飞机前起落架模型的Hopf分岔及控制研究  

Hopf Bifurcation Analysis and Bifurcation Control of Aircraft Nose Landing Gear System

作　　者：张瑜[1] 张文[1] 乐源[1] Zhang Yu;Zhang Wen;Yue Yuan(School of Mechanics and Aerospace Engineering,Southwest Jiaotong University,Chengdu 610031,China)

机构地区：[1]西南交通大学力学与航空航天学院,成都610031

出　　处：《动力学与控制学报》2024年第8期13-22,共10页Journal of Dynamics and Control

基　　金：国家自然科学基金资助项目(12072291)。

摘　　要：以一类单轮式飞机前起落架动力学模型为研究对象,将非光滑项进行光滑拟合后,通过坐标变换将系统转化为规范形.运用Hopf分岔理论计算了系统的极限环曲率系数,根据它的符号判断Hopf分岔的类型,并通过数值模拟验证了理论推导的正确性.对系统施加线性反馈控制器,分析控制参数对系统Hopf分岔行为的影响;对系统施加非线性立方反馈控制器,通过幅值计算公式,讨论控制参数对极限环幅值的影响.结果表明,线性控制器能使系统的Hopf分岔点后移,从而减小Hopf分岔的不稳定区域;非线性控制器在不改变系统Hopf分岔点的情况下,能减小Hopf分岔产生的极限环的幅值.该结果可以为飞机前起落架系统的结构优化提供一定理论指导.In this paper,the dynamic model of the nose landing gear of a single-wheeled aircraft is investigated.After smooth fitting of the non-smooth term,the system is transformed into normal form by coordinate transformation.We calculated the first Lyapunov coefficient of the landing gear system by using the Hopf bifurcation theory,and judge the type of Hopf bifurcation according to its sign.The correctness of the theoretical derivation is verified by numerical simulation.And then,we applied linear feedback control to the system and analyzed the influence of control parameters on Hopf bifurcation behavior.A nonlinear cubic feedback controller is applied to the system,and the influence of the control parameters on the amplitude of the limit cycle is discussed through the amplitude calculation formula.The results show that the linear controller can make the Hopf bifurcation point of the system move back,thus reducing the unstable region of Hopf bifurcation.The nonlinear controller can reduce the amplitude of the limit cycle generated by Hopf bifurcation without changing the Hopf bifurcation point of the system.The results can provide some theoretical guidance for the structural optimization of aircraft nose landing gear system.

关 键 词：起落架 HOPF分岔 极限环曲率系数 线性反馈控制 非线性立方反馈控制 

分 类 号：O313[理学—一般力学与力学基础]