帶阻尼的部分充液衛星非線性動力分析及渾沌控制

Abstract

本篇論文研究一帶阻尼的部份充液衛星受到幹擾所產生的動態行 為。由李亞普諾夫直接法可求得系統平稀點的穩定條件。利用中心流 型理論，一個餘維數一的分歧分析應用於自治系統的退化點後，發現 系統存在著Hopf分歧行為。應用一些數值分析，如相位圖、功率譜法、 龐加萊映射法(Poincare map)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，系統每個吸子之吸引區由改進式內插胞映射法(modified interpolated cdll mapping)求得。最後，利用運滯回控制、外加的 定力矩、 外加的週期外力及適應控制等方法能有效的控制渾沌現象。

The dynamics behaviors of a damped satellite with partially-filled liquid which is subjected by external disturbance are studied in the thesis. The Lyapunov direct method is applied to obtain conditions of stability of the equilibrium points of the system. A condimension one bifurcation analysis for the autonomous system is carried out near the degenerate point. It is founded the Hopf bifurcation occurs in the system by center manifold theory. By applying numerical results, phase diagrams, power spectrum, Poincare 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,t he basins of attraction of each attractors of the system are located by employing the modified interpolated cell mapping (MICM) method. Finally, several methods, the delayed feedback control, the addition of constant motor torque, the addition of periodic force, and adaptive control algorithm are used to control chaos effectively.