起落架摆振主动控制分岔研究

Active control for landing gear shimmy with bifurcation theories

研究起落架摆振及其主动控制的非线性动力学问题。根据分岔理论,应用数值延拓算法求解参数化非线性摆振微分方程,得到摆振的Hopf分岔点(临界摆振速度)和摆振极限环的幅值,通过李亚普诺夫指数确定极限环的稳定性。在此基础上,提出采用主动控制策略抑制摆振,建立相应数学模型,应用数值延拓算法求解加入控制后的非线性摆振微分方程。结果表明,适当选取控制参数,在飞机滑跑速度范围内,应用主动控制策略可以达到完全抑制摆振的目的,并且对系统参数的变化具有强鲁棒性。

The nonlinear dynamic characteristics of landing gear shimmy and active control of shimmy were studied.According to bifurcation theories,the Hopf point and the shimmy limit-cycle amplitude were gained by solving the nonlinear shimmy differential equations with numerical continuation.The stability of the limit-cycle was determined by calculating Lyapunov exponent.On this basis,the active control was used to suppress the shimmy and the appropriate mathematical model was constructed.And the nonlinear shimmy differential equations were solved after active control was applied.The results showed that the active control strategy of landing gear can fully suppress the shimmy in airplane taxiing speed range by choosing proper control parameters,and has good robustness against varying system parameters.