Hysteresis characteristics of pneumatic artificial muscle based on improved Maxwell model
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摘要:
针对气动人工肌肉非线性程度高、迟滞模型建立困难的问题，研究了气动人工肌肉的迟滞特性，提出了一种基于滑移算子的改进Maxwell模型。搭建了气动人工肌肉的收缩力测试平台，进行了静态力实验和动态力实验，得到了气动人工肌肉的迟滞力曲线，并分别考虑了不同行程、不同充气压力和不同伸缩速率对迟滞环的影响，得到了气动人工肌肉的各项迟滞特性。针对传统Maxwell模型无法很好地表现气动人工肌肉的非对称迟滞特性，将迟滞力曲线分别从上部和下部收缩，得到的各项算子较好地表现了气动人工肌肉收缩力曲线的非局部记忆性和非对称性，将最大误差控制在了6.8%以内，中段误差控制在了2.0%以内，较好地匹配了实验曲线，验证了所提模型的普适性。
Abstract:In view of the high nonlinearity of pneumatic artificial muscle and the difficulty in establishing a hysteresis model, the hysteresis characteristics of pneumatic artificial muscle were studied, and an improved Maxwell model based on slip operator was proposed. First of all, the contraction force test platform of pneumatic artificial muscle was set,on which the static force experiment and dynamic force experiment were carried out. The hysteresis force curve of the pneumatic artificial muscle was obtained, and the effects of different strokes, different inflation pressures, and different expansion rates on the hysteresis loop were considered respectively.The hysteresis characteristics of the pneumatic artificial muscle were obtained. Then, since the traditional Maxwell model could not represent the asymmetrical hysteresis characteristics of pneumatic artificial muscle very well, the hysteresis curves were contracted from the upper and lower parts, respectively, and the obtained operators could represent the non-local memory and asymmetry of the contraction curves of the pneumatic artificial muscle better. The maximum error was controlled within 6.8%, andthe error of the middle section was controlled within 2.0%, matching the experimental curve well and verifyingthe universality of the model.
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图 5 等长实验的压强与收缩力关系
Figure 5. Relationship between pressure and contraction force in isometric test
图 14 基于原始曲线的Maxwell算子参数
Figure 14. Maxwell operator parameters based on original curve
图 16 0.40 MPa充气压力下的拟合情况
Figure 16. Fitting situation at inflation pressure of 0.40 MPa
表 1 等长实验主要元件
Table 1. Main element of isometric test
元件名称 元件型号 主要性能指标 气动人工肌肉 DSMP-10-300N-RM-RM 初始长度300 mm，最大抗拉力600 N 数据采集卡 NI PCIE-6353 16位计数器，输出电压−10～10 V 拉力传感器 NTJL-1 0～500 N 空气压缩机 HX750A 最大供气压力1 MPa 压力传感器 MIK-P300 测量范围−0.1～60 MPa 比例方向控制阀 FESTO MPYE-5-M5-010-B 最大工作压力：1 MPa 位移传感器 PANASONIC HG-C1200 测量范围0～40 mm，精度0.01 mm 
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表 2 参数拟合结果
Table 2. Parameter fitting results
$ P/\mathrm{\rm{M}Pa} $ $ \alpha (P) $ $ \beta (P) $ $ \gamma (P) $ $ \lambda (P) $ 0.25 0.0336 −28.703 8188.214 − 779376.024 0.3 0.0262 −22.197 6276.948 − 592287.396 0.35 0.00994 −8.201 2259.785 − 207967.509 0.4 0.00785 −6.431 1760.549 − 161040.129 0.45 0.0057 −4.619 1252.389 − 113560.093 0.5 0.0047 −3.808 1033.544 − 93900.544
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表 3 滑移算子的代表性参数
Table 3. Representative parameters of slip operators
参数 数值 参数 数值 k1 4.0797 w1 18.3585 k2 1.3121 w2 5.9045 k3 0.7226 w3 3.252 k4 0.4981 w4 2.2415 k5 0.0541 w5 0.2435 k6 4.8055 w6 21.625 k7 0.5834 w7 2.6225 k8 0.6996 w8 3.148 k9 0.4940 w9 2.223 k10 0.0841 w10 0.3748
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