Adaptive Iterative Learning Economic Model Predictive Control for Batch Processes With Non-repetitive Disturbances
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摘要: 迭代学习模型预测控制作为一种重要的批次过程先进控制方法, 具备较强的学习能力和闭环性能. 传统的迭代学习模型预测控制算法能有效消除重复扰动影响, 同时对小范围实时扰动鲁棒性较强. 当被控系统存在较大实时干扰时, 经济性能和系统稳定性通常难以保障. 对此, 提出一种面向非重复扰动的自适应迭代学习经济模型预测控制策略, 沿迭代方向和时间方向对系统动态进行分解, 将系统扰动拆分为重复部分和非重复部分, 分别建立批次间和批次内的动态经济优化问题. 批次间执行基于迭代学习控制的离线经济优化, 消除重复扰动影响; 批次内引入扩展状态观测器对非重复扰动进行估计, 基于批次间优化结果在线实施经济模型预测控制, 在抑制实时扰动的同时提高系统动态经济性. 论文结合观测器稳定性分析方法, 对所提自适应迭代学习经济模型预测控制策略的稳定性进行理论证明, 并通过间歇反应器仿真实验对算法实施有效性进行验证.Abstract: Iterative learning model predictive control, as an important advanced control method for batch processes, has strong learning capability and closed-loop performance. The traditional iterative learning model predictive control algorithm can effectively eliminate the effect of repetitive disturbances, and at the same time, it is robust to small-scale real-time disturbances. When there is a large real-time disturbance in the controlled system, the economic performance and system stability are usually difficult to guarantee. In this paper, an adaptive iterative learning economic model predictive control strategy for non-repetitive disturbances is proposed to decompose the system dynamics along the iteration direction and time direction, to split the system disturbances into repetitive and non-repetitive parts, and to establish the dynamic economic optimization problems in the batch-to-batch design and within-batch design, respectively. The batch-to-batch design is to apply offline economic optimization based on iterative learning control to eliminate the effects of repetitive disturbances; and the within-batch design is to estimate the non-repetitive disturbances by introducing an extended state observer, and economic model predictive control is implemented online based on the batch-to-batch optimization results, which improves the dynamic economy of the system while suppressing real-time disturbances. The stability of the proposed adaptive iterative learning economic model predictive control strategy is theoretically demonstrated by combining the observer stability analysis method, and the effectiveness of the algorithm implementation is verified by batch reactor simulation experiments.
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图 2 ILEMPC下反应物$A$浓度$(C_A)$的变化曲线
Fig. 2 The change curves of the concentration of reactant $A$ $(C_A)$ under the ILEMPC
图 3 ILEMPC下反应物$B$浓度$(C_B)$的变化曲线
Fig. 3 The change curves of the concentration of reactant $B$ $(C_B)$ under the ILEMPC
图 4 ILEMPC下反应温度$(T_r)$的变化曲线
Fig. 4 The change curves of the reaction temperature $(T_r)$ under the ILEMPC
图 5 ILEMPC下冷却夹套温度$(T_J)$的变化曲线
Fig. 5 The change curves of the temperature of the cooling jacket $(T_J)$ under the ILEMPC
图 6 ILEMPC下冷却水流速$(F_{ow})$的变化曲线
Fig. 6 The change curves of the cooling water flow rate $(F_{ow})$ under the ILEMPC
图 7 重复扰动下ILEMPC与ILMPC系统经济成本$(V_k)$变化曲线
Fig. 7 The change curves of the economic cost $(V_k)$ of ILEMPC and ILMPC systems under repetitive disturbances
图 8 不同扰动下ESO-ILEMPC与ILEMPC系统输入$(F_{ow})$变化曲线
Fig. 8 The change curves of the input $(F_{ow})$ for ESO-ILEMPC and ILEMPC under different disturbances
图 9 非重复扰动下ESO-ILEMPC与ILEMPC系统经济成本$(V_k)$变化曲线
Fig. 9 The change curves of the economic cost $(V_k)$ of ESO-ILEMPC and ILEMPC systems under non-repetitive disturbances
表 1 非重复扰动下ESO-ILEMPC与ILEMPC系统经济成本比较
Table 1 The comparison of the economic cost of ESO-ILEMPC and ILEMPC systems under non-repetitive disturbances
控制器 经济成本$ {(k=2)} $ 经济成本$ {(k=13)} $ 经济成本$ {(k=20)} $ ESO-ILEMPC 0.9201 (−7.56%)0.4789 (−18.15%)0.4182 (−19.27%)ILEMPC 0.9954 0.5851 0.5180 
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