動載懸掛軌道系統非線性動力分析與渾沌之控制

Abstract

本篇論文探討一動載懸掛軌道系統之詳細動力分析。經由系統受到簡諧激勵力矩和周期外力，得到豐富的動力行為。系統展現規則與渾沌運動。相對平衡位置的穩定性可由李亞普諾夫直接法得到。運用屈達耶夫定理，得到系統的不穩定性。由許多數值分析的結果，如相平面圖、龐加萊映射、時間響應和功率譜法，可觀察其周期解及渾沌行為。參數變化對系統的影響可以由分歧圖表現出來。利用李亞普諾夫指數和李亞普諾夫維度可驗證系統之渾沌現象。以修正式內插包映射法對吸引區邊界及吸引子結構作全局分析。 本文進一步利用外加定力矩，外加周期外力，延遲回授控制，適應控制及Bang-Bang 控制法有效地改變渾沌現象。

The thesis is to present the detailed dynamic analysis of a suspended track with moving load. By subjecting to a harmonic torque and external periodic force, rich of dynamics behaviors of the system are presented. It has shown that the system exhibits both regular and chaotic motion. By using the Lyapunov direct method the conditions of stability of the relative equilibrium position can be determined. The instability of the system is studied by using Chetaev's theorem. By applying various numerical results such as phase plane, Poincare map, time history and power spectrum analysis, a variety of the periodic solutions and the phenomena of the chaotic motion can be presented. The effects of the changes of parameters in the system can be found in the bifurcation diagrams. Further,chaotic behavior can be verified by using Lyapunov exponents and Lyapunov dimensions.The modified interpolated cell mapping method (MICM) is used to study the basins of attraction of periodic attractors and fractal structure. Furthermore, addition of a constant torque, addition of a period torque, delayed feedback control, adaptive control, and bang-bang control are used to controlling of chaos phenomenal effectively.