Aircraft nonlinear stability analysis and multidimensional stability region estimation under icing conditions

Icing is one of the crucial factors that could pose great threat to flight safety,and thus research on stability and stability region of aircraft safety under icing conditions is significant for control and flight.Nonlinear dynamical equations and models of aerodynamic coefficients of an aircraft are set up in this paper to study the stability and stability region of the aircraft under an icing condition.Firstly,the equilibrium points of the iced aircraft system are calculated and analyzed based on the theory of differential equation stability.Secondly,according to the correlation theory about equilibrium points and the stability region,this paper estimates the multidimensional stability region of the aircraft,based on which the stability regions before and after icing are compared.Finally,the results are confirmed by the time history analysis.The results can give a reference for stability analysis and envelope protection of the nonlinear system of an iced aircraft.

积冰对飞机本体纵向非线性动力学稳定域的影响

积冰威胁飞行安全,研究积冰对飞机稳定性的影响对确保飞行安全具有重要意义。积冰导致飞机失速迎角降低,仅研究飞机在小迎角线性段的稳定性是不充分的,还需对其非线性动力学稳定域进行研究。首先,基于积冰条件下的飞机气动系数曲线,建立积冰飞机纵向运动的非线性模型;然后,根据非线性动力学理论构造出飞机纵向运动的稳定域边界,并利用时域仿真对稳定域边界进行验证;最后,通过对比无冰与积冰条件下稳定域的变化,分析积冰对飞机稳定域的影响,并将积冰对飞机稳定域的影响和其对气动系数的影响进行对比。积冰条件下飞机稳定域在俯仰角速度方向上收缩约20%,稳定域边界处的最大迎角减小约1°。研究结果表明,积冰条件下飞机稳定域的变化与气动系数的变化一致,积冰导致飞机的稳定域缩小,容易引起飞行事故。

基于逆轨迹方法的简单电力系统稳定域的可视化

基于逆轨迹方法实现了对简单(2阶和3阶)电力系统稳定域的准确估计和可视化研究。依据非线性系统理论,稳定边界由该稳定边界上的所有不稳定平衡点的稳定流形的并集构成。首先,采用偏微分方程的Taylor级数解近似不稳定平衡点的稳定流形,从而得到了不稳定平衡点邻域内的近似稳定边界。进而,以该邻域内近似稳定边界上的点作为初值沿时间逆向积分,即采用逆轨迹来近似不稳定平衡点的稳定流形,从而实现了对稳定域的估计。实际仿真结果表明,采用该方法可以实现对简单电力系统(电力系统的两机经典模型、考虑发电机励磁控制的单机模型等)稳定域的可视化研究。