高维汽车侧向动力学系统的分岔与失稳分析

Analysis on Bifurcation and Destabilization of High-dimensional Vehicle Lateral Dynamics

为建立汽车实际状态响应与轮胎侧偏刚度间的联系,采用二次多项式轮胎模型建立了包含侧倾运动和平面运动的四维非线性侧向动力学系统;应用中心流形定理对其进行了降维处理并转换为中心流形上的一阶约化系统。应用非线性分岔和稳定性理论以及时域仿真分别对均匀路面工况和对开路面工况的稳定性进行了分析。结果表明,奇异点处发生鞍结分岔将导致汽车失稳,可以通过改变前轮转向角来改变分岔特性,改善汽车极限工况下的稳定性,从而实现非线性动力学分析方法与主动转向控制系统的分析和设计相结合,以减小基于线性轮胎模型的控制方案的局限性,提高底盘控制系统的控制性能。

In order to formulate the relationship between vehicle state responses and tire stiffness, a 4 - D nonlinear vehicle lateral dynamic system consisting of roll and planar motions was founded by utilizing a quadratic tire model. Then the 4 - D nonlinear system has been simplified to the center manifold to a one order system with the center manifold theory. The stability characteristics in symmetrical and u- split road conditions were analyzed by bifurcation theory and time-domain simulations. The results demonstrated that the singular point corresponded to the critical state where if bifurcation occurred the vehicle would lose stability. So the vehicle stability at the critical conditions could be improved by changing the front wheel steering angle and it would be a new idea to combine the bifurcation theory and the active steering control technique.