Adaptive guidance control of super-twisting sliding mode for virtual track train
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摘要: 为提高虚拟轨道列车在参数不确定和未知外部扰动环境中自导向控制的鲁棒性能，针对列车运行中多输入多输出的过驱动控制问题，基于拉格朗日方程建立了多铰接列车的非线性导向控制模型，将等效轮胎侧偏力作为控制输入量；利用虚拟轨道离散点坐标与列车运行速度，建立了计算列车位置、速度与加速度的参考模型，设计了独立的列车导向控制器与纵向速度控制器；利用李雅普诺夫方法，基于传统滑模控制(SMC)和自适应超螺旋滑模(ASTSM)分别设计了2种列车导向控制器，利用轮胎逆模型计算了线控转向系统的转角控制量；建立了轮速分配模型，基于参考速度矢量，将列车纵向速度控制转换为每个轮毂电机的转速与电磁转矩控制；建立了7节编组列车的动力学仿真模型，通过变速和综合线路测试分析了轮毂电机转速和电磁转矩的响应过程，研究了车辆模块之间铰接作用力的分布规律，比较了SMC和ASTSM在参数不确定和未知外部扰动工况下的鲁棒性能。研究结果表明：建立的列车导向控制模型、运动参考模型与轮速分配模型是有效的；车辆模块的纵向速度跟踪误差小于1.5 km·h-1，车轮转速跟踪误差率小于1%；与SMC相比，当存在未建模动态、50%负载变化与未知扰动时，提出的ASTSM具有更好的自适应鲁棒性能，使车轴中心位置偏差能在有限时间内收敛至0附近；在侧向力干扰下，ASTSM的车轴中心偏差均方根与最大值分别为10和42 mm，分别降低了82%和61%；ASTSM在曲线路段中无明显的稳态偏差，且车间铰接角能一致地收敛至稳态值，保证了虚拟轨道列车的运行稳定性。Abstract: In order to improve the robust performance of autonomous guidance control of virtual track trains subject to parameter uncertainties and unknown external disturbances, the multi-input and multi-output overdrive control problem during train operation was studied, a nonlinear guidance control model of multi-articulated virtual track train was established based on Lagrange's formula, and the equivalent lateral tire force was used as the control input. By employing discrete point coordinates of the virtual track and the speed of the train, a reference model was built to calculate the location, speed, and acceleration of the train, and an independent guidance controller and longitudinal speed controller of the train were designed. By applying Lyapunov method, based on the traditional sliding mode control (SMC) and adaptive super-twisting sliding mode (ASTSM), two guidance controllers of the train were designed, respectively, and the control command of a steer-by-wire system was calculated by an inverse tire model. Moreover, a wheel speed allocation model was established, in which the longitudinal train speed control was converted to the speed and electromagnetic torque control of each in-wheel motor on the basis of the reference velocity vector. A dynamics simulation model composed of seven carriages was constructed, and the responses of in-wheel motor speed and electromagnetic torque were analyzed by variable speed and compound path test. The distribution law of the articulated force between vehicle modules was revealed, and the robustnesses of SMC and ASTSM under uncertain parameters and unknown external disturbances were compared. Research results show that the proposed guidance control model, motion reference model, and wheel speed allocation model are effective. The tracking errors of longitudinal velocities of vehicle modules are less than 1.5 km·h-1, and the tracking error rates of wheel speeds are not more than 1%. Compared with the SMC, the proposed ASTSM has better adaptive robustness in the presence of unmodeled dynamics, 50% load changes, and unknown disturbances, and the deviation of each axle center can gradually converge to around 0 in finite time. Under the lateral force interference, the root mean square deviation and maximum deviation of the ASTSM for all axis centers are 10 and 42 mm, and decrease by 82% and 61%, respectively. In addition, the steady-state deviation of the ASTSM on the curved section is not significant, and the articulated angles can consistently converge to a stable value, which guarantees the stability of the virtual track train.
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图 11 工况1中SMC与ASTSM的跟踪偏差对比
Figure 11. Comparison of tracking errors between SMC and ASTSM in Case 1
图 12 工况2中SMC与ASTSM的跟踪偏差对比
Figure 12. Comparison of tracking errors between SMC and ASTSM in Case 2
图 13 工况3中SMC与ASTSM的跟踪偏差对比
Figure 13. Comparison of tracking errors between SMC and ASTSM in Case 3
图 17 ASTSM作用下的等效车轮偏转角响应
Figure 17. Responses of equivalent wheel steering angles under ASTSM
表 1 综合测试线路参数
Table 1. Parameters of compound testing path
路段 线路参数/m 速度/(km·h-1) P1 路段长度L1 = 60 20 P2 曲率半径R1 = 35 20 P3 线路长度L2 = 100 30 P4 曲率半径R2 = 80 30 P5 线路长度L3 = 115 15 P6 曲率半径R3 = 25 15 P7 线路长度L4 = 135 54 P8 曲率半径R4 = 250 54 P9 线路长度L5 = 150 0 
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