帶回授的部分充液衛星的規則以及渾沌動力分析及其控制

Abstract

本篇論文將呈現一帶回授的部份充液衛星之詳細動力分析。經 由在縱軸所受到簡諧激勵力矩，系統得到豐富的動力行為。系統展現 規則與渾沌運動。運用李雅普諾夫直接法研究其漸進穩定性。運用數 值的方法得出相圖，龐加萊映射，李亞普諾夫指數，功率譜法以及系 統的碎形維度。以修正式內插胞映射法對吸引區邊界及吸引子結構作 全局分析。 更進一步用增量諧波平衡法處理強非線性系統和得到不穩定解的 分析。並用中心流型理論分析其定性行為。 除此之外利用時間延遲反饋控制，定值的力矩，週期激振為力矩， 自適應控制法與Bang-bang控制法則有效的抑制渾沌行為。

This thesis is to present the detail dynamic analysis of satellite with partially-filled fluid. A rich of dynamics behaviors of a satellite excited byharmonic torque on longitudinal axis are presented. It has shown that the system exhibits both regular and chaotic motion. The stability of the system is studied by using the Lyapunov direct method. Numerical methods are used to botain the phase plane, Pioncare map, the Lyapunov exponents, their fractal dimensions and the power spectra. The global analyses of basin boundary and attractors are observed by the modified interpolated cell mapping method (MICM). Further, The incremental harmonic balance method (IHB) can be used to analyze the strong nonlinearity and to find the unstable solutions. The qualitative behavior of the system are studied by the center manifold theorem. Furthermore, the delayed feedback control, the additon of constant torque, the addition of periodic torque, adaptive control, and bang-bang control algorithm are used to control chaos effectively.