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间歇过程的批内自优化控制

叶凌箭

叶凌箭. 间歇过程的批内自优化控制. 自动化学报, 2022, 48(11): 2777−2787 doi: 10.16383/j.aas.c190855
引用本文: 叶凌箭. 间歇过程的批内自优化控制. 自动化学报, 2022, 48(11): 2777−2787 doi: 10.16383/j.aas.c190855
Ye Ling-Jian. Within-batch self-optimizing control for batch processes. Acta Automatica Sinica, 2022, 48(11): 2777−2787 doi: 10.16383/j.aas.c190855
Citation: Ye Ling-Jian. Within-batch self-optimizing control for batch processes. Acta Automatica Sinica, 2022, 48(11): 2777−2787 doi: 10.16383/j.aas.c190855

间歇过程的批内自优化控制

doi: 10.16383/j.aas.c190855
基金项目: 国家自然科学基金(61673349), 轻工过程先进控制教育部重点实验室开放课题(江南大学)基金(APCLI1802), 宁波市自然科学基金(2018A610188)资助
详细信息
    作者简介:

    叶凌箭:浙大宁波理工学院信息学院教授, 现为湖州师范学院教授. 2006年, 2011年分别获得浙江大学化工系学士, 控制系博士学位. 主要研究方向为控制结构设计, 不确定系统的实时优化. E-mail: lingjian.ye@zjhu.edu.cn

Within-batch Self-optimizing Control for Batch Processes

Funds: Supported by National Natural Science Foundation of China (61673349), Foundation of Key Laboratory of Advanced Process Control for Light Industry (Jiangnan University) (APCLI1802), and Ningbo Natural Science Foundation (2018A610188)
More Information
    Author Bio:

    YE Ling-Jian Professor at NingboTech University (current affiliation: Huzhou University). He received his bachelor and Ph.D. degrees in the Department of Chemical Engineering and the Department of Control Science and Engineering from Zhejiang University in 2006 and 2011, respectively. His research interest covers control structure design and real-time optimization of uncertain processes

  • 摘要: 针对间歇过程的实时优化问题, 提出了一种基于自优化控制的批内优化方法. 以测量变量的线性组合为被控变量, 在单批次内跟踪控制被控变量实现间歇过程的实时优化. 根据是否在间歇过程的不同阶段切换被控变量, 给出了两种自优化控制策略, 对每种策略又分别提出两种设定轨线选取方案. 为求解这些情形下的最优被控变量(组合矩阵), 以最小化平均经济损失为目标, 推导了组合矩阵和经济损失之间的函数关系, 分别将其描述为相应的非线性规划问题. 在此基础上, 进一步引入了扩张组合矩阵, 将这些非线性规划问题归纳为求解扩张组合矩阵的一致形式(扩张组合矩阵具有不同的结构约束), 并推导得到了其中一种方案的解析解计算方法. 以一个间歇反应器为研究对象, 验证了方法的有效性.
  • 图  1  间歇过程的离散化变量及自优化控制策略

    Fig.  1  Discretization of batch processes and self-optimizing control strategy

    图  2  最优扩张组合矩阵$\bar H$的求解步骤

    Fig.  2  Procedure for solving the optimal extended combination matrix $\bar H$

    图  3  标称点的最优输入轨迹

    Fig.  3  Optimal input trajectory at the nominal point

    图  4  策略2 (方案1)的设定值轨线

    Fig.  4  Setpoint trajectory for Strategy 2 (Scheme 1)

    图  5  批内自优化控制效果 $( k_1 $: +20%, $ k_2 $: −20%)

    Fig.  5  Within-batch self-optimizing performance $ (k_1 $: +20%, $ k_2 $: −20%)

    图  6  批内自优化控制效果 $( k_1 $: +40%, $ k_2 $: −40%)

    Fig.  6  Within-batch self-optimizing performance $( k_1 $: +40%, $ k_2 $: −40%)

    表  1  间歇反应器参数及标称值

    Table  1  Parameters for the reactor model and nominal values

    符号 物理含义 标称值
    $ k_1 $ 主反应的反应常数 0.053 L·mol/min
    $ k_2 $ 副反应的反应常数 0.128 L·mol/min
    $ u_L $ $ u $下限 0 L/min
    $ u_U $ $ u $上限 0.001 L/min
    $ c_{Bin} $ B 进料浓度 5 mol/L
    $ c_{Ao} $ A 初始浓度 0.72 mol/L
    $ c_{Bo} $ B 初始浓度 0.0614 mol/L
    $ V_o $ V 初始值 1 L
    $ t_f $ 批次运行时间 250 min
    下载: 导出CSV

    表  2  损失函数$ L_{\rm{av}} $

    Table  2  Loss function $ L_{\rm{av}} $

    策略及方案 $ N = 2 $ $ N = 20 $
    策略 2 (方案 1) 0.0371 0.0083
    策略 2 (方案 2) 0.03423 0.0024
    策略 3 (方案 3) 0.0368 0.0069
    策略 3 (方案 4) 0.03420 0.0022
    下载: 导出CSV

    表  3  100组随机扰动下的非线性损失统计量

    Table  3  Statistics of nonlinear losses for 100 groups of random disturbances

    方案 平均损失 最大损失 标准差
    标称操作 0.0036 0.0227 0.0068
    控制$ c_B $ 0.0042 0.0165 0.0054
    策略 2 (方案 1) 0.0026 0.0167 0.0050
    策略 2 (方案 2) 0.0007 0.0053 0.0016
    下载: 导出CSV
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出版历程
  • 收稿日期:  2019-12-17
  • 录用日期:  2020-06-11
  • 网络出版日期:  2022-10-19
  • 刊出日期:  2022-11-22

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