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电熔镁砂熔炼过程电极电流饱和约束一步最优控制

富月 李宝

富月, 李宝. 电熔镁砂熔炼过程电极电流饱和约束一步最优控制. 自动化学报, 2021, 47(x): 1−10 doi: 10.16383/j.aas.c200896
引用本文: 富月, 李宝. 电熔镁砂熔炼过程电极电流饱和约束一步最优控制. 自动化学报, 2021, 47(x): 1−10 doi: 10.16383/j.aas.c200896
Fu Yue, LI Bao. Saturation constraint one-step optimal control of electrode current for the fused magnesia smelting process. Acta Automatica Sinica, 2021, 47(x): 1−10 doi: 10.16383/j.aas.c200896
Citation: Fu Yue, LI Bao. Saturation constraint one-step optimal control of electrode current for the fused magnesia smelting process. Acta Automatica Sinica, 2021, 47(x): 1−10 doi: 10.16383/j.aas.c200896

电熔镁砂熔炼过程电极电流饱和约束一步最优控制

doi: 10.16383/j.aas.c200896
基金项目: 国家自然科学基金(61991403, 61991400), 辽宁省教育厅创新人才项目(ZX20200070), 辽宁省重大科技专项(2020JH1/10100008) 资助
详细信息
    作者简介:

    富月:东北大学流程工业综合自动化国家重点实验室教授. 2009年获得东北大学控制理论与控制工程专业博士学位. 主要研究方向为复杂工业过程自适应控制, 智能解耦控制, 近似动态规划以及工业过程运行控制. 本文通信作者. E-mail: fuyue@mail.neu.edu.cn

    李宝:东北大学流程工业综合自动化国家重点实验室硕士研究生. 于2019年获得东北大学学士学位. 主要研究方向为复杂工业过程自适应控制和最优控制. E-mail: libao0128@126.com

Saturation Constraint One-step Optimal Control of Electrode Current for the Fused Magnesia Smelting Process

Funds: Supported by National Natural Science Foundation of China (61991403, 61991400), the Innovative Talent Project of Liaoning Education Committee (ZX20200070), the Science and Technology Major Project of Liaoning Province (2020JH1/10100008)
More Information
    Author Bio:

    FU Yue Associate professor at the State Key Laboratory of Synthetical Automation for Process Industries, Northeastern University. She received her Ph. D. degree from Northeastern University in 2009. Her research interest covers adaptive control, intelligent decoupling control, approximate dynamic programming, and industrial operational control. Corresponding author of this paper

    LI Bao Master student at the State Key Laboratory of Synthetical Automation for Process Industries, Northeastern University. He received his bachelor degree from Northeastern University in 2019. His research interest covers adaptive control and optimal control for complex industry process

  • 摘要: 电熔镁砂熔炼过程通过电极电流熔化物料, 采用埋弧方式, 边熔化边加料, 其被控对象是以转动方向与频率为输入, 以电极电流为输出的三相电机. 本文通过引入中间变量并转化控制目标, 将电熔镁砂熔炼过程三相电极电流的复杂非线性控制问题简化为线性控制问题, 提出了一种简化的电极电流饱和约束一步最优控制方法, 并通过引入拉格朗日乘子向量和松弛向量验证了该方法的最优性. 理论分析和仿真对比实验结果表明本文所提简化控制方法的有效性和优越性. 此外, 当考虑电熔镁砂熔炼过程中存在的不可测外部干扰时, 在上述简化的电极电流饱和约束算法的基础上设计了高阶干扰观测器, 理论分析和仿真结果验证了具有高阶干扰观测器的简化算法的优越性.
  • 图  1  电熔镁砂熔炼过程

    Fig.  1  Fused magnesia smelting process

    图  2  饱和约束一步最优控制结构图

    Fig.  2  Structure diagram of one-step optimal control with saturation constraint

    图  3  随机噪声信号

    Fig.  3  Random noise signal

    图  4  采用本文控制方法时A相电极电流$y_1$

    Fig.  4  A-phase electrode current $y_1$ using the control method in this paper

    图  5  采用文[1]控制方法时A相电极电流$y_1$

    Fig.  5  A-phase electrode current $y_1$ using the control method in the literature [1]

    图  6  采用文[23]控制方法时A相电极电流$y_1$

    Fig.  6  A-phase electrode current $y_1$ using the control method in the literature [23]

    图  7  采用文[23]控制方法时A相电极电流误差概率分布

    Fig.  7  Error probability distribution of A-phase electrode current using the control method in the literature [23]

    图  8  采用本文控制方法时A相电极电流误差概率分布

    Fig.  8  Error probability distribution of A-phase electrode current using the control method in this paper

    图  9  加入不可测干扰时A相电极电流$y_1$

    Fig.  9  A-phase electrode current $y_1$ when unmeasurable disturbance is introduced

    图  10  加入不可测干扰时控制器输出$u_1$

    Fig.  10  Controller output $u_1$ when unmeasurable disturbance is introduced

    图  11  采用高阶干扰观测器控制时A相电极电流$y_1$

    Fig.  11  A-phase electrode current $y_1$ using the proposed high-order disturbance observer based controller

    图  12  采用高阶干扰观测器时控制器输出$u_1$

    Fig.  12  Controller output $u_1$ using the proposed high-order disturbance observer based controller

    图  13  未知干扰$d_1$的估计值

    Fig.  13  Estimated value of unknown disturbance $d_1$

    图  14  采用文[24]控制方法时A相电极电流$y_1$

    Fig.  14  A-phase electrode current $y_1$ using the control method in the literature [24]

    图  15  采用文[24]控制方法时控制器输出$u_1$

    Fig.  15  Controller output $u_1$ using the method in the literature [24]

    表  1  电极电流动态模型中参数的符号及物理意义

    Table  1  Symbols and meanings of parameters in dynamic model of electrode current

    符号 物理意义
    $f_{1}(\cdot)$ 随原料颗粒长度和杂质成分变化的埋弧电阻率
    $f_{2}(\cdot)$ 随原料颗粒长度和杂质成分变化的熔池电阻率
    $r_{\rm {iarc}}$ 埋弧等效弧柱半径
    $h_{\rm {ipool }}(\cdot)$ 随原料颗粒长度、杂质和电极电流变化的熔池高度
    $U$ 熔炼电压
    $p$ 电极极对数
    $r_{d}$ 升降机构等效齿轮半径
    $s$ 转差率
    下载: 导出CSV

    表  2  采用文[1]控制方法、文[23]控制方法和本文控制方法时A相电极电流$y_1$的性能评价

    Table  2  Performance evaluating of A-phase electrode current $y_1$ using the control method proposed in this paper and described in literatures [1] and [23]

    文献[1]的控制方法 $0.4502 \times 10^{6}$ $0.2787 \times 10^{6}$
    文献[23]的控制方法 $0.6631 \times 10^{6}$ $0.2115 \times 10^{6}$
    本文提出的控制方法 $0.1294 \times 10^{6}$ $0.0679 \times 10^{6}$
    与文献[1]相比降低 $71.27 \%$ $75.64 \%$
    与文献[23]相比降低 $80.48 \%$ $67.89 \%$
    下载: 导出CSV

    表  3  采用文[24]控制方法和本文控制方法时A相电极电流$y_1$的性能评价

    Table  3  Performance evaluating of A-phase electrode current $y_1$ using the control method proposed in this paper and described in the literature [24]

    ${\rm {MSE}}$ ${\rm {IAE}}$
    采用本文第三节控制方法 $0.4970 \times 10^{6}$ $0.0854 \times 10^{6}$
    文[24]的控制方法 $0.5906 \times 10^{6}$ $0.2879 \times 10^{6}$
    本文控制方法 $0.2951 \times 10^{6}$ $0.0784 \times 10^{6}$
    与第三节方法相比降低 $40.62 \%$ $8.20 \%$
    与文[24]方法相比降低 $50.03 \%$ $72.77 \%$
    下载: 导出CSV
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  • 收稿日期:  2020-10-26
  • 录用日期:  2021-02-09
  • 网络出版日期:  2021-03-19

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