In this paper, the Maxwell-slip model is extended to a distributed parameter Maxwell-slip (DPMS) model, and a DPMS model parameter identification process is proposed for the hysteresis in piezoelectric actuators (PEAs). This model is governed by a saturation deformation function (SDF) and a stiffness function (SF); it requires only a few parameters and can capture nonconvex hysteresis. It has a clear interpretation in the mechanical domain and provides insight into the mechanism of hysteresis generation; hence, it can predict the performance in the unidentified range. With a linear SDF, exponential, power-law, and polynomial SFs are studied for a PEA-based nanopositioning system. The normalized root-mean-square (NRMS) errors for these SFs are 0.60%, 0.43%, and 0.47%, respectively. With parameters identified from the middle hysteresis loop, the NRMS error is 0.68%. For the nonconvex hysteresis, the NRMS error is 2.78%. With compensation by DPMS models with the above three SFs, the hysteresis decreases by 86.95%, 87.13%, and 97.13%, respectively. The rate dependence of the frequency response is eliminated, and the $-$3-dB bandwidth increases from 320 to 890 Hz.

中文翻译：

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压电驱动器迟滞分布参数麦克斯韦滑移模型

在本文中，Maxwell-slip 模型被扩展到分布参数 Maxwell-slip (DPMS) 模型，并针对压电致动器 (PEA) 中的滞后提出了 DPMS 模型参数识别过程。该模型由饱和变形函数 (SDF) 和刚度函数 (SF) 控制；它只需要几个参数并且可以捕获非凸滞后。它在机械领域有明确的解释，并提供对滞后产生机制的洞察；因此，它可以预测未知范围内的性能。使用线性 SDF，研究基于 PEA 的纳米定位系统的指数、幂律和多项式 SF。这些 SF 的归一化均方根 (NRMS) 误差分别为 0.60%、0.43% 和 0.47%。使用从中间磁滞回线确定的参数，NRMS 误差为 0.68%。对于非凸滞后，NRMS 误差为 2.78%。通过具有上述三个SFs的DPMS模型补偿，滞后分别降低了86.95%、87.13%和97.13%。消除了频率响应的速率依赖性，$-$3-dB 带宽从 320 Hz 增加到 890 Hz。