單時間尺度直流馬達的渾沌反控制與同步

Abstract

本篇論文是在探討單時間尺度無刷直流馬達的渾沌反控制與同步。藉由數值方法，如相位圖、分歧圖與李亞普諾夫指數，分析週期與渾沌現象。再利用外加的常數項、週期項與非線性項，達成渾沌反控制。接著利用耦合項、李亞普諾夫穩定理論與線性化動態誤差方程法，達到無刷直流馬達及杜芬系統兩不同階系統間的同步。最後利用適應控制、改良型反步進設計法、葛西高林理論與外加監視器，達到兩個相同無刷直流馬達之間的渾沌同步。並更進一步利用適應控制與隨機最佳化法，達到參數確認。

Anti-control and synchronization of chaos of single time scale brushless dc motors are studied in this thesis. In order to analyze a variety of periodic and chaotic phenomena, we employ several numerical techniques such as phase portrait, bifurcation diagram, and Lyapunov exponents. By addition of an external constant term, an external periodic term, and an external nonlinear term, we can obtain anti-control of chaos. Then, by addition of the coupling terms, by the use of Lyapunov stability theorem, and by the linearization of the error dynamics, chaos synchronizations between BLDCM and Duffing system are presented. Finally, by the adaptive control, the improved backstepping design method, the Gerschgorin theorem, and by addition of a monitor, chaos synchronization of two identical BLDCM systems are given. And further, by the adaptive control, and the random optimization method, parameters identification is approached.