Data-driven Model-free Adaptive Integral Sliding Mode Predictive Control for High-speed Electric Multiple Unit
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摘要: 同许多复杂系统一样, 动车组(Electric multiple unit, EMU) 运行过程也具有多变量、强耦合以及非线性等特性, 这严重影响着列控系统的性能. 针对包含外部扰动的动车组自动驾驶系统, 提出一种新型的多输入多输出(Multi-input-multi-output, MIMO) 数据驱动积分滑模预测控制(Integral sliding mode predictive control, ISMPC)算法. 首先, 该算法基于与动车组运行过程等效的全格式动态线性化(Full format dynamic linearization, FFDL)数据模型, 设计一种离散积分滑模控制(Integral sliding mode control, ISMC) 律. 为了使系统能够获得更高的输出跟踪误差精度, 利用模型预测控制(Model predictive control, MPC) 代替ISMC的切换控制, 进一步推导出ISMPC算法. 同时, 通过对FFDL 数据模型的未知扰动、参数误差等不确定项进行延时估计, 提升了算法的控制性能和对系统的等价描述程度. 在提供两种算法的稳定性证明分析之后, 以实验室配备的 CRH380A 型动车组仿真实验台对提出的ISMC和ISMPC算法进行仿真测试, 并与其他方法进行对比, 仿真结果表明ISMPC算法控制性能较好, 动车组各动力单元速度跟踪误差均在 ±0.132 km/h 以内, 满足列车的跟踪精度需求; 控制力和加速度分别在[−52 kN, 42 kN] 和 ±0.9249 m/s2 以内且变化平稳.Abstract: Like many complex systems, the electric multiple unit (EMU) operation process also has the characteristics of multivariable, strong coupling and nonlinearity, which seriously affect the performance of the train control system. A new multi-input-multi-output (MIMO) data-driven integral sliding mode predictive control (ISMPC) algorithm is proposed for the EMU autopilot system with external disturbances. Based on the full format dynamic linearization (FFDL) data model equivalent to the EMU operation process, a discrete integral sliding mode control (ISMC) law is designed. To achieve higher output tracking error accuracy, the switching control with ISMC is replaced by model predictive control (MPC), leading to the further derivation of the ISMPC algorithm. Through the delay estimation of the unknown disturbance, parameter error and other uncertainties of the FFDL data model, the control performance of the algorithm and the equivalent description of the system are improved. After providing the stability proof analysis of the two algorithms, the ISMC and ISMPC algorithms proposed in this paper are simulated and tested on the CRH380A EMU simulation test bench equipped in the laboratory, and compared with other methods. The simulation results show that the ISMPC algorithm has better control performance, and the speed tracking error of each power unit of the EMU is within ±0.132 km/h, which meets the tracking accuracy requirements of the train; The control force and acceleration are within [−52 kN, 42 kN] and ±0.9249 m/s2 respectively and change smoothly.
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图 4 CRH380A 型动车组济南西至徐州东的实际曲线
Fig. 4 The actual curves of CRH380A EMU from Jinan west to Xuzhou east
图 5 CRH380A 型动车组牵引/制动特性曲线
Fig. 5 The traction/braking characteristic curves of CRH380A EMU
图 6 本文方法与其他方法速度跟踪曲线对比
Fig. 6 The velocity tracking curves of the proposed method are compared with those of other methods
图 7 本文方法与其他方法各动力单元速度跟踪误差对比
Fig. 7 The velocity tracking errors of the proposed method are compared with those of other methods
图 8 本文方法与其他方法分级速度跟踪曲线对比
Fig. 8 The proposed method and other methods classify the speed tracking curve
图 9 本文方法与其他方法单位控制力变化对比
Fig. 9 The variation of unit control force of the proposed method is compared with this of other methods
图 10 本文方法与其他方法加速度变化对比
Fig. 10 The acceleration changes of the proposed method are compared with those of other methods
表 1 CRH380A 型动车组模型参数
Table 1 The CRH380A EMU model parameters
参数名称 参数值 单位 动力单元质量$M_1$ $ 1.836 \times 10^5$ kg 动力单元质量$M_2$ $ 1.123 \times 10^5 $ kg 动力单元质量$M_3$ $ 1.836 \times 10^5 $ kg 列车阻力系数$a_r$ 5.200 N/kg 列车阻力系数$b_r$ $ 3.600 \times 10^{-2} $ N·s2/(kg·m) 列车阻力系数$c_r$ $ 1.200 \times 10^{-3} $ N·s2/(kg·m2) 车钩弹性系数$k$ $ 2.000 \times 10^7 $ N/m 车钩阻尼系数$d$ $ 5.000 \times 10^6 $ N·s/m 
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表 2 各个控制方法的若干性能指标对比
Table 2 Comparison of several performance indexes of each control method
控制方法 MSE IAE MA FFDL-ISMPC 0.052 324 0.9249 FFDL-ISMC 0.161 940 0.9432 FFDL-MFAC 0.287 1814 0.9749 GPC 0.346 2421 1.0124
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