高攻角飛行之分叉特性分析與控制

Abstract

本論文主要針對飛機的縱向飛行動態之三階模式，以分叉理論為基礎，探 討其可能發生的非線性現象。由系統的線性化模式分析得知，此系統於飛 行動態中，可能發生靜態 {\aa saddle-node} 分叉和動態振盪分叉等現 象。另外，我們以 {\aa F-8} 飛機的縱向三階模式做數值之研究與模擬 ，來驗證所獲得之理論分析結果，如系統平衡點之不連續性及靜態和動態 之分叉現象的存在等。除此之外，針對 {\aa F-8} 之三階模式，我們應 用{\aa washout filter} 與直接迴授兩種控制方法設計穩定化之控制法 則，以使不穩定之平衡點及由分叉點所產生之不穩定週期解成為穩定。 In order to increase the performance of aircraft, the modern aircraft is being designed for maneuvering at high angle-of- attack. The flight of high angle-of-attack offers a substantial increase in agility but also results in a greater risk of loss of flight stability. In this thesis, we apply the bifurcation theory toanalyze the nonlinear phenomena and study the bifurcation control of the third-order model for longitudinal flight dynamics. Analysis of system linearization reveals that both stationary andHopf bifurcations may occur at some critical values of the elevator commands. Numerical study of a third- order model of longitudinal dynamics for F-8 aircraft is obtained to verify the results of bifurcation analysis and bifurcation control. Discontinuity of system equilibria is observed in the numerical simulations as either the elevator deflection angle or the mass of the aircraft changes. This agrees with our theoretical analysis of the existence of system equilibria. Furthermore, bifurcation control using both washout filter and direct state feedback are applied to two examples of F-8 flight dynamics to develop stabilizing laws for system equilibria and periodic solutions emerged from bifurcation points.