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变参考轨迹下的鲁棒迭代学习模型预测控制

马乐乐 刘向杰

马乐乐, 刘向杰. 变参考轨迹下的鲁棒迭代学习模型预测控制. 自动化学报, 2019, 45(10): 1933-1945. doi: 10.16383/j.aas.c180681
引用本文: 马乐乐, 刘向杰. 变参考轨迹下的鲁棒迭代学习模型预测控制. 自动化学报, 2019, 45(10): 1933-1945. doi: 10.16383/j.aas.c180681
MA Le-Le, LIU Xiang-Jie. Robust Model Predictive Iterative Learning Control With Iteration-varying Reference Trajectory. ACTA AUTOMATICA SINICA, 2019, 45(10): 1933-1945. doi: 10.16383/j.aas.c180681
Citation: MA Le-Le, LIU Xiang-Jie. Robust Model Predictive Iterative Learning Control With Iteration-varying Reference Trajectory. ACTA AUTOMATICA SINICA, 2019, 45(10): 1933-1945. doi: 10.16383/j.aas.c180681

变参考轨迹下的鲁棒迭代学习模型预测控制

doi: 10.16383/j.aas.c180681
基金项目: 

国家自然科学基金 61533013

中央高校基本科研业务费专项基金 2017ZZD004

国家自然科学基金 U1709211

国家自然科学基金 61673171

详细信息
    作者简介:

    马乐乐   华北电力大学控制与计算机工程学院博士研究生.2016年获得华北电力大学自动化专业学士学位.主要研究方向为预测控制及其应用.E-mail:1172127008@ncepu.edu.cn

    通讯作者:

    刘向杰  华北电力大学控制与计算机工程学院教授.1989年获得东北大学工业电气自动化专业学士学位.1997年获得东北大学自动化研究中心博士学位.主要研究方向为先进控制策略在电力过程控制中的应用.本文通信作者.E-mail:liuxj@ncepu.edu.cn

Robust Model Predictive Iterative Learning Control With Iteration-varying Reference Trajectory

Funds: 

National Natural Science Foundation of China 61533013

the Fundamental Research Funds for the Central Universities 2017ZZD004

National Natural Science Foundation of China U1709211

National Natural Science Foundation of China 61673171

More Information
    Author Bio:

      Ph. D. candidate at the School of Control and Computer Engineering, North China Electric Power University. She received her bachelor degree in automation from North China Electric Power University in 2016. Her research interest covers predictive control and its application

    Corresponding author: LIU Xiang-Jie   Professor at the School of Control and Computer Engineering, North China Electric Power University. He received his bachelor degree in industrial electronic automation from Northeastern University in 1989, and the Ph. D. degree from the Research Center of Automation, Northeastern University in 1997. His research interest covers application of advanced control strategy in power process control. Corresponding author of this paper
  • 摘要: 迭代学习模型预测控制是针对间歇过程的先进控制方法.它能通过迭代高精度跟踪给定参考轨迹,并保证时域上的闭环稳定性.然而,现有的迭代学习模型预测控制算法大多基于线性/线性化系统,且没有考虑参考轨迹变化的情况.本文基于线性参变系统提出一种能有效跟踪变参考轨迹的鲁棒迭代学习模型预测控制算法.首先,采用线性参变模型准确涵盖原始非线性系统的动态特性.然后,将鲁棒H控制与传统迭代学习模型预测控制相结合,抑制变参考轨迹带来的跟踪误差波动,通过优化线性矩阵不等式约束下的目标函数求得控制输入.深入分析了鲁棒迭代学习模型预测控制的鲁棒稳定性和迭代收敛性.最后,通过对数值例子和连续搅拌反应釜系统的仿真验证了所提出算法的有效性.
    1)  本文责任编委 魏庆来
  • 图  1  参考轨迹$y_{r_1}$, $y_{r_2}$

    Fig.  1  The reference trajectories $y_{r_1}$, $y_{r_2}$

    图  2  RMPILC控制下参考轨迹跟踪曲线

    Fig.  2  The tracking trajectories under RMPILC

    图  3  RMPILC控制下控制输入轨迹

    Fig.  3  The control input trajectory under RMPILC

    图  4  MPILC控制下参考轨迹跟踪曲线

    Fig.  4  The tracking trajectories under MPILC

    图  5  MPILC和RMPILC控制下MSE随批次变化情况

    Fig.  5  The MSE along batches under MPILC and RMPILC

    图  6  RMPILC控制下第5批次当$\varepsilon=5.8$、$\varepsilon=10$和$\varepsilon=15$时的跟踪曲线

    Fig.  6  The tracking trajectories in the fifth batch when $\varepsilon=5.8, 10, 15$

    图  7  RMPILC控制下$\varepsilon=5.8$、$\varepsilon=10$和$\varepsilon=15$时的不变集$\Omega_{\tilde{x}_k}$在原状态空间的象集

    Fig.  7  The image set of $\Omega_{\tilde{x}_k}$ when $\varepsilon=5.8, 10, 15$

    图  8  CSTR反应温度$T$参考轨迹

    Fig.  8  The reference trajectories of CSTR reaction temperature $T$

    图  9  RMPILC控制下反应温度$T$参考轨迹跟踪曲线

    Fig.  9  The tracking trajectories for $T$ under RMPILC control

    图  10  RMPILC控制下控制输入$T_c$轨迹

    Fig.  10  The trajectories of control input $T_c$ under RMPILC

    图  11  MPILC控制下反应温度跟踪曲线

    Fig.  11  The tracking trajectories for $T$ under MPILC

    图  12  RMPILC、MPILC控制下MSE随批次变化情况

    Fig.  12  The MSE along batches under RMPILC and MPILC

    表  1  $F_k(t)$优化值

    Table  1  Optimized feedback control law

    批次($k$) $F_k(61)$
    2 [$-$46.7539  $-$24.0899  $-$5.0529  0.0000]
    3 [$-$42.9654  $-$25.0475  $-$3.7597  0.0000]
    4 [$-$57.4573  $-$29.2520  $-$5.4621  $-$0.0000]
    5 [$-$16.9782  $-$7.8604  $-$1.2311  $-$0.0000]
    6 [$-$37.0429  $-$26.9746  $-$3.0976  0.0000]
    7 [$-$41.3123  $-$27.2625  $-$2.9534  $-$0.0000]
    8 [$-$54.1913  $-$32.1226  $-$4.9777  0.0000]
    下载: 导出CSV

    表  2  $F_k(t)$优化值

    Table  2  Optimized feedback control law

    批次$k$ $F_k(200)$
    2 [-7.8076  -12.6079  -7.9428  -0.0000]
    3 [-8.4202  -12.9000  -8.2264  -0.0000]
    4 [-7.8744  -12.6839  -7.9521  -0.0000]
    5 [-8.9258  -13.1178  -8.4572  -0.0000]
    6 [-9.7286  -13.2893  -9.0092  0.0000]
    7 [-6.9490  -11.3713  -7.6883  0.0000]
    8 [-7.5195  -12.4532  -8.0074  -0.0000]
    9 [-7.7803  -12.6691  -7.9535  -0.0000]
    下载: 导出CSV
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