整數階與分數階帶離心調速器之旋轉機械系統的渾沌同步與渾沌激發之超渾沌

Abstract

本篇論文研究整數階與分數階帶離心式調速器之旋轉機器系統的渾沌同步與渾沌激發之超渾沌。透過數值分析，如相圖，分叉圖，和Lyapunov指數，可以觀察到週期與渾沌運動。利用線性回饋控制與適應性控制，使得整數階系統達成渾沌同步。接著,提出一個新的概念：透過渾沌系統之狀態驅動的渾沌取代透過正弦時間函數驅動的渾沌。此研究乃一個完全新的領域，觀察到超渾沌與廣範圍的渾沌。最後，發現分數階系統的階數少於或多於原系統的狀態數目時皆存在渾沌現象。利用類似於用在整數階系統的方法，系統可以達成渾沌控制與渾沌同步。

Chaos synchronization and chaos-excited hyperchaos, for integral and fractional order rotational machine system with centrifugal governor are studied in this thesis. By applying numerical analysis such as phase portrait, bifurcation diagram and Lyapunov exponent, periodic and chaotic motions are observed. Chaos synchronization for integral order system is accomplished by employing both linear feedback control and adaptive control based on Lyapunov first approximation theorem and asymptotical stability theorem. Then a new concept of chaos driven by states of chaotic system instead of driven by sinusoidal time function is put forward. This research is a completely new field, hyperchaos and broader ranges of chaos are obtained. Finally, it is found that chaos exists in the fractional order system with order less and more than number of states of the system. By utilizing the similar scheme as that for their integral order correspondence, chaos control and chaos synchronization are accomplished.