帶振動的離心調速器的旋轉機械非線性動力學及渾沌控制

Abstract

本篇論文探討一帶振動離心調速器之旋轉機械受到簡諧激力所產生的動態行為。由李亞普諾夫直接法可求得系統運動的穩定條件。此外藉相位圖、功率譜法、龐加萊映射法及李亞普諾夫指數可觀察到週期性及渾沌運動。並且參數變化對系統的影響可以由分歧圖即參數圖表現出來。及全局分析中，系統每個吸引子之吸引區即運動的全貌由改進式內插包映射法(modified interpolated cell mapping)求得。最後，利用外加定值的力矩、週期力矩、輸入週期脈衝、延遲迴授控制、最佳控制、bang-bang控制、適應控制及輸入一顫振訊號法則來有效地抑制渾沌行為。

The dynamic behaviors of the rotational machine with vibrating fly-ball governor that is subjected by two different forms of external disturbances are studied in the thesis. The Lyapunov direct method is applied to obtain conditions of stability of the motions of system. By applying numerical result, phase diagrams, power spectrum, Poincare maps, and Lyapunov exponents are presented to observer periodic and chaotic motions. The effect of the parameters changed in the system can be found in the bifurcation and parametric diagrams. For global analysis, the basins of attraction of each attractors of the system are located by employing the modified interpolated cell mapping (MICM) method. Finally, various methods, such as the addition of periodic torque, using periodic impulse input as control torque, the delayed feedback control, optimal control, bang-bang control, adaptive control algorithm and the injection of a dither signal method are used to control chaos effectively.