臺灣博碩士論文加值系統

本論文係探討一具輸出濾波器之昇降壓型電壓轉換器的混沌行為。有別於傳統電壓轉換器的建模方式，本論文因考慮二極體的非線性現象，故加入二極體的指數型模型。而在系統分析方面，本文採用三種不同的電壓迴路補償器，分別是比例控制器(P-type compensator)、比例-積分控制器(PI-type compensator)以及比例-積分-微分控制器(PID-type compensator)。在使用三種不同的控制器的情況下，本文試著改變系統的參數，如輸入電壓、輸出電阻、脈波調變的週期等等，以探討系統平衡點的穩定度，並計算李亞普諾夫指數(Lyapunov exponents)和碎形維度(Fractal dimension)。由數值模擬結果顯示，系統在輸入電壓或脈波調變(Pulse-width Modulation)的週期超過一臨界值時，會產生分歧現象以及準週期運動。而在控制混沌方面，本文採用OGY(Ott, Grebogi, and Yorke)控制和時間延遲回饋控制(Time-Delayed Feedback Control)。經由數值模擬可發現，當系統軌跡呈現準週期性或週期加倍(period doubling)時，此兩種控制法則的確可將系統軌跡拉回到龐加萊映射(Poincaré map)的平衡點，使系統呈現週期性運動。

This thesis investigates the chaotic behavior of a buck-boost converter with an output low-pass filter. Unlike the conventional approaches for modeling a DC-DC converter, the exponential model of the diode is employed in this thesis to account for the nonlinear characteristics of the diode. As for the system analysis, three voltage-loop compensators are adopted: P-type compensator, PI-type compensators, and PID-type compensator. With these three compensators, the values of different system parameters, such as input voltage and PWM (Pulse-width Modulation) period, are varied to analyze the stability of the fixed point and compute the Lyapunov exponents as well as the fractal dimension. In numerical simulations, it is observed that bifurcation and quasi-periodicity occur as the system parameters are beyond certain critical values. In addition, for controlling chaos, two methods, OGY (Ott, Grebogi, and Yorke) and TDFC (Time-Delayed Feedback Control), are adopted. These two approaches are found effective to pull the system trajectory back to the fixed on the Poincaré map when the system’s behavior is period-doubling or quasi-periodic.

中文摘要…………………………………………………………………Ⅰ
ENGLISH ABSTRACT………………………………………………………Ⅱ
ACKNOWLEDGEMENT……………………………………………………… Ⅲ
CONTENTS…………………………………………………………………Ⅴ
LIST OF TABLES…………………………………………………………Ⅷ
LIST OF FIGURES……………………………………………………… Ⅸ
1. Introduction………………………………………………… 1
1.1 Motivation…………………………………………………… 1
1.2 Literature Review……………………………………………2
1.3 Contribution………………………………………………… 5
1.4 Organization of the Thesis……………………………… 5
2. Preliminaries…………………………………………………7
2.1 Poincaré Maps…………………………………………………7
2.2 Quasi-periodicity………………………………………… 11
2.3 Bifurcation………………………………………………… 13
2.4 Strange Attractors…………………………………………16
2.5 Lyapunov Exponents…………………………………………18
2.6 Dimension Calculation…………………………………… 23
2.6.1 Capacity Dimension…………………………………………23
2.6.2 Correlation Dimension…………………………………… 26
3. Modeling of the Buck-Boost Converter…………………29
3.1 Introduction of the Buck-Boost Converter……………29
3.1.1 Continuous-Conduction Mode (CCM)………………………31
3.1.2 Discontinuous-Conduction Mode (DCM)………………… 34
3.2 Piecewise Linear Model of the Buck-Boost Converter34
3.2.1 Buck-Boost Converter with P-type Compensator………38
3.2.2 Buck-Boost Converter with PI-type Compensator…… 40
3.2.3 Buck-Boost Converter with PID-type Compensator……42
3.3 Nonlinear Modeling of the Buck-Boost Converter……43
3.3.1 Buck-Boost Converter with P-type Compensator………44
3.3.2 Buck-Boost Converter with PI-type Compensator…… 45
3.3.3 Buck-Boost Converter with PID-type Compensator……46
3.4 Problem Formulation……………………………………… 47
4. Chaos Analysis of the Buck-Boost Converter…………48
4.1 Construction of the Poincaré Map………………………48
4.2 Derivations of the Jacobian matrix……………………50
4.3 System Specifications…………………………………… 56
4.4 Buck-Boost Converter with P-Type Compensator………57
4.4.1 Simulation Results…………………………………………57
4.4.1.1 Variations of System Parameters……………………… 57
4.4.1.2 Different PWM Waveforms………………………………… 75
4.5 Buck-Boost Converter with PI-Type Compensator… …78
4.5.1 Simulation Results…………………………………………78
4.5.1.1 Variations of System Parameters……………………… 78
4.5.1.2 Different PWM Waveforms……………………………… …90
4.6 Buck-Boost Converter with PID-Type Compensator……94
4.6.1 Simulation Results…………………………………………94
4.6.1.1 Variations of System Parameters……………………… 94
4.6.1.2 Different PWM Waveforms………………………………… 98
4.7 Summary………………………………………………………102
5. Control of Chaos………………………………………… 104
5.1 OGY Control…………………………………………………105
5.1.1 Brief Introduction of OGY Control……………………105
5.1.2 Simulation Results……………………………………… 106
5.2 Time Delay Feedback Control……………………………111
5.2.1 Brief Introduction of Time Delay Feedback Control111
5.2.2 Simulation Results……………………………………… 112
6. Conclusions and Future Work……………………………117
6.1 Conclusions…………………………………………………117
6.2 Future Work…………………………………………………118
Reference………………………………………………………………120

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