二自由度揚聲器機電系統之渾沌反控制及同步研究

Abstract

本篇論文是在探討二自由度揚聲器機電系統的渾沌反控制與同步。首先利用外加的控制項使得原來的週期行為控制到渾沌行為，而使用的控制方法有以下六種：加常數外力、加週期方波、加週期鋸齒波、加週期三角波、加週期整流弦波、加 項。藉由數值分析方法的結果，如分歧圖、李亞普諾夫指數來驗證其控制結果。接著對不同階系統做同步的研究。分別使用增加耦合項法與誤差動力學線性化法以達到同步，並藉由數值分析法的相圖與時間響應圖驗證結果。就相同系統的同步的探討而言，運用適應控制與Gerschgorin原理，使得兩個不同初始值的渾沌系統達到同步。最後，對相同系統利用適應控制方法與隨機最佳化方法以完成參數之確認。

The chaos anti-control and synchronization of a two-degrees-of-freedom loudspeaker system are studied in this thesis. Anti-control term is added to change state from regular to chaos. The anti-control methods such as addition of a constant force, of a periodic square wave, of a periodic saw tooth wave, of a periodic triangle wave, of a periodic rectified sinusoidal wave and of the term are used. The results are illustrated by numerical results, i.e. bifurcation diagram and Lyapunov exponents. Next, chaos synchronization of different order system is studied. Two methods are presented to achieve the synchronization: the addition of the coupling terms, the linearization of the error dynamics. The results are illustrated by phase diagram and time response. Then the identical systems are discussed for synchronization of chaos. Two methods are used to synchronize two identical chaotic systems with different initial condition: the adaptive control and the Gerschgorin’s theorem. Finally we research the parameter identification for two identical two-degrees-of-freedom loudspeaker systems by adaptive control and random optimization method.