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基于扰动补偿的磁悬浮转台分数阶滑模控制

许贤泽 宋明星 龚勇兴 徐逢秋 王递进 隋博文 郭清泉

许贤泽, 宋明星, 龚勇兴, 徐逢秋, 王递进, 隋博文, 郭清泉. 基于扰动补偿的磁悬浮转台分数阶滑模控制[J]. 西南交通大学学报. doi: 10.3969/j.issn.0258-2724.20230412
引用本文: 许贤泽, 宋明星, 龚勇兴, 徐逢秋, 王递进, 隋博文, 郭清泉. 基于扰动补偿的磁悬浮转台分数阶滑模控制[J]. 西南交通大学学报. doi: 10.3969/j.issn.0258-2724.20230412
XU Xianze, SONG Mingxing, GONG Yongxing, XU Fengqiu, WANG Dijin, SUI Bowen, GUO Qingquan. Fractional-Order Sliding Mode Control for Maglev Rotary Table Based on Disturbance Compensation[J]. Journal of Southwest Jiaotong University. doi: 10.3969/j.issn.0258-2724.20230412
Citation: XU Xianze, SONG Mingxing, GONG Yongxing, XU Fengqiu, WANG Dijin, SUI Bowen, GUO Qingquan. Fractional-Order Sliding Mode Control for Maglev Rotary Table Based on Disturbance Compensation[J]. Journal of Southwest Jiaotong University. doi: 10.3969/j.issn.0258-2724.20230412

基于扰动补偿的磁悬浮转台分数阶滑模控制

doi: 10.3969/j.issn.0258-2724.20230412
基金项目: 国家自然科学基金(52275569);扬州市重点研发项目(YZ2022013);云南省专家工作站项目(202205AF150061);湖北省技术创新计划重点研发专项(2023BAB050);武汉东湖新技术开发区“揭榜挂帅”项目(2022KJB129);中国科协青年人才托举工程(2022QNRC001)
详细信息
    作者简介:

    许贤泽(1967—),男,教授,博士,研究方向为精密测量与控制和磁悬浮控制技术,E-mail:xuxianze@whu.edu.cn

    通讯作者:

    徐逢秋(1990—),男,副教授,博士,研究方向为磁悬浮系统设计和磁悬浮平面电机运动控制,E-mail:hncxu@whu.edu.cn

  • 中图分类号: TP273

Fractional-Order Sliding Mode Control for Maglev Rotary Table Based on Disturbance Compensation

  • 摘要:

    针对存在非线性、耦合性和不确定性的磁悬浮转台的高精度运动控制问题,提出一种基于非线性干扰观测器的分数阶滑模控制方法以提高跟踪精度. 首先,基于系统电磁力模型和动态解耦方法,构建六自由度磁悬浮转台系统动力学模型;其次,设计非线性干扰观测器,对包含系统误差、六自由度间耦合项和外界干扰的集总扰动进行估计,证明了估计误差有界且可调节到任意小;然后,在离散域提出了一种分数阶滑模面,采用分数幂函数替代传统符号函数来抑制抖振,引入分数阶微积分来减小跟踪误差;最后,设计有限时间收敛的分数阶滑模控制策略,并利用李雅普诺夫稳定性理论证明闭环系统稳定性. 实验结果表明:与整数阶滑模控制方法相比,采用所提方法,2个水平自由度和绕竖直方向旋转自由度对三角波的跟踪误差均方根分别减小了12.8%、16.8%和23.7%,最大跟踪误差分别减小9.26%、13.0%和33.2%;跟踪圆形轨迹时,2个水平自由度的跟踪误差均方值分别减小6.39%和12.4%,最大跟踪误差分别减小9.90%和12.1%.

     

  • 图 1  磁悬浮转台俯视示意

    Figure 1.  Top view of maglev rotary table

    图 2  磁通密度分布示意

    Figure 2.  Magnetic flux density distribution

    图 3  磁悬浮转台控制系统框图

    Figure 3.  Block diagram of maglev rotary table control system

    图 4  磁悬浮转台实验平台

    Figure 4.  Experimental setup of maglev rotary table

    图 5  阶跃信号跟踪波形

    Figure 5.  Tracking waveform of step signal

    图 6  三角波跟踪波形与跟踪误差

    Figure 6.  Tracking waveform and error of triangular wave

    图 7  圆轨迹跟踪效果

    Figure 7.  Tracking performance of circular trajectory

    表  1  磁悬浮转台系统参数

    Table  1.   Maglev rotary table system parameters

    参数 数值
    永磁体长/lm、宽/wm、高hm/mm 30,8,8
    φm/(°) 7.5
    r/mm 80
    Br/T 1.2
    线圈尺寸(lc,wc,hc,rc)/mm 60,10,10,10
    线圈匝数 N/匝 300
    m/kg 2.37
    ${J_\alpha }$,${J_\beta }$,${J_\gamma }$/(kg·m2 9.37×10−3, ~ ,1.87×10−2
    采样间隔/ms 1
    重力加速度/(m·s−2 9.8
    下载: 导出CSV

    表  2  控制器参数

    Table  2.   Controller parameters

    自由度 PID DTSMC 和所提方法
    KPID k1 k2 l1 l2
    x,y,z 0.124 1 19.3 8.84 21.4
    α,β 4.90 × 10−4 3.95 × 10−3 0.0763 0.0348 0.0846
    γ 9.78 × 10−4 7.89 × 10−3 0.152 0.0694 0.169
    下载: 导出CSV

    表  3  三角波跟踪误差

    Table  3.   Tracking error of triangular wave

    控制方法x/mmy/mmγ/mrad
    eRMSeMAXeRMSeMAXeRMSeMAX
    PID0.01480.09660.01550.09770.07060.212
    DTSMC0.01170.08750.01490.09530.04100.170
    所提方法0.01020.07940.01240.08290.03130.113
    下载: 导出CSV

    表  4  圆轨迹跟踪误差

    Table  4.   Tracking error of circular trajectory

    控制方法 x/mm y/mm
    eRMS eMAX eRMS eMAX
    PID 0.0109 0.0686 0.0226 0.163
    DTSMC 0.0101 0.0657 0.0251 0.158
    所提方法 0.0091 0.0615 0.0220 0.138
    下载: 导出CSV
  • [1] XU X Z, ZHENG C L, XU F Q. A real-time numerical decoupling method for multi-DoF magnetic levitation rotary table[J]. Applied Sciences, 2019, 9(16): 3263.1-3263.16.
    [2] ZHU H Y, TEO T J, PANG C K. Flexure-based magnetically levitated dual-stage system for high-bandwidth positioning[J]. IEEE Transactions on Industrial Informatics, 2019, 15(8): 4665-4675. doi: 10.1109/TII.2019.2890951
    [3] LAHDO M, STRÖHLA T, KOVALEV S. Design and implementation of an new 6-DoF magnetic levitation positioning system[J]. IEEE Transactions on Magnetics, 2019, 55(12): 8107407.1-8107407.7.
    [4] SILVA-RIVAS J C, KIM W J. Multivariable control and optimization of a compact 6-DOF precision positioner with hybrid H2/H∞ and digital filtering[J]. IEEE Transactions on Control Systems Technology, 2013, 21(5): 1641-1651. doi: 10.1109/TCST.2012.2215035
    [5] LI D F, GUTIERREZ H. Observer-based sliding mode control of a 6-DOF precision maglev positioning stage[C]//2008 34th Annual Conference of IEEE Industrial Electronics. Orlando: IEEE, 2008: 2562-2567.
    [6] 魏静波,罗浩,关子津. 基于干扰观测器的磁悬浮球系统全局快速终端滑模控制[J]. 西南交通大学学报,2023,58(4): 836-844.

    WEI Jingbo, LUO Hao, GUAN Zijin. Global fast terminal sliding mode control for maglev ball system based on disturbance observer[J]. Journal of Southwest Jiaotong University, 2023, 58(4): 836-844.
    [7] DU H B, YU X H, LI S H. Dynamical behaviors of discrete-time fast terminal sliding mode control systems[M]//Recent Advances in Sliding Modes: From Control to Intelligent Mechatronics. Cham: Springer, 2015: 77-97.
    [8] ZHANG L, ZHANG Z, HUANG L. Hybrid non-linear differentiator design for a permanent-electro magnetic suspension maglev system[J]. IET Signal Processing, 2012, 6(6): 559. doi: 10.1049/iet-spr.2011.0264
    [9] NGUYEN S D, LAM B D, NGO V H. Fractional-order sliding-mode controller for semi-active vehicle MRD suspensions[J]. Nonlinear Dynamics, 2020, 101(2): 795-821. doi: 10.1007/s11071-020-05818-w
    [10] SUN G H, MA Z Q, YU J Y. Discrete-time fractional order terminal sliding mode tracking control for linear motor[J]. IEEE Transactions on Industrial Electronics, 2018, 65(4): 3386-3394. doi: 10.1109/TIE.2017.2748045
    [11] KUANG Z A, GAO H J, TOMIZUKA M. Precise linear-motor synchronization control via cross-coupled second-order discrete-time fractional-order sliding mode[J]. IEEE/ASME Transactions on Mechatronics, 2021, 26(1): 358-368.
    [12] HU C X, WANG Z, ZHU Y, et al. Performance-oriented precision LARC tracking motion control of a magnetically levitated planar motor with comparative experiments[J]. IEEE Transactions on Industrial Electronics, 2016, 63(9): 5763-5773. doi: 10.1109/TIE.2016.2538743
    [13] JANSEN J W, VAN LIEROP C M M, LOMONOVA E A, et al. Magnetically levitated planar actuator with moving magnets[J]. IEEE Transactions on Industry Applications, 2008, 44(4): 1108-1115. doi: 10.1109/TIA.2008.926065
    [14] DYCK M, LU X D, ALTINTAS Y. Magnetically levitated rotary table with six degrees of freedom[J]. IEEE/ASME Transactions on Mechatronics, 2017, 22(1): 530-540. doi: 10.1109/TMECH.2016.2621108
    [15] YANG H L, DENG F, HE Y, et al. Robust nonlinear model predictive control for reference tracking of dynamic positioning ships based on nonlinear disturbance observer[J]. Ocean Engineering, 2020, 215: 107885.1-107885.7.
    [16] LU X, XU F Q, XU X Z, et al. Directed-driven 8-phase magnetically levitated rotary table based on an analytical-numerical model[J]. IEEE Access, 2020, 8: 31159-31170. doi: 10.1109/ACCESS.2020.2973223
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出版历程
  • 收稿日期:  2023-08-18
  • 修回日期:  2023-10-24
  • 网络出版日期:  2024-04-03

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