具有时滞的非线性纵向飞行模型稳定性和分支分析  

Stability and bifurcation analysis of nonlinear model for longitudinal motion with time delay

作　　者：范丽[1,2] 史忠科[1] 

机构地区：[1]西北工业大学自动化学院,西安710072 [2]陕西师范大学数学与信息科学学院,西安710062

出　　处：《控制与决策》2013年第7期985-990,共6页Control and Decision

基　　金：国家自然科学基金项目(61134004;61273311);中央高校基本科研业务费专项基金项目(GK201302004)

摘　　要：研究一类具有时滞的非线性飞行模型的稳定性和分支问题.首先考虑数据测量的时间延迟,给出了含时滞的大迎角纵向多项式飞行模型;然后应用泛函微分方程Hopf分支理论和中心流形等非线性方法给出了该模型稳定性和分支的解析分析,得到了由时滞引起的Hopf分支存在条件、分支点计算公式以及分支周期解的稳定性判别准则;最后利用所得结论进行了飞行实例分析,分析结果表明,数据测量延时可能会引起飞行稳定性的改变,而且延时超过一定临界值时将产生Hopf分支,出现纵向周期振荡,其结论具有实际参考意义.The stability and bifurcations of a nonlinear flight system with time delay are investigated.Firstly,considering the time delay in measurement of angle of attack,a polynomial differential system with time delay for aircraft longitudinal motion is suggested.Then by applying Hopf bifurcation and center manifold theories of functional differential equations,the stability and bifurcations of the time-delayed system are studied analytically,and existence conditions for Hopf bifurcations as well as formulas for calculating bifurcation points and stability of the bifurcation limit cycle are derived.Finally,the theoretical conclusions are applied to analyze a practical example of high angle-of-attack flight.The results show that the delay in the measurement of angle of attack can cause instability,moreover,the Hopf bifurcation occurs and the periodic oscillation of longitudinal direction arises when the measurement delay exceeds the critical value.The conclusion has the reference significance in practice.

关 键 词：非线性 纵向运动 时滞 分支 稳定性 

分 类 号：V211.12[航空宇航科学与技术—航空宇航推进理论与工程]