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                    SEAs導納控制的μ綜合方法

                    李思奇 黃遠燦

                    李思奇, 黃遠燦. SEAs導納控制的 μ綜合方法. 自動化學報, 2019, 45(x): 1?9 doi: 10.16383/j.aas.c180576
                    引用本文: 李思奇, 黃遠燦. SEAs導納控制的 μ 綜合方法. 自動化學報, 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導納控制的μ綜合方法

                    doi: 10.16383/j.aas.c180576
                    基金項目: 國家自然科學基金(61773065, 61075080), 哈爾濱工業大學機器人與系統國家重點實驗室開放式基金(SKLRS-2017-KF-05)資助
                    詳細信息
                      作者簡介:

                      李思奇:北京理工大學機電學院博士研究生. 2011年獲得太原科技大學機械工程碩士學位. 主要研究方向為電路設計, 魯棒控制, 人 ? 機交互控制. E-mail: rxjrlsq@163.com

                      黃遠燦:北京理工大學機電學院副教授. 主要研究方向為柔性機器人, 阻抗控制和非線性系統控制. 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具有在確保機器人性能的基礎上兼顧其安全性的特點, 因此被廣泛地應用在康復機器人中. 為實現良好的康復訓練效果, 機器人需根據實際要求呈現不同的阻抗特性. 本文采用μ綜合技術解決了SEAs導納控制器的設計問題. 首先, 考慮參數攝動, 傳感器噪聲, 輸入干擾及控制輸入限制等不確定性因素, 建立SEAs模型. 其次, 應用混合穩定性原理分析系統的交互穩定性. 由于無源環境的阻抗在高頻段必然呈現小增益特性, 所以, 當端口導納在低頻段滿足無源性, 高頻段具有小增益時, 就能確保交互的穩定性. 然后, 將SEAs的導納控制綜合問題轉化為實際端口導納與期望導納匹配的μ綜合問題. 最后, 通過調節加權函數, 不僅讓SEAs閉環系統的端口導納逼近期望的端口導納, 還能同時滿足交互穩定性條件, 從而可以獨立于環境因素來設計導納控制器. 仿真結果表明, 基于μ綜合方法設計的控制器, 能精確地逼近期望的端口導納, 且確保交互穩定性. 另外, 通過Hankel逼近方法得到的降階控制器也具有滿意的控制效果.
                    • 圖  1  SEAs模型

                      Fig.  1  The SEAs model

                      圖  2  SEAs結構框圖

                      Fig.  2  The block diagram of SEAs equation

                      圖  3  混合交互穩定性實例

                      Fig.  3  A example of “mix” interaction stability

                      圖  11  導納模式(彈簧 ? 阻尼 ? 質量塊并聯模型)控制器降階前后的比較

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

                      圖  4  廣義對象結構簡圖

                      Fig.  4  Generalized plant structure diagram

                      圖  5  導納控制結構

                      Fig.  5  Admittance control configuration

                      圖  6  導納控制器的求解過程

                      Fig.  6  The solving procedure of admittance controller

                      圖  10  四種導納模式的交互設計

                      Fig.  10  Interactive design of four admittance modes

                      圖  7  人手臂阻抗圖

                      Fig.  7  Impedance of human arm

                      圖  8  控制器求解和交互仿真驗證流程圖

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

                      圖  9  零阻抗的頻率響應圖

                      Fig.  9  Bode diagrams of zero impedance

                      圖  12  零阻抗的交互仿真

                      Fig.  12  Interactive simulation of zero impedance

                      圖  13  導納模式(彈簧-阻尼-質量塊并聯模型)的交互仿真

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

                      表  1  SEAs仿真參數

                      Table  1  The SEAs simulation parameter values

                      參數 單位 參數 單位
                      $M_{mn}$ $0.61$ $kg\cdot m^2$ $m_{hn}$ $0.4$ $kg\cdot m^2$
                      $\delta_{m}$ $0.06$ $---$ $m_{hd}$ $0.1$ $kg\cdot m^2$
                      $D_{mn}$ $4.9$ $N\cdot m\cdot s/rad$ $b_{hn}$ $2.1$ $N\cdot m\cdot s/rad$
                      $D_{md}$ $1.0$ $N\cdot m\cdot s/rad$ $b_{hd}$ $0.5$ $N\cdot m\cdot s/rad$
                      $k_{n}$ $696.9$ $N\cdot m/rad$ $k_{hn}$ $30$ $N\cdot m/rad$
                      $k_{d}$ $20$ $N\cdot m/rad$ $k_{hd}$ $5$ $N\cdot m/rad$
                      $M_{l}$ $0.14$ $kg\cdot m^2$ $D_{l}$ $0.01$ $N\cdot m\cdot s/rad$
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                    • 收稿日期:  2018-08-29
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