高超声速飞行器横侧向失稳非线性分岔分析

NONLINEAR BIFURCATION ANALYSIS OF LATERAL LOSS OF STABILITY FOR HYPERSONIC VEHICLE

针对滑翔式高超声速飞行器大攻角横侧向失稳问题,采用延拓算法和分岔理论,求解并分析了以俯仰舵偏为连续参数的稳态平衡分岔图和以副翼舵偏为连续参数的横侧向机动稳态平衡分岔图,对平衡分支的稳定性和突变点进行了分析,并给出了特征根拓扑结构变化.研究表明,高超声速飞行器存在极限分岔点、Hopf分岔点以及叉型分岔点,且从叉型分岔点延伸出多个平衡分支,引起横侧向的自滚转失稳;从Hopf分岔点延伸出极限环分支,该分支对应较为复杂的极限环运动,其中还包含倍周期分岔、花环分岔、极限环极限点分岔等复杂的分岔现象;在横侧向机动飞行情况下,模型存在横向操作偏离失稳问题,且存在多个不稳定的平衡点.研究结果为实现高超声速飞行器的稳定飞行和控制器的设计提供了极其重要的动力学信息.

Aiming at addressing the loss of stability in lateral motion of hypersonic gliding vehicle with high angle of attack, the bifurcation theory and the continuation approach were used to obtain the branches of the steady equilibria where the elevator was considered as a continuation parameter. Meanwhile, the lateral maneuver branches of equilibria were also computed where the aileron was employed as a continuation parameter for the selected characteristic points. Then, the stability and bifurcation points were analyzed in detail, and the topologies for the 5 dimension model were given. It was found that the limit points, Hopf points and branch points exist for the branches. The pitchfork branches were stretched out from the BP points where the loss of stability for auto-rotation was triggered; the branches extending out from the Hopf point were also researched in detail where the complicated limit circle motion was presented involving perioddoubling bifurcation, Neimark--Sacker bifurcation, limit point of circle bifurcation etc.; furthermore, through analyzing the branches of equilibria for lateral maneuver condition, problems of loss of stability for maneuver, multi-equilibrium points and loss of stability for lateral control dynamics exist. The results of the research could provide the important dynamic information for realizing the flight stability and designing of the controller.