飞机起降滑行过程中的非线性振动及其时滞反馈控制研究

Study on Nonlinear Vibration and Delayed Feedback Control of Aircraft in Take-Off and Sliding

摘要: 本文主要研究飞机起降滑行过程中垂直方向上的非线性振动特性并对其主系统(飞机机体)的振动进行时滞反馈主动控制。首先对飞机机体和起落架建立二自由度非线性系统模型，并得到模型的运动微分方程组，坐标转换进行解耦，再利用多尺度法求解方程组的近似解析表达式，模拟分析外激励频率趋近一阶振动模态频率时主系统的振动幅值，这里着重研究系统的1:5内共振情况。然后研究非线性系统动力学的行为并考察主动控制时的反馈增益系数和时滞量对主系统振动的幅值影响，得到主系统的振幅——时滞响应曲线，从而利用时滞反馈来控制主系统的振动。最后对系统的控制参数进行优化设计，同时对系统的稳定性进行分析。研究结果表明，对含有时滞项的非线性振动系统，通过调节合理的反馈增益系数和时滞量，对主系统能起到很好的减振作用，机体的减振幅度最高可以达到48%。与之相对的，如果其参数选择的不合适，对比无时滞项的初系统，机体的振幅将会增大，振动特性变得更加恶劣。本文的研究结果有助于飞机起落架的减振控制系统的进一步完善，同时也为飞机减振器的设计和研发提供一个新的思考方向。

Abstract: In the present paper, the vertical nonlinear vibration characteristics of landing gear system are investigated when the aircraft is taxiing. The delayed feedback control is employed to control and suppress the vibration of the aircraft body. The differential equations of a two degree of freedom nonlinear vibrating system is obtained and approximate analytical solution is achieved by the method of decouping and multiple scales. The dynamical behavior of vibrating system is investigated when the external frequency approaches the first order modal frequency and 1:5 internal resonance occurs simultaneously. The focus is to analyze the effect of gain and time delay on the vibration of the vibrating system. The response curve of primary system and time delay is obtained and the stability of the system is investigated. The results show that the vibration of the aircraft body is suppressed about 48% when the controlling parameters are chosen appropriately. However, the vibration of the aircraft body may lose its stability and destroyed when the controlling parameters are chosen unreasonably. The results of the present paper may improve the vibrating theory of aircraft landing gear system and provide valuable reference for engineering designers.