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基于初次控制信号提取的迭代学习控制方法

徐建明 王耀东 孙明轩

徐建明, 王耀东, 孙明轩. 基于初次控制信号提取的迭代学习控制方法. 自动化学报, 2020, 46(2): 294-306. doi: 10.16383/j.aas.c170622
引用本文: 徐建明, 王耀东, 孙明轩. 基于初次控制信号提取的迭代学习控制方法. 自动化学报, 2020, 46(2): 294-306. doi: 10.16383/j.aas.c170622
XU Jian-Ming, WANG Yao-Dong, SUN Ming-Xuan. Iterative Learning Control Based on Extracting Initial Iterative Control Signals. ACTA AUTOMATICA SINICA, 2020, 46(2): 294-306. doi: 10.16383/j.aas.c170622
Citation: XU Jian-Ming, WANG Yao-Dong, SUN Ming-Xuan. Iterative Learning Control Based on Extracting Initial Iterative Control Signals. ACTA AUTOMATICA SINICA, 2020, 46(2): 294-306. doi: 10.16383/j.aas.c170622

基于初次控制信号提取的迭代学习控制方法

doi: 10.16383/j.aas.c170622
基金项目: 

国家自然科学基金 61374103

国家自然科学基金 61573320

详细信息
    作者简介:

    王耀东   2018年获得浙江工业大学信息工程学院硕士学位.主要研究方向为迭代学习控制. E-mail: wangyd@zjut.edu.cn

    孙明轩   浙江工业大学信息工程学院教授.主要研究方向为迭代学习控制.E-mail: mxsun@zjut.edu.cn

    通讯作者:

    徐建明   浙江工业大学信息工程学院教授.主要研究方向为迭代学习控制, 运动控制.本文通信作者. E-mail: xujm@zjut.edu.cn

Iterative Learning Control Based on Extracting Initial Iterative Control Signals

Funds: 

National Natural Science Foundation of China 61374103

National Natural Science Foundation of China 61573320

More Information
    Author Bio:

    WANG Yao-Dong   He received his master degree from the College of Information Engineering, Zhejiang Univer sity of Technology in 2018. His main research interest is iterative learning control

    SUN Ming-Xuan    Professor at the College of Information Engineering, Zhejiang University of Technology. His main research interest is iterative learning control

    Corresponding author: XU Jian-Ming    Professor at the College of Information Engineering, Zhejiang University of Technology. His research interest covers iterative learning control and motion control. Corresponding author of this paper
  • 摘要: 在同一迭代学习控制(Iterative learning control, ILC)系统中, 选取一个合适的初次迭代控制信号相对于从零开始学习达到目标跟踪精度的迭代次数更少.本文针对线性系统研究从历次轨迹跟踪控制信息中通过期望轨迹匹配提取初次迭代控制信号的方法.首先提出了一种轨迹基元优化匹配算法, 在满足一定相似度的情况下, 通过轨迹分割、平移与旋转变换, 在轨迹基元库中寻找与当前期望轨迹叠合的轨迹基元组合轨迹; 进而, 依据线性叠加原理和轨迹叠合的平移矢量与旋转变换矩阵, 获取与期望轨迹叠合的轨迹基元控制信号; 在此基础上, 通过轨迹基元控制信号串联组合和时间尺度变换, 提取出当前期望轨迹的初次迭代控制信号.对于初次迭代控制信号在拼接处由边界条件差异引起的干扰, 给出了一种${H_\infty }$反馈辅助ILC方法.最后, 在$XYZ$三轴运动平台实现所提算法, 实验结果表明本文所提方法的有效性.
    Recommended by Associate Editor HOU Zhong-Sheng
    1)  本文责任编委 侯忠生
  • 图  1  轨迹基元匹配的ILC系统原理示意图

    Fig.  1  ILC system schematic diagram of trajectory primitive matching

    图  2  优化匹配算法流程图

    Fig.  2  Structure flow chart of the optimal matching algorithm

    图  3  原始相似组合轨迹基元序列${l^{A}_{p1j}(t_{1j})}, $ ${l^{A}_{p2j}(t_{2j})}$

    Fig.  3  Original similar combination of primitive sequences ${l^{A}_{p1j}(t_{1j})}, $ ${l^{A}_{p2j}(t_{2j})}$

    图  4  重新分割后的相似组合轨迹基元序列$\bar l_{p1r}^{A}({t_{1r}}), $ $\bar l_{p2r}^{A}({t_{2r}})$

    Fig.  4  Re-segmented similar combinations of primitive sequences $\bar l_{p1r}^{A}({t_{1r}}), $ $\bar l_{p2r}^{A}({t_{2r}})$

    图  5  ${H_\infty }$反馈辅助迭代学习控制系统

    Fig.  5  ${H_\infty }$ feedback assisted iterative learning control system

    图  6  ${H_\infty }$控制问题

    Fig.  6  ${H_\infty }$ control problem

    图  7  $XYZ$三轴运动平台结构

    Fig.  7  $XYZ$ three axis motion platform structure

    图  8  三轴$XYZ$平台装置

    Fig.  8  $XYZ$ triaxial platform device

    图  9  轨迹库七条轨迹

    Fig.  9  Seven three-dimensional trajectories in the library

    图  10  分割成十段的期望轨迹及各段质心坐标系

    Fig.  10  The desired trajectory split into 10 segments and its centroid coordinates

    图  11  分割成九段的期望轨迹及各段质心坐标系

    Fig.  11  The desired trajectory split into 9 segments and its centroid coordinates

    图  12  十段匹配基元及质心坐标系

    Fig.  12  Ten-segment matching primitives and centroid coordinates

    图  13  九段匹配基元及质心坐标系

    Fig.  13  Nine-segment matching primitives and centroid coordinates

    图  14  $X$轴初次控制信号及第15次迭代控制信号

    Fig.  14  $X$ axis initial control signal and 15th iteration control signal

    图  15  $Y$轴初次控制信号及第15次迭代控制信号

    Fig.  15  $Y$ axis initial control signal and 15th iteration control signal

    图  16  $Z$轴初次控制信号及第15次迭代控制信号

    Fig.  16  $Z$ axis initial control signal and 15th iteration control signal

    图  17  $X$轴跟踪轨迹和误差

    Fig.  17  The $X$ axis tracking trajectory and error

    图  18  $Y$轴跟踪轨迹和误差

    Fig.  18  The $Y$ axis tracking trajectory and error

    图  19  $Z$轴跟踪轨迹和误差

    Fig.  19  The $Z$ axis tracking trajectory and error

    图  20  $X$、$Y$、$Z$轴采用提取的初次控制信号的均方根误差

    Fig.  20  The RMS of $X$, $Y$, $Z$ axis for ILC using the extracted initial control signal

    图  21  初次控制信号为零的$X$、$Y$、$Z$轴的均方根误差

    Fig.  21  The RMS of $X$, $Y$, $Z$ axis for ILC using the zero initial control signal

    图  22  采用提取的初次控制信号的三维轨迹跟踪效果

    Fig.  22  3-D trajectory tracking performances of ILC using the extracted initial control signal

    图  23  初次控制信号为零的三维轨迹跟踪效果

    Fig.  23  3-D trajectory tracking performances of ILC using the zero initial control signal

    表  1  各基元轨迹段与相应期望轨迹段之间的时间尺度

    Table  1  Each primitive corresponding to the desired track segment and a time scale between trajectories segments

    第$r$段 $\overline \alpha _1^{r}$ $\overline \alpha _2^{r}$ 第$r$段 $\overline \alpha _1^{r}$ $\overline \alpha _2^{r}$
    1 1.56 3.76 10 1.24 0.39
    2 1.32 3.76 11 1.24 0.36
    3 1.32 2.74 12 0.87 0.63
    4 1.79 2.74 13 0.87 1.32
    5 1.79 2.74 14 0.61 1.32
    6 0.99 1.65 15 0.61 1.13
    7 0.99 2.16 16 0.91 1.13
    8 0.98 2.16 17 0.91 0.89
    9 0.98 0.39 18 1.16 0.89
    下载: 导出CSV

    表  2  采用提取初次控制信号的跟踪误差

    Table  2  The tracking error of ILC using the extracted initial control signal

    跟踪指标 $X$轴(mm) $Y$轴(mm) $Z$轴(mm)
    最大跟踪误差 0.5211 0.4923 0.4991
    第一次迭代均方差 0.1300 0.1692 0.1154
    第八次迭代均方差 0.0481 0.0499 0.0233
    下载: 导出CSV

    表  3  初次控制信号为零的跟踪误差

    Table  3  The tracking error of ILC using the zero initial control signal

    跟踪指标 $X$轴(mm) $Y$轴(mm) $Z$轴(mm)
    最大跟踪误差 2.5134 2.0189 1.2174
    第一次迭代均方差 1.2260 1.3610 0.4649
    第八次迭代均方差 0.1221 0.0614 0.0308
    下载: 导出CSV
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  • 收稿日期:  2017-11-08
  • 录用日期:  2018-06-10
  • 刊出日期:  2020-03-06

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