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研究生:林宗南
研究生(外文):Tsung-Nan Lin
論文名稱:陀螺體系統的渾沌、渾沌控制、同步及渾沌反控制研究
論文名稱(外文):Chaos, Chaos Control, Synchronization and Chaos Anticontrol of Gyrostat Systems
指導教授:戈正銘戈正銘引用關係
指導教授(外文):Zheng-Ming Ge
學位類別:博士
校院名稱:國立交通大學
系所名稱:機械工程系
學門:工程學門
學類:機械工程學類
論文種類:學術論文
論文出版年:2002
畢業學年度:90
語文別:中文
論文頁數:93
中文關鍵詞:渾沌渾沌控制渾沌同步渾沌反控制陀螺體系統
外文關鍵詞:ChaosChaos ControlChaos SynchronizationChaos AnticontrolGyrostat Systems
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本篇論文研究機械及機電陀螺體受到外力所產生的動態行為。應用一些數值分析,如相位圖、功率譜法、週期-T映射及李亞普諾夫指數可觀察到週期解及渾沌運動。參數變化對系統的影響可以由分歧圖及參數圖表現出來。在全局分析中,系統每個吸引子之吸引區由改進式內插胞映射法(modified interpolated cell mapping)求得。六種控制方法,利用遲滯回饋控制、外加的定力矩、外加的週期外力矩、外加週期脈衝力矩及適應控制和 Bang-Bang 控制等方法能有效的控制渾沌現象。陀螺體系統的渾沌同步可由外加線性迴饋項、外加正旋函數項、外加指數函數項、系統互耦合的型式及適應迴饋方法來研究。最後,利用外加定力矩及外加週期力矩來研究機械及機電陀螺體系統的渾沌反控制。
The dynamic behaviors of mechanical and electro-mechanical gyrostat systems subjected to external disturbance are studied in this dissertation. By applying numerical results, phase diagrams, power spectrum, period-T maps, and Lyapunov exponents are presented to observe periodic and chaotic motions. The effect of the parameters changed in the system can be found in the bifurcation and parametric diagrams. For global analysis, the basins of attraction of each attractor of the system are located by employing the modified interpolated cell mapping (MICM) method. Six methods, the delayed feedback control, the addition of constant torque, the addition periodic torque, the addition of periodic impulse torque, adaptive control algorithm (ACA) and bang-bang control, are used to control chaos effectively. Synchronization of chaos in the gyrostat systems are studied by the addition of linear feedback term, the addition of sinusoidal feedback term, the addition of exponential feedback term, coupled form of the system and adaptive feedback methods. Finally, anticontrols of chaos in the mechanical and electro-mechanical gyrostat systems are studied by the addition of constant torque and periodic torque.
CHINESE ABSTRACT i
ABSTRACT ii
ACKNOWLEDGMENTS iii
CONTENTS iv
FIGURES AND TABLES LIST vi
Chapter 1 Introduction 1
Chapter 2 Chaos, Chaos Control and Synchronization of
Mechanical Gyrostat System 3
2.1 Preliminary 3
2.2 Equation of Motion 3
2.3 Phase Portraits, Period-T Map and Power Spectrum4
2.4 Bifurcation Diagram and Parameter 5
2.5 Lyapunov Exponent and Lyapunov 6
2.6 Global Analysis by Modified Interpolated Cell
Mapping Method 7
2.7 Controlling 9
2.7.1Controlling of Chaos by Delayed Feedback Control
9
2.7.2 Controlling of Chaos by Addition of Constant
Torque 10
2.7.3 Control of Chaos by Addition of Periodic Torque
10
2.7.4 Controlling Chaos by Adaptive Control Algorithm
(ACA) 11
2.7.5 Controlling Chaos by Bang-Bang Control 12
2.7.6 Controlling Chaos by Addition of Periodic Impulse
13
2.8 Synchronization of Chaos 13
2.8.1 Synchronization by the Addition of Linear
Feedback Term 14
2.8.2 Synchronization by the Addition of Sinusoidal
Feedback Term 14
2.8.3 Synchronization by the Addition of Exponential
Feedback Term 15
2.8.4 Synchronization by Coupled Form of the System15
2.9 Remarks
Chapter 3 Chaos, Chaos Control and Synchronization of Electro-
Mechanical Gyrostat System 18
3.1 Preliminary 18
3.2 Equations of Motion 18
3.3 Phase Portraits, Period-T Map and Power Spectrum
20
3.4 Bifurcation Diagram and Parameter Diagram 21
3.5 Lyapunov Exponent and Lyapunov Dimension 21
3.6 Controlling Chaos 22
3.6.1 Controlling of Chaos by Delayed Feedback Control
22
3.6.2 Controlling Chaos by Adaptive Control Algorithm
(ACA) 23
3.7 Synchronization of Chaos 23
3.8 Remarks 26
Chapter 4 Anticontrol of Chaos 27
4.1 Preliminary 27
4.2 Anticontrol of chaos by the addition of constant
motor torque 27
4.3 Anticontrol of chaos by the addition of periodic
motor torque 28
4.4 Parameters diagram of anticontrol of chaos 28
Chapter 5 Conclusions 30
REFERENCES 32
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