揚聲器機電系統之穩定性,渾沌,渾沌控制及同步研究

Abstract

本篇論文研究二自由度揚聲器機電系統穩定性、渾沌等豐富的動態行為、渾沌控制及渾沌同步。由於系統中的非線性項的存在，系統會表現出週期和渾沌現象。運用李亞普諾夫直接法，可以得到平衡點的穩定的條件。藉由數值分析方法，如相平面、龐加萊映射法、時間響應、功率譜法，可以觀察其週期解及渾沌現象。改變外力參數對系統的影響可以由分歧圖及參數圖來顯示。利用李亞普諾夫指數可以區分出系統的週期或渾沌行為。 探討了八個控制渾沌的方法，如外加定力、外加週期力、外加週期脈衝、延遲迴授控制、Bang-Bang 控制、適應控制、最佳化控制及開迴路和閉迴路混合控制。這些控制方法可以使系統的渾沌行為控制為週期解。最後，討論成對的渾沌系統的同步現象，包括相互耦合渾沌系統之同步、同步時間、同步相似函數及外加激勵之相位差對同步之影響。本篇論文中，這些方法將被廣泛討論。

The dynamic behaviors of the stability and chaos, chaos control and synchronization of two degrees of freedom nonlinear loudspeaker system are studied in the thesis. Because of the nonlinear terms of the systems, the systems exhibit both regular and chaotic motions. By using the Lyapunov direct method, the stability of the relative equilibrium position can be determined. And by applying various numerical results, such as phase portraits, Poincaré maps, time history and power spectrum analysis, the behaviors of the periodic and chaotic motion are presented. The effects of the change of parameters in the system can be found in the bifurcation diagrams and parametric diagrams. The method of Lyapunov exponents is used to identify the chaos or regular motions of the systems. Eight controlling methods are applied into the systems. Addition of a constant force, Addition of a periodic force, Addition of a periodic impulse, Delay feedback, Bang-Bang feedback, Adaptive, Injecting dither signal, Optimal controls are studied. It is found that each controller can effectively control the chaotic orbits to the regular ones. Finally, the phenomenon of synchronization of coupled chaotic oscillators is presented. Including synchronization of mutually coupled chaotic systems, synchronization time, similarity function and effect of the phase difference of external excitations. In this letter, coupled chaotic system will be studied.