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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 the bifurcation problem of a class of nonlinear flight model with time delay are studied. Firstly, considering the time delay of data measurement, the vertical polynomial flight model with time delay at high angle of attack is given. Then the Hopf bifurcation theory of functional differential equation And central manifold, the stability and branching analysis of the model are given. The existence conditions of Hopf bifurcation, the calculation formulas of bifurcation points and the criterion of stability of bifurcation periodic solutions are obtained. Finally, Conclusion The flight examples are analyzed. The results show that the delay of data measurement may cause the change of flight stability. When the delay exceeds a certain critical value, the Hopf bifurcation will occur and the longitudinal periodic oscillation will occur. The conclusion is of practical significance.