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摘要: 为改善现代无轨列车车体横摆稳定性和路径跟踪性能较差的问题，基于拉格朗日方程建立车辆动力学模型，分析了液压杆刚度对车辆转向性能的影响；为解决方程中含有未知约束力，导致其定量关系无法求解的问题，以横摆角速度误差和轨迹跟踪误差为优化目标，采用遗传算法离线优化了刚度参数，并利用函数插值方法在线预测，得到了不同车速、不同前轮转角下的最优液压杆刚度；为提高车辆轨迹跟踪性能，将横摆角速度跟踪误差与轨迹跟踪误差作为评价车辆横摆稳定性的标准，定义了车辆行驶过程中各个轴的侧向误差与航向角误差，基于滑模控制(SMC)算法设计了车辆横摆运动控制器，计算了期望横摆角速度，并进行了稳定性证明和稳态误差分析；由比例积分(PI)控制器计算分配到各个驱动轴的车体横摆力矩，并在U型弯路径上进行了仿真与试验。研究结果表明：车辆稳态转向时，液压杆刚度与车速、前轮转角直接相关，且在任何情况下，连接模块前部液压杆刚度一定大于后部液压杆刚度，车速在22 km·h-1左右时最优液压杆刚度最小；车速大于22 km·h-1时，速度越大，最优液压杆刚度越大，且前部液压杆刚度变化率明显大于后部；车速小于22 km·h-1时，速度越小，最优液压杆刚度越大；直线路段上车轴侧向误差小于0.03 m，航向角误差小于0.03 rad；弯道路段上车轴侧向误差小于0.06 m，航向角误差小于0.06 rad；行驶过程中，车体横摆角速度可以快速跟踪给定值，车辆的行驶稳定性得到了提高，验证了控制策略的有效性。Abstract: To improve the problem of poor yaw stability and path tracking performance of modern trackless trains, a vehicle dynamics model was established based on the Lagrange equation, and the influence of hydraulic rod stiffness on the vehicle steering performance was analyzed. To solve the problem that the unknown constraints in the equation made it difficult to solve its quantitative relationship, the yaw rate error and trajectory tracking error were taken as optimization objectives, and the genetic algorithm was used for offline optimization of stiffness parameters. The function interpolation method was adopted for online prediction to obtain the optimal hydraulic rod stiffnesses under different vehicle speeds and front wheel angles. To improve the vehicle trajectory tracking performance, the yaw rate tracking error and trajectory tracking error were used as the criteria to evaluate the vehicle yaw stability. The lateral error and heading angle error of each axis in the vehicle driving process were defined. A vehicle yaw motion controller was designed based on the sliding mode control (SMC) algorithm, the expected yaw rate was calculated, and the stability proof and steady state error analysis were carried out. The proportional integral (PI) controller was used to calculate the yaw moment of the vehicle body distributed to each drive shaft, and simulation and test were conducted on the U-shaped curve path. Research results show that the hydraulic rod stiffness is directly related to the vehicle speed and the front wheel angle when the vehicle turns in a steady state, and in any case, the front hydraulic rod stiffness of the connection module must be greater than the rear hydraulic rod stiffness. When the vehicle speed is about 22 km·h-1, the optimal hydraulic rod stiffness is the smallest. When the vehicle speed is greater than 22 km·h-1, as the speed increases, the optimal hydraulic rod stiffness rises, and the change rate of the front hydraulic rod stiffness is significantly greater than that of the rear hydraulic rod stiffness. When the speed is less than 22 km·h-1, as the speed gets smaller, the optimal hydraulic rod stiffness becomes greater. The lateral error of the axle on the straight section is less than 0.03 m, and the heading angle error is less than 0.03 rad. The lateral error of the axle on the curve section is less than 0.06 m, and the heading angle error is less than 0.06 rad. In the driving process, the yaw rate of the vehicle body can quickly track the given value, and the driving stability of the vehicle improves, which verifies the effectiveness of the control strategy.
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Key words:
- vehicle dynamics /
- modern trackless train /
- driving stability /
- genetic algorithm /
- sliding mode control
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图 5 液压杆刚度与车速和前轮转角的关系
Figure 5. Relationships between vehicle speed, front wheel angle and hydraulic rod stiffness
表 1 车辆仿真系统参数
Table 1. Parameters of vehicle simulation system
参数 驾驶模块 连接模块 拖车模块 mi/kg 12 800 4 100 8 400 ai/m 2.70 1.05 2.50 li/m 5.15 1.05 2.50 
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表 2 模型车参数
Table 2. Parametersof model vehicle
参数 驾驶模块 连接模块 拖车模块 mi/kg 1.339 0.805 1.202 ai/m 4.00×10-3 4.25×10-3 8.50×10-3 li/m 1.125×10-2 4.250×10-3 8.500×10-3
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