陀螺體系統的渾沌、渾沌控制、同步及渾沌反控制研究

Abstract

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.