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SEAs导纳控制的μ综合方法

李思奇 黄远灿

李思奇,  黄远灿.  SEAs导纳控制的μ综合方法.  自动化学报,  2021,  47(7): 1539−1547 doi: 10.16383/j.aas.c180576
引用本文: 李思奇,  黄远灿.  SEAs导纳控制的μ综合方法.  自动化学报,  2021,  47(7): 1539−1547 doi: 10.16383/j.aas.c180576
Li Si-Qi,  Huang Yuan-Can.  μ-Synthesis for admittance control of SEAs.  Acta Automatica Sinica,  2021,  47(7): 1539−1547 doi: 10.16383/j.aas.c180576
Citation: Li Si-Qi,  Huang Yuan-Can.  μ-Synthesis for admittance control of SEAs.  Acta Automatica Sinica,  2021,  47(7): 1539−1547 doi: 10.16383/j.aas.c180576

SEAs导纳控制的μ综合方法

doi: 10.16383/j.aas.c180576
基金项目: 国家自然科学基金(61773065, 61075080), 哈尔滨工业大学机器人与系统国家重点实验室开放式基金(SKLRS-2017-KF-05)资助
详细信息
    作者简介:

    李思奇:北京理工大学机电学院博士研究生. 2011年获得太原科技大学机械工程硕士学位. 主要研究方向为电路设计, 鲁棒控制, 人 − 机交互控制. E-mail: rxjrlsq@163.com

    黄远灿:北京理工大学机电学院副教授,博士. 主要研究方向为柔性机器人, 阻抗控制和非线性系统控制. 本文通信作者. E-mail: yuancanhuang@bit.edu.cn

μ-Synthesis for Admittance Control of SEAs

Funds: Supported by National Natural Science Foundation of China (61773065, 61075080), State Key Laboratory of Robotics and System, Harbin Institute of Technology (SKLRS-2017-KF-05)
More Information
    Author Bio:

    LI Si-Qi Ph.D. candidate at the School of Mechatronical Engineering, Beijing Institute of Technology. She received her master degree in mechanical engineering from Taiyuan University of Science and Technology in 2011. Her research interest covers circuit design, robust control, and human-robot interaction control

    HUANG Yuan-Can Ph.D., associate professor at the School of Mechatronical Engineering, Beijing Institute of Technology. His research interest covers flexible robot, impedance control, and nonlinear system control. Corresponding author of this paper

  • 摘要:

    SEAs (Series elastic actuators)具有在确保机器人性能的基础上兼顾其安全性的特点, 因此被广泛地应用在康复机器人中. 为实现良好的康复训练效果, 机器人需根据实际要求呈现不同的阻抗特性. 本文采用μ综合技术解决了SEAs导纳控制器的设计问题. 首先, 考虑参数摄动、传感器噪声、输入干扰及控制输入限制等不确定性因素, 建立SEAs模型. 其次, 应用混合稳定性原理分析系统的交互稳定性. 由于无源环境的阻抗在高频段必然呈现小增益特性, 所以, 当端口导纳在低频段满足无源性, 高频段具有小增益时, 就能确保交互的稳定性. 然后, 将SEAs的导纳控制综合问题转化为实际端口导纳与期望导纳匹配的μ综合问题. 最后, 通过调节加权函数, 不仅让SEAs闭环系统的端口导纳逼近期望的端口导纳, 还能同时满足交互稳定性条件, 从而可以独立于环境因素来设计导纳控制器. 仿真结果表明, 基于μ综合方法设计的控制器, 能精确地逼近期望的端口导纳, 且确保交互稳定性. 另外, 通过Hankel逼近方法得到的降阶控制器也具有满意的控制效果.

  • 图  1  SEAs模型

    Fig.  1  The SEAs model

    图  2  SEAs结构框图

    Fig.  2  The block diagram of SEAs equation

    图  3  混合交互稳定性实例

    Fig.  3  An example of “mix” interaction stability

    图  11  导纳模式(弹簧 − 阻尼 − 质量块并联模型)控制器降阶前后的比较

    Fig.  11  Demotion of the admittance mode controller (spring-damper-mass connect in parallel)

    图  4  广义对象结构简图

    Fig.  4  Generalized plant structure diagram

    图  5  导纳控制结构

    Fig.  5  Admittance control configuration

    图  6  导纳控制器的求解过程

    Fig.  6  The solving procedure of admittance controller

    图  10  4种导纳模式的交互设计

    Fig.  10  Interactive design of four admittance modes

    图  7  人手臂阻抗图

    Fig.  7  Impedance of human arm

    图  8  控制器求解和交互仿真验证流程图

    Fig.  8  Flow chart of controller solving and interactive simulation verification

    图  9  零阻抗的频率响应图

    Fig.  9  Bode diagrams of zero impedance

    图  12  零阻抗的交互仿真

    Fig.  12  Interactive simulation of zero impedance

    图  13  导纳模式(弹簧-阻尼-质量块并联模型)的交互仿真

    Fig.  13  Interactive simulation of admittance mode (spring-damper-mass connect in parallel)

    表  1  SEAs仿真参数

    Table  1  The SEAs simulation parameter values

    参数 单位 参数 单位
    $M_{mn}$ $0.61$ ${\rm kg}\cdot {\rm m}^2$ $m_{hn}$ $0.4$ ${\rm kg}\cdot {\rm m}^2$
    $\delta_{m}$ $0.06$ $—$ $m_{hd}$ $0.1$ ${\rm kg}\cdot {\rm m}^2$
    $D_{mn}$ $4.9$ ${\rm N}\cdot {\rm m}\cdot {\rm s/rad}$ $b_{hn}$ $2.1$ ${\rm N}\cdot {\rm m}\cdot {\rm s/rad}$
    $D_{md}$ $1.0$ ${\rm N}\cdot {\rm m}\cdot {\rm s/rad}$ $b_{hd}$ $0.5$ ${\rm N}\cdot {\rm m}\cdot {\rm s/rad}$
    $k_{n}$ $696.9$ ${\rm N}\cdot {\rm m} {\rm /rad}$ $k_{hn}$ $30$ ${\rm N}\cdot {\rm m} {\rm /rad}$
    $k_{d}$ $20$ ${\rm N}\cdot {\rm m} {\rm /rad}$ $k_{hd}$ $5$ ${\rm N}\cdot {\rm m} {\rm /rad}$
    $M_{l}$ $0.14$ ${\rm kg}\cdot {\rm m}^2$ $D_{l}$ $0.01$ ${\rm N}\cdot {\rm m}\cdot {\rm s/rad}$
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出版历程
  • 收稿日期:  2018-08-29
  • 录用日期:  2018-12-24
  • 网络出版日期:  2019-12-30
  • 刊出日期:  2021-07-27

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