二自由度對稱重陀螺儀的渾沌反控制與同步研究

Abstract

本篇論文探討二自由度對稱重陀螺儀的渾沌反控制與同步系統。由於系統中非線性項的存在，系統會表現出週期和渾沌行為。運用數值分析的結果，例如李亞普諾夫指數、分歧圖、相平面圖、時間響應可以觀察到週期與渾沌的運動行為。接著，討論了四個渾沌反控制的方法，如外加常數項、外加週期方波項、外加週期鋸齒波項、外加週期三角波項。這些反控制方法都可以使系統呈現渾沌行為的參數範圍大為增加。再次，利用偶合項及線性化誤差動態方程以達成兩個不同階系統的渾沌同步。最後運用外加控制項及李亞普諾夫穩定性理論與隨機的最佳化方法來研究兩個相同系統的同步並進一步追蹤系統的參數。

The anti-control and synchronization of chaos for a two-degree-of –freedom heavy symmetric gyroscope system are studied in this thesis. Because of the nonlinear terms of the system, the system exhibits both regular and chaotic motions. By applying numerical results, Lyapunov exponent, bifurcation diagram, phase diagram, time history are used to observe periodic and chaotic motions. Four chaos anti-control methods are applied for the system, such as adding a constant term, adding a periodic square wave term, adding a periodic saw tooth wave term and adding a periodic triangle wave term. It is found that each anti-control method can effectively increase the range of chaotic motion. Then coupled terms and linearization of error dynamics are used to accomplish the chaotic synchronization between two different order systems. Finally, by Lyapunov stability theory with control terms, and by random optimization method, the synchronization of two identical systems and tracking of the parameter of the systems are studied.