淮阴工学院学报

针对智能车辆的纵横向控制需要提出一种基于线性二次最优控制（LQR）与比例微积分控制（PID）的纵横向耦合控制方法。首先，建立车辆二自由度动力学模型，设计LQR横向动力学控制器；然后，设计位置PID和速度PID双比例微积分纵向控制策略；最后，搭建Prescan/CarSim/MATLAB联合仿真平台，设计两种典型行驶工况对该控制算法的有效性进行测试。结果表明：在满足多约束条件下，所提出的横纵向耦合控制系统提升了车辆的路径跟踪性能，在纯跟踪工况下可将纵向位移稳态误差维持在0.2～0.5 m，横向位移稳态误差维持在0.1～0.2 m；将纯跟踪工况与障碍物工况进行对比，纵向稳态误差无明显波动，横向误差仅在车辆前轮转角较大时产生0.28 m以内的波动。横纵向耦合控制器整体表现良好，控制误差在合理范围内，且控制算法的空间复杂度相对连续LQR显著降低，运算量下降，系统响应迅速。

A longitudinal-transverse coupling control method based on the Linear Quadratic Regulator(LQR) and Proportional-Integral-Derivative(PID) control is proposed to address the longitudinal and lateral control requirements of intelligent vehicles. First,a two-degree-of-freedom vehicle dynamics model is established,and an LQR lateral dynamics controller is designed. Then,a dual PID control strategy combining position PID and speed PID is developed for longitudinal control. Finally,the control algorithm is tested under two typical driving conditions through joint simulations using Prescan,CarSim,and MATLAB. Simulation results show that the proposed longitudinal-transverse coupling control system can effectively follow the trajectory provided by the decision-making and planning system while satisfying various vehicle constraints. Under pure tracking conditions,the longitudinal displacement steady-state error is maintained between 0.2m and 0.5m,and the lateral displacement steady-state error is between 0.1m and 0.2m. When comparing the obstacle-present condition with the obstacle-free condition,the longitudinal steady-state error shows no significant fluctuation,while the lateral error fluctuates within 0.28m only when the front wheel steering angle is large. The longitudinal-transverse coupling controller demonstrates generally good performance,with control errors within reasonable ranges.Additionally,the spatial complexity of the control algorithm is significantly lower than that of the continuous LQR,resulting in reduced computational load and a rapid system response.