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摘要: 为提高虚拟编组列车的协同跟踪效率和编队的稳定性，提出了一种基于分布式模型预测控制(DMPC)的多列车交互协同跟踪控制方法，基于单元列车动力学分析建立了虚拟编组领导者-跟随者列车双向拓扑结构的状态空间模型，以改善单向拓扑结构的局限性，使得通信结构更稳固；在代价指标函数中引入邻接系统状态信息，并与自身状态信息进行加权融合，设计了改进的DMPC算法，在运行速度限制、距离限制和控制量限制等约束条件下，通过求解改进的代价指标函数得到了列车最优控制量和最优状态量，实现了虚拟编组列车的分布式协同控制，并从理论上证明了算法的可行性与闭环稳定性；采用实验室配备的列车追踪运行半实物仿真系统进行仿真，以4列CRH380A单元列车组成的虚拟编组列车为控制对象，使其跟踪设定的期望速度曲线，并与其他传统算法进行了对比。仿真结果表明：在不同初始条件下，虚拟编组列车的距离误差和速度误差均能在300 s后收敛，控制输出能满足乘客舒适性要求，且各单元列车在收到速度调整指令后仍可保持稳定编组队形；采用提出的方法得到的虚拟编组列车的速度和距离均方根误差分别为3.32×10-8 km·h-1和6.11×10-7 m，相比传统方法均降低了99.99%，可见，提出的方法的控制跟踪性能优于传统控制方法，且各单元列车的采样时刻仿真时长均能保证在3 ms内，满足高速列车控制系统的要求。Abstract: To improve the cooperative tracking efficiency and stability of virtual coupled trains, a multi-train interactive cooperative tracking control method was proposed based on the distributed model predictive control (DMPC). A state-space model of virtual coupled leader-follower trains bidirectional topology was established based on the unit train dynamics analysis, so as to improve the limitation of unidirectional topology and make the communication structure more stable. The improved DMPC algorithm was designed by introducing the neighboring system state information into the cost index function and weighting it with the self-state information. Under the constraints of running velocity limit, distance limit, and control quantity limit, the optimal control quantity and state quantity of trains were obtained by solving the improved cost index function, the distributed cooperative control of virtual coupled trains was realized, and the feasibility and closed-loop stability of the algorithm were theoretically proven. The semi-physical simulation system for train tracking and running in the laboratory was used for simulation. The virtual coupled trains consisting of four CRH380A unit trains were controlled to track a specified velocity curve and compared the proposed algorithm with other traditional algorithms. Simulation results indicate that under different initial conditions, the distance and velocity errors of virtual coupled trains can converge after 300 s, the control output can meet the requirements of passenger comfort, and each unit train can still maintain a stable coupled formation after receiving the velocity adjustment instruction. The root mean square errors of velocity and distance of virtual coupled trains obtained by the proposed method are 3.32×10-8 km·h-1 and 6.11×10-7 m, respectively, which are 99.99% lower than traditional methods. Therefore, the control and tracking performance of the proposed method is superior to that of traditional control methods, and the sampling time simulation duration of each unit train can be guaranteed within 3 ms, meeting the requirements of high-speed train control system.
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图 5 CRH380A高速列车虚拟编组模拟试验台
Figure 5. Simulation test bench for CRH380A high-speed train virtual coupling
图 17 列车0与列车1速度误差对比
Figure 17. Comparison of velocity errors between train 0 and train 1
图 18 列车0与列车1距离误差对比
Figure 18. Comparison of distance errors between train 0 and train 1
图 19 列车1与列车2速度误差对比
Figure 19. Comparison of velocity errors between train 1 and train 2
图 20 列车1与列车2距离误差对比
Figure 20. Comparison of distance errors between train 1 and train 2
图 21 列车2与列车3速度误差对比
Figure 21. Comparison of velocity errors between train 2 and train 3
图 22 列车2与列车3距离误差对比
Figure 22. Comparison of distance errors between train 2 and train 3
表 1 系统参数
Table 1. System parameters
参数 取值 单元列车质量m/t 480 单元列车车长L/m 100 基本运行阻力系数c0/(N·kg-1) 0.755 0 基本运行阻力系数c1/(N·h·kg-1·km-1) 0.006 36 基本运行阻力系数c2/(N·h2·kg-1·km-2) 0.000 115 最大加速度Umax(t)/(m·s-2) 1 最小加速度Umin(t)/(m·s-2) 1 
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表 2 测试参数
Table 2. Test parameters
试验编号 初始速度误差/(km·h-1) 初始距离误差/m ev0, 1(0) ev1, 2(0) ev2, 3(0) es0, 1(0) es1, 2(0) es2, 3(0) 1 -5 10 -5 10 20 10 2 5 -10 10 15 25 10 3 -10 5 5 -5 10 -20 4 10 -5 -5 -10 5 10
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表 3 列车性能调整比较
Table 3. Comparison of train performance adjustment
试验编号 性能 初始状态 稳定状态 1 各单元列车速度/(km·h-1) v0(t) 280 280 v1(t) 285 280 v2(t) 275 280 v3(t) 280 280 各单元列车间距/m es0, 1(t) 110 100 es1, 2(t) 120 100 es2, 3(t) 110 100 2 各单元列车速度/(km·h-1) v0(t) 280 280 v1(t) 275 280 v2(t) 285 280 v3(t) 275 280 各单元列车间距/m es0, 1(t) 115 100 es1, 2(t) 125 100 es2, 3(t) 110 100 3 各单元列车速度/(km·h-1) v0(t) 280 280 v1(t) 290 280 v2(t) 285 280 v3(t) 280 280 各单元列车间距/m es0, 1(t) 95 100 es1, 2(t) 110 100 es2, 3(t) 80 100 4 各单元列车速度/(km·h-1) v0(t) 280 280 v1(t) 270 280 v2(t) 275 280 v3(t) 280 280 各单元列车间距/m es0, 1(t) 90 100 es1, 2(t) 105 100 es2, 3(t) 110 100
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表 4 算法性能指标对比
Table 4. Comparison of algorithm performance indexes
算法 Mev/(km·h-1) Mes/m W/(m2·s-4) CMPC 1.08×10-3 0.140 2 5.959 2 DMPC 8.12×10-6 2.80×10-4 3.772 5 IMDMPC 3.32×10-8 6.11×10-7 3.579 4
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