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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.
Abstract:Series elastic actuators (SEAs) are an effective technique to balance robot safety and performance. Therefore, SEAs are widely used in rehabilitation robots. For the application of robots in rehabilitation training to be effective, specific requirements such as admittance-controlling are necessary. In this paper, the μ synthesis technique is used to design an admittance controller for the SEAs. Firstly, the unpredictable nature of factors like parameter perturbation, sensor noise, input disturbance and control input restriction is an essential consideration in the modeling of the SEAs. Second, the concept of mixed stability is adopted to analyze interaction stability. Since passive environments must have small-gain property in high-frequency range in reality, interaction stability is maintained as long as the port admittance displays passivity in low-frequency range and small gain in high-frequency where the small-gain theorem is satisfied. Third, the admittance control synthesis converts into the admittance matching μ synthesis problem. By selecting the appropriate weight functions, the actual port admittance is forced to approach the desired admittance while the mixed stability conditions are satisfied. Consequently, an admittance controller can be devised independently of the interacted environment. Simulation results show that the controller based on μ synthesis can not only force the SEAs system to achieve the desired admittance, but can also guarantee the interaction stability. Furthermore, the reduced controllers based on Hankel approximation displayed satisfactory control performance.
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Key words:
- Series elastic actuators (SEAs) /
- μ-synthesis /
- admittance control /
- mixed stability
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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 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 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 值 单位 参数 值 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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