慣性測速器非線性動力分析及渾沌控制

Abstract

本篇論文討論一慣性測速器且基座受外部垂直振動干擾所產生的動態行為。由李亞普諾夫直接法和切達耶夫定理可求得到系統平衡點的穩定條件及穩定分析。應用數值分析的結果，例如相位圖、功率譜法、龐加萊映射及李亞普諾夫指數可以觀察到週期與渾沌的運動行為。參數變化對系統的影響可以經由分歧圖與參數圖表現出。最後，利用九個渾沌控制方法來控制系統從渾沌現象回到週期現象或進一步追蹤指定的軌跡。

The dynamic behaviors of an inertial tachometer that is subjected to a disturbance of external vertical vibration to basement are studied in the thesis. The Lyapunov direct method and center manifold theory are applied to obtain conditions of stability and stability analysis of the equilibrium points of system. By applying numerical result, phase diagrams, power spectrum, Poincare maps, and Lyapunov exponents are used to observe periodic and chaotic motions. The effect of the parameters changed in the system can be found in the bifurcation and parametric diagrams. Finally, nine chaos control methods are used to control a chaotic motion to periodic motion or tracking an appointed trajectory.