六邊形離心調速器的旋轉機械之渾沌控制及渾沌同步

Abstract

本篇論文研究一帶六邊形調速器之旋轉機械的渾沌動力行為，自治、非自治及時滯系統均予以討論。由李亞普諾夫直接法可求得自治系統平衡點的穩定條件。應用一些數值分析，如相圖、功率譜法、龐加萊映射法、及李亞普諾夫指數可觀察到週期解與渾沌運動。參數變化對系統的影響可以由分歧圖及參數圖表現出來。除此之外，利用一些控制方法來有效地控制渾沌現象。最後，對於系統的渾沌反控制與渾沌同步，也提供了控制器設計的一些方法。

The chaotic dynamics of the rotational machine with a hexagonal centrifugal governor are studied in this thesis. Autonomous, nonautonomous and time-delay systems are discussed. The Lyapunov direct method is applied to obtain conditions of stability of the equilibrium points of autonomous system. By applying numerical results, phase diagrams, power spectrum, Poincaré maps, and Lyapunov exponents are presented to observe periodic and chaotic motions. The effect of the parameter changes in the system can be found in the bifurcation and parametric diagrams. Besides, several methods are used to control chaos effectively. Finally, some different procedures for the design of the controller are proposed for anticontrol and synchronization of chaos of the governor system.