运用Lyapunov指数方法的车辆横向运动混沌分析及其滑模变结构控制

建立了考虑车辆横摆、侧向以及侧倾运动的3自由度非线性整车模型：运用Lyapunov指数方法对所建立的非线性整车模型进行了混沌的数值仿真分析．通过最大Lyapunov指数图和分岔图发现，车辆的横向运动非常复杂，包含了倍周期、拟周期以及混沌运动，对于车辆极限工况时的横向运动稳定性是不利的．利用滑模变结构控制（sliding mode variable structure control，SMVSC）方法，设计了SMVSC控制器，对车辆横向运动中的混沌进行了控制．为了减少SMVSC控制系统的抖振，进一步提高车辆在极限工况下行驶的横向运动稳定性，采用了幂次趋近律，利用模糊控制的方法实现了趋近律的自适应策略．最后将所设计的自适应趋近律的SMVSC系统在Matlab中进行了仿真，并将未加控制，SMVSC控制以及自适应趋近SMVSC控制三种仿真结果进行了对比分析，发现采用了自适应趋近的SMVSC控制对混沌的控制效果比其他的都要好，有效抑制了车辆横向运动中的混沌，显著提高了车辆在极限工况下行驶的横向稳定性，充分证明了该控制策略是有效的．

Vehicle lateral motion chaos analysis based on the Lyapunov exponent method and sliding mode variable structure control

In this paper, a 3-DOF nonlinear model including the yaw, lateral and rolls motion was constructed, and then the chaos numerical simulation analysis was performed based on the Lyapunov exponent method. Through the Lyapunov exponent and bifurcation diagrams, the vehicle motion was relatively complex, containing double-periodic, quasi-periodic and chaotic motions, which was harmful for the stability of the lateral motion of vehicles. In order to realize the control of chaos during vehicle lateral motion, the SMVSC controller was designed by using the sliding mode variable structure control （SMVSC） method. To decrease the chattering of the SMVSC system and further improve the stability of vehicle lateral motion under extreme operation conditions, the adaptive power reaching law was realized by using the fuzzy control method. Finally, the SMVSC system based on the designed adaptive reaching law was simulated in the Matlab/simulink, and the simulation results of uncontrol, SMVSC control and SMVSC control based on the adaptive reaching law were compared. It can be found that the SMVSC control based on the adaptive reaching law can present better performance than that of others by effectively suppressing the chaos during vehicle lateral motion and significantly improving the stability of vehicle lateral motions under extreme operation conditions. Therefore, it is proved that the control strategy is effective.