Data-driven Model-free Adaptive Control Method for High-speed Electric Multiple Unit
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摘要: 针对动车组的速度跟踪控制问题, 同时考虑到现有基于模型的控制方法对系统动力学模型的依赖性, 以及传统无模型自适应控制时变参数估计算法的复杂性, 将改进的多输入多输出(Multiple-input multiple-output, MIMO)偏格式动态线性化无模型自适应控制(Partial form dynamic linearization-improved model-free adaptive control, PFDL-iMFAC)方法引入到动车组自动驾驶系统中. 该控制方法在无模型自适应控制的基础上, 考虑滑动时间窗口, 增加了可调自由度和设计灵活性, 并在输入准则函数中加上对能量函数的惩罚项, 减少能量损耗, 为动车组的跟踪精度和节能运行提供了一种优化的方法, 在满足动车组速度跟踪效果好的前提下实现节能运行. 最后以CRH380A动车组为对象进行仿真实验, 通过与传统无模型自适应控制对比: 所提出的控制算法各动力单元速度跟踪误差在 ±0.2 km/h以内, 加速度在 ±0.65 m/s2以内且变化平稳, 比传统无模型自适应控制方法节约9.86%的能量.Abstract: For the speed tracking control problem of electric multiple unit, the dependence of the existing model-based control methods on the system dynamic model and the complexity of the time-varying parameter estimation algorithm of the traditional model-free adaptive control are both considered. The improved multiple-input multiple-output (MIMO) partial format dynamic linearization-improved model-free adaptive control (PFDL-iMFAC) method is introduced into the automatic train operation system. On the basis of model-free adaptive control, this control method considers the sliding time window, increases the adjustable degree of freedom and design flexibility, and adds the penalty term to the energy function in the input criterion function to reduce the energy loss. It provides a compromise method for the tracking accuracy and energy-saving operation of electric multiple unit, and realizes energy-saving operation under the premise of satisfying the good speed tracking effect of electric multiple unit. Finally, CRH380A electric multiple unit is taken as the object for simulation experiment. Compared with the traditional model-free adaptive control, the speed tracking error of each power unit in the proposed control algorithm is within ±0.2 km/h, and the acceleration one is within ±0.65 m/s2 and the change is stable, saving 9.86% of energy compared with the traditional model-free adaptive control method.
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图 1 动车组运行过程动力学描述
Fig. 1 Dynamic description of electric multiple unit operation process
图 2 CRH380A型动车组动力单元分布
Fig. 2 Distribution of CRH380A electric multiple unit power unit
图 3 改进的动车组无模型自适应控制结构框图
Fig. 3 An improved block diagram of model-free adaptive control structure for electricmultiple unit
图 4 本文方法与其他方法速度跟踪曲线对比
Fig. 4 The velocity tracking curves of the proposed method are compared with those of other methods
图 5 本文方法与其他方法各动力单元速度跟踪误差对比
Fig. 5 The velocity tracking errors of the proposed method are compared with those of other methods
图 6 本文方法与其他方法单位控制力变化对比
Fig. 6 The variation of unit control force is compared with other methods
图 7 本文方法与其他方法加速度变化对比
Fig. 7 The acceleration changes of the proposed method are compared with other methods
表 1 CRH380A型动车组模型参数
Table 1 The CRH380A electric multiple unitmodel 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$a_r$ 5.2 N/kg 列车阻力系数$b_r$ $ 3.6\times 10^{-2} $ ${\rm{N} } \cdot {\rm{s} }^2/({\rm{kg} } \cdot {\rm{m} })$ 列车阻力系数$c_r$ $ 1.2\times 10^{-3} $ ${\rm{N} } \cdot {\rm{s} }^2/({\rm{kg} } \cdot {\rm{m}^2 })$ 车钩弹性系数$k$ $ 2\times 10^7 $ N/m 车钩阻尼系数$d$ $ 5\times 10^6 $ ${\rm{N}} \cdot {\rm{s/m} }$ 
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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 均方误差 最大加减速度 (m/s2) 能量损耗 节约率 (%) 文献[19] $1.2\times 10^{-2} $ 1.0848 $ 2.41\times 10^6 $ — PFDL-MFAC $6.2\times 10^{-3} $ 0.7309 $2.29\times 10^6 $ $5.04$ PFDL-iMFAC $6.6\times 10^{-3} $ 0.6572 $2.17\times 10^6$ $9.86 $
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