is easy and convenient for system analysis and design. Firstly, because of the equivalent transformation of the system, we can preserves (1) the transfer matrix of the system, (2) the set of system poles and zeros, and (3) characteristic polynomial of the system. So we use the singular value decomposition method to decompose the singular systems. After decomposing the singular system and using transformation, we can get the simplified singular system configuration. We also provide two methods to obtain the state feedback gain. One is the direct method; the other is time scale transformation method. Comparing these two methods it is found that, the second method is easier to give the state feedback gain than the first one. Finally, we use fuzzy logic controller design for singular system with state feedback to achieve output tracking of the system.

Contents
中文摘要I
AbstractII
AcknowledgmentIII
List of FigureVII
List of TablesVIII
Chapter 1. Introduction 1
1.1Introduction1
1.2Organization of thesis2
Chapter 2. Mathematical Descriptions of Singular Systems4
2.1Introduction4
2.2Basic properties of singular systems.4
2.3Equivalence of Singular systems7
2.3.1 Singular values decomposition form (SVD)7
2.3.2 Weierstrass form8
2.3.3 Standard form9
2.4 Impulse immunity10
2.5 Controllability, R-controllability, and impulse controllability14
2.6 Observability, R-observability, and impulse observability16
2.7 Stability17
2.8 Summary18
Chapter 3. Fuzzy Logic Controller19
3.1Introduction19
3.2Fuzzy logic controller20
3.2.1Fuzzy inference system (FI)21
3.2.2Decision-making logic (DML)23
3.2.3 Knowledge base (KB)25
3.2.4 Defuzzification interface system (DFI)26
3.3Summary…27
Chapter 4. Application of Fuzzy Logic Controller in Singular Systems with Output Feedback28
4.1Introduction28
4.2Computation of the transfer function matrix of singular systems29
4.2.1The direct method…29
4.2.2Generalized Leverrier method33
4.3Simulation and results36
4.4Summary40
Chapter 5. The Integration Strategy of FLC and State Feedback in Singular Systems41
5.1Introduction41
5.2Pole placement of the single input singular systems42
5.2.1 Direct method43
5.2.2 Time-scale transformation method45
5.3Infinite pole placement49
5.4Decomposition of singular systems51
5.5The integration of fuzzy logic controller (FLC) and state feedback
in singular system control58
5.5.1 The FLC in the singular system with state feedback for
output tracking59
5.5.2 The FLC in the perturbed singular system with state feedback
for output tracking60
5.5.3 The FLC for singular system with initial condition in state
variables62
5.6Summary64
Chapter 6. Conclusions65
References67
Biography

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