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快速刀具伺服系统位置域重复控制设计及其数字实现

周兰 杨秦 潘昌忠 肖文彬 李美柳

周兰, 杨秦, 潘昌忠, 肖文彬, 李美柳. 快速刀具伺服系统位置域重复控制设计及其数字实现. 自动化学报, 2024, 50(7): 1432−1444 doi: 10.16383/j.aas.c230381
引用本文: 周兰, 杨秦, 潘昌忠, 肖文彬, 李美柳. 快速刀具伺服系统位置域重复控制设计及其数字实现. 自动化学报, 2024, 50(7): 1432−1444 doi: 10.16383/j.aas.c230381
Zhou Lan, Yang Qin, Pan Chang-Zhong, Xiao Wen-Bin, Li Mei-Liu. Design and digital implementation of spatial repetitive control for fast tool servo system. Acta Automatica Sinica, 2024, 50(7): 1432−1444 doi: 10.16383/j.aas.c230381
Citation: Zhou Lan, Yang Qin, Pan Chang-Zhong, Xiao Wen-Bin, Li Mei-Liu. Design and digital implementation of spatial repetitive control for fast tool servo system. Acta Automatica Sinica, 2024, 50(7): 1432−1444 doi: 10.16383/j.aas.c230381

快速刀具伺服系统位置域重复控制设计及其数字实现

doi: 10.16383/j.aas.c230381
基金项目: 国家自然科学基金(62373145, 62173138, 62303179), 湖南省重点研发计划项目(2023GK2027), 湖南省自然科学基金(2021JJ30006, 2023JJ40297, 2023JJ40295), 湖南省教育厅科研项目(21A0321, 22B0468, 22C0244), 湖南省研究生科研创新项目(CX20221055)资助
详细信息
    作者简介:

    周兰:湖南科技大学信息与电气工程学院教授. 主要研究方向为非线性系统, 鲁棒控制和重复控制理论及应用. 本文通信作者. E-mail: zhoulan75@163.com

    杨秦:湖南科技大学信息与电气工程学院硕士研究生. 主要研究方向为重复控制, 数控加工及机电系统设计. E-mail: YangQin7699@163.com

    潘昌忠:湖南科技大学信息与电气工程学院教授. 主要研究方向为非线性控制理论与应用, 机电系统与机器人控制和智能控制. E-mail: pancz@hnust.edu.cn

    肖文彬:湖南科技大学信息与电气工程学院讲师. 主要研究方向为非线性系统自适应控制和多智能体系统分布式控制. E-mail: xiaowb992@163.com

    李美柳:湖南科技大学信息与电气工程学院讲师. 主要研究方向为网络化系统, 扰动估计与补偿和时滞系统鲁棒控制. E-mail: limeiliu@hnust.edu.cn

Design and Digital Implementation of Spatial Repetitive Control for Fast Tool Servo System

Funds: Supported by National Natural Science Foundation of China (62373145, 62173138, 62303179), the Key Research and Development Programs of Department of Science and Technology of Hunan Province (2023GK2027), the Natural Science Foundation of Hunan Province (2021JJ30006, 2023JJ40297, 2023JJ40295), the Scientific Research Fund of Hunan Provincial Education Department (21A0321, 22B0468, 22C0244), and the Graduate Scientific Research Innovation Project of Hunan Province (CX20221055)
More Information
    Author Bio:

    ZHOU Lan Professor at the School of Information and Electrical Engineering, Hunan University of Science and Technology. Her research interest covers nonlinear system, robust control and theory and application of repetitive control. Corresponding author of this paper

    YANG Qin Master student at the School of Information and Electrical Engineering, Hunan University of Science and Technology. His research interest covers repetitive control, numerical control machining, and mechatronic system design design

    PAN Chang-Zhong Professor at the School of Information and Electrical Engineering, Hunan University of Science and Technology. His research interest covers nonlinear control theory and applications, mechatronics and robot control, and intelligent control

    XIAO Wen-Bin Lecturer at the School of Information and Electrical Engineering, Hunan University of Science and Technology. Her research interest covers adaptive control for nonlinear systems and distributed control for multi-agent systems

    LI Mei-Liu Lecturer at the School of Information and Electrical Engineering, Hunan University of Science and Technology. Her research interest covers networked systems, disturbance estimation and compensation, and robust control in time-delay systems

  • 摘要: 在非圆零件车削过程中, 快速刀具伺服(Fast tool servo, FTS)的运动精度直接影响零件的加工质量. 主轴变速加工使得FTS的参考目标信号周期时变而不确定, 这对实现其渐近跟踪提出了极大的挑战. 本文利用FTS的位置域周期特性, 提出一种基于位置域重复控制和时域速度反馈镇定的FTS系统复合控制设计方法, 并给出位置域改进型重复控制器(Spatial modified repetitive controller, SMRC)的数字实现算法, 实现对时变周期参考目标信号的高精度跟踪. 首先, 建立包含位置相关时变周期参考目标信号内模的SMRC, 并引入位置域相位超前装置对镇定补偿器引起的相位滞后进行补偿, 在此基础上构建复合控制律. 然后应用小增益定理和算子理论, 推导出控制系统的稳定性条件, 在保持系统采样频率不变的条件下, 应用插值法建立SMRC的数字实现算法, 确保位置域重复控制和时域镇定控制器的同步执行. 最后, 通过仿真验证所设计的FTS控制系统具有满意的时变周期跟踪性能和鲁棒性, 并通过与其他位置域重复控制方法的比较, 说明所提方法同时具有更好的暂态和稳态性能.
  • 图  1  椭圆零件加工示意图

    Fig.  1  Elliptical workpiece machining schematic

    图  2  基于位置域改进型重复控制的FTS系统框图

    Fig.  2  Block diagram of SMRC-based FTS system

    图  3  位置域基本重复控制器和改进型重复控制器的零极点分布图和幅值特性曲线

    Fig.  3  Zero-pole map and Amplitude-frequency characteristics of spatial basic repetitive controller and SMRC

    图  4  $r(t)=0$时FTS控制系统的等价形式

    Fig.  4  Equivalent form of FTS control system when $r(t)=0$

    图  5  时域纯时滞环节的数字实现

    Fig.  5  Digital implementation of the pure time-delay link in the time domain

    图  6  位置域时滞单元输入输出曲线

    Fig.  6  Input and output curves of the delay element in position domain

    图  7  位置相关周期信号等时采样示意图

    Fig.  7  Diagram of isochronous sampling of a position-dependent periodic signal

    图  8  位置域改进型重复控制器数字实现算法流程图

    Fig.  8  Flowchart of the digital implementation algorithm for SMRC

    图  9  参考信号在时间域和位置域的曲线

    Fig.  9  Reference signal curves in the time and position domains

    图  10  $Q_{{{\rm m}}}(s)$和$1+G(s)$的伯德图

    Fig.  10  Bode plots of $Q_{{{\rm m}}}(s)$ and $1+G(s)$

    图  11  基于SMRC方法的FTS输出响应

    Fig.  11  Output response of the SMRC-based FTS

    图  12  不同相位补偿因子的跟踪误差

    Fig.  12  Tracking errors with different phase compensation factors

    图  13  存在参数摄动时的跟踪误差

    Fig.  13  Tracking error with parameter perturbation

    图  14  无速度反馈时的$Q_{{{{\rm{m}}}}}(s)$和$1+G^{\prime}(s)$伯德图

    Fig.  14  Bode plots of $Q_{{{{\rm{m}}}}}(s)$ and $1+G^{\prime}(s)$ without velocity feedback

    图  15  本文方法与传统定周期时域重复控制方法的对比

    Fig.  15  Comparison of our method with the conventional fixed-period time-domain repetitive control method

    图  16  本文方法与Liu等[32]和Yao等[33]的跟踪误差对比

    Fig.  16  Comparison of the tracking error between our method and the methods proposed by Liu et al.[32] and Yao et al.[33]

    表  1  音圈式直线电机相关参数

    Table  1  Parameters of the voice coil type linear motor

    参数 符号 单位 数值
    弹簧刚度系数 $ K $ ${\rm{N/m }} $ 4 980
    阻尼系数 $ C $ ${\rm{N\cdot s\cdot m^{-1}}}$ 14.51
    动子质量 $ M $ ${\rm{kg } }$ 0.32
    电机力常数 $ K_{m} $ ${\rm{N/A }} $ 12.325
    放大器增益 $ K_a $ ${\rm{A/v}} $ 1.6
    下载: 导出CSV

    表  2  性能指标对比

    Table  2  Comparison of performance indices

    控制方法 $\max|e(t)|_{0<t\leq 20}$ $e_{pp}\;(0 < t\leq 20)$ $\max|e(t)|_{t>20} $ $e_{pp}\;(t > 20)$
    CRC $8.744\times10^{-2} $ $17.393\times10^{-2} $ $9.707\times10^{-3} $ $1.580\times10^{-2} $
    Liu等[32] $3.246\times10^{-2} $ $5.993\times10^{-2} $ $1.006\times10^{-3} $ $1.992\times10^{-3} $
    Yao等[33] $2.315\times10^{-2} $ $3.684\times10^{-2} $ $6.737\times10^{-3} $ $1.347\times10^{-2} $
    本文方法 2.315 × 10−2 3.665 × 10−2 6.759 × 10−4 1.334 × 10−3
    下载: 导出CSV
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  • 收稿日期:  2023-06-19
  • 录用日期:  2023-09-08
  • 网络出版日期:  2023-10-25
  • 刊出日期:  2024-07-23

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