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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, 2019, 45(x): 1−9 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, 2019, 45(x): 1−9 doi: 10.16383/j.aas.c180576
Li Si-Qi, Huang Yuan-Can. μ-Synthesis for admittance control of SEAs. Acta Automatica Sinica, 2019, 45(x): 1−9 doi: 10.16383/j.aas.c180576
Citation: Li Si-Qi, Huang Yuan-Can. μ-Synthesis for admittance control of SEAs. Acta Automatica Sinica, 2019, 45(x): 1−9 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. 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, Harbing Institute of Technology (SKLRS-2017-KF-05)
  • 摘要: SEAs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  A 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  四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
    $M_{mn}$ $0.61$ $kg\cdot m^2$ $m_{hn}$ $0.4$ $kg\cdot m^2$
    $\delta_{m}$ $0.06$ $---$ $m_{hd}$ $0.1$ $kg\cdot m^2$
    $D_{mn}$ $4.9$ $N\cdot m\cdot s/rad$ $b_{hn}$ $2.1$ $N\cdot m\cdot s/rad$
    $D_{md}$ $1.0$ $N\cdot m\cdot s/rad$ $b_{hd}$ $0.5$ $N\cdot m\cdot s/rad$
    $k_{n}$ $696.9$ $N\cdot m/rad$ $k_{hn}$ $30$ $N\cdot m/rad$
    $k_{d}$ $20$ $N\cdot m/rad$ $k_{hd}$ $5$ $N\cdot m/rad$
    $M_{l}$ $0.14$ $kg\cdot m^2$ $D_{l}$ $0.01$ $N\cdot m\cdot s/rad$
    下载: 导出CSV
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  • 收稿日期:  2018-08-29
  • 录用日期:  2018-12-24
  • 网络出版日期:  2019-12-30

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