具考慮連桿與套管質量之離心調速器的旋轉機械之

Abstract

本篇論文探討一考慮連桿與套管質量的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以求得系統運動的穩定條件。利用中心流型理論,一個餘維數一的分歧分析應用於自治系統的退化點後,發現系統存在著Hopf分歧行為,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與參數圖表現出來。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等八種方法來有效地抑制渾沌行為。

The dynamic behaviors of a 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. A codimension one-bifurcation analysis for the autonomous system is carried out near the degenerate point. It is founded that Hopf bifurcation occurs in the system by center manifold theory. By applying numerical result phase diagrams, power spectrum, Poincare maps, and Lyapunov exponents are used to observer periodic and chaotic motions. The effect of the parameters changed in the system can be found in the bifurcation and parametric diagrams. Finally, eight methods, i.e. the addition of constant torque and period torque, using periodic impulse input as control torque, the delayed feedback control, optimal control, bang-bang control, adaptive control and the injection of a dither signal method are used to control chaos effectively,