三時間尺度直流馬達的渾沌反控制與同步

Abstract

本篇論文探討一無刷直流馬達的渾沌反控制及同步。藉由解析方法可得到一三時間尺度的動態方程式，並利用數值方法，如相位圖、分歧圖、李亞普諾夫指數，觀察週期解與渾沌的動態行為。利用外加常數值、週期方波、鋸齒波、三角波，以及 項產生渾沌反控制，使系統渾沌現象更趨豐富。接著利用耦合項與線性化動態誤差方程方法，使無刷直流馬達與速率陀螺儀兩個不同階系統達成部分同步。最後探討兩個相同系統的同步。使用外加控制項及李亞普諾夫穩定性理論，使兩系統同步。並進一步藉由適應控制法及隨機最佳化以追蹤系統參數。

Chaotic anticontrol and chaos synchronization of brushless DC motor system are studied in this thesis. Nondimensional dynamic equations of three time scale brushless DC motor system are presented. Using numerical results, such as phase diagram, bifurcation diagram, and Lyapunov exponent, periodic and chaotic motions can be observed. By adding constant term, periodic square wave, the periodic triangle wave, the periodic sawtooth wave, and term, to anticontrol the chaotic or periodic systems, it is found that more chaotic phenomena of the system can be observed. Then, by coupled terms and linearization of error dynamics , we obtain the partial synchronization of two different order systems, i.e. brushless DC motor system and rate gyroscope system. Finally, chaos synchronization of two identical systems via additional inputs and Lyapunov stability theory is studied. And further, the parameter of the system is traced via adaptive control and random optimization method.