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摘要: 针对动车组运行过程中存在非线性扰动、参数时变等问题，以提高动车组的速度跟踪精度和乘客舒适性要求为目标，提出了一种基于预测控制的高速动车组迭代学习控制方法；通过采集动车组先前运行过程中的输入输出数据，使用带遗忘因子的最小二乘法实时辨识广义预测控制(GPC)中的预测模型参数并计算预测输出，根据以往过程的平均模型误差修正该预测输出，利用修正后预测输出引出迭代学习控制律，在线实时计算得到新的控制量，实现动车组速度跟踪；采用修正后预测输出设计二次型迭代学习控制律，通过充分学习列车系统的重复性特性来解决传统比例积分微分(PID)型迭代学习参数整定难、收敛速度慢和鲁棒性差等问题，并给出算法的收敛性证明；以实验室配备的CRH380A型动车组半实物仿真平台对该方法进行了测试，建立了列车的三动力单元模型，使其跟踪设定速度曲线，并与一些传统算法进行对比。仿真结果表明：在第8次迭代过程，基于预测控制的高速动车组迭代学习控制方法得到的动力单元速度与其设定的速度和加速度误差分别在0.3 km·h-1和0.5 m·s-2以内，且变化平稳，其性能优于PID、GPC和P型迭代学习控制(P-ILC)，满足列车跟踪精度与乘客舒适性要求；在模型参数突变的情况下，采用提出的方法可使列车更为及时地校正模型失配、时变和干扰等引起的不确定性。Abstract: Addressing the issues of nonlinear disturbance and time-varying parameters in the operation of electric multiple units (EMUs), an iterative learning control method for EMUs based on the predictive control was proposed to improve the speed tracking accuracy and passenger comfort requirements of EMUs. By collecting the input and output data from the previous operation of the EMUs, the least square method with a forgetting factor was used to identify the parameters of the predictive model in the generalized predictive control (GPC) in real time and calculate the predicted output. The predicted output was corrected based on the average model error from the previous process, and the iterative learning control law was derived from the corrected predicted output. The new control quantity was calculated in real time through the online calculation to realize the speed tracking of the EMUs. The modified predictive output was adopted to design the quadratic iterative learning control law. The problems of difficult parameter tuning, slow convergence speed and poor robustness of the traditional proportional integral differential (PID) iterative learning were solved by fully learning the repetitive characteristics of the train system. In addition, the convergence proof of the algorithm was provided. The proposed method was tested using the semi-physical simulation platform of CRH380A EMUs equipped in the laboratory. A three-power unit model of the train was established to track the set speed curve, and a comparison was made with some traditional algorithms. Simulation results show that in the eighth iteration process, the iterative learning control method for high-speed EMUs based on the predictive control achieves the power unit speed and acceleration errors within 0.3 km·h-1 and 0.5 m·s-2, respectively, and the changes are stable. Its performance is better than PID, GPC and proportional iterative learning control (P-ILC), and meets the requirements of train tracking accuracy and passenger comfort. In the case of sudden changes in model parameters, the proposed method can enable the train to timely correct the uncertainties caused by the model mismatch, time-variation and interference.
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图 3 基于GPC的动车组迭代学习控制算法
Figure 3. Iterative learning control algorithm for EMUs based on GPC
图 8 参数突变时各种方法的控制效果
Figure 8. Control effects of various methods in case of parameter sudden change
表 1 CRH380A模型参数
Table 1. Model parameters of CRH380A
参数名称 数值 θ1 (-0.939 1, 0.167 2, 0.012 5, 0.008 3) θ2 (-0.938 9, 0.012 6, 0.168 6, 0.012 6) θ3 (-0.939 1, 0.008 4, 0.012 6, 0.167 5) 
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表 2 各控制方法的跟踪误差
Table 2. Tracking errors of each control method
方法 速度误差/(km·h-1) 总位移误差/km PID (-1.493, 1.985) 0.647 1 GPC (-0.993, 1.157) 0.327 7 P-ILC (-0.685, 0.664) 0.188 7 本文方法 (-0.291, 0.282) 0.076 1
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表 3 各控制方法的若干性能指标
Table 3. Several performance indexes of each control method
方法 均方根误差/(km·h-1) 最大加/减速度/(m·s-2) PID 1.6×10-1 0.847 1 GPC 6.1×10-2 0.587 4 P-ILC 1.5×10-2 0.784 5 本文方法 7.8×10-3 0.568 1
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