SUMMARY Prandtl–Ishlinskii (PI) model has an excellent compromise to characterize an asymmetric saturated hysteresis behavior of shape-memory-alloy (SMA)-driven systems, but it cannot consider thermomechanical relations between components of SMA-driven systems. On the other hand, constitutive models are composed of these relations, but their precision needs to be improved. In this paper, PI model is proposed to boost constitutive models in two cases. In the first case, PI model is used to characterize martensite volume fraction (MVF) called hybrid model. In the second case, the model is applied as a regulator in the output of a constitutive model called PI-based output (PIO) regulator. Due to simplicity and ability of Liang–Rogers (LR) model in transformation phases, it is considered as an MVF in the original constitutive model. The performance of both proposed models is compared with the original LR-based constitutive model. Unknown parameters of all three models are identified using genetic algorithm in MATLAB Toolbox. The performance of the three models is investigated at three different frequencies of \[\frac{{2\pi }}{8}\] , \[\frac{{2\pi }}{{15}}\] , and \[\frac{{2\pi }}{{30}}\] Hz because the excitation frequency changes the hysteresis behavior. Results show that the proposed hybrid model keeps the precision of the original constitutive model at different frequencies. In addition, the proposed PIO model shows the best performance to predict hysteresis behavior at different frequencies.

中文翻译：

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混合 Prandtl-Ishlinskii 和形状记忆合金驱动执行器滞后的本构模型的开发

总结 Prandtl-Ishlinskii (PI) 模型在表征形状记忆合金 (SMA) 驱动系统的不对称饱和滞后行为方面具有出色的折衷，但它不能考虑 SMA 驱动系统组件之间的热机械关系。另一方面，本构模型是由这些关系组成的，但它们的精度有待提高。在本文中，提出了 PI 模型来增强本构模型的两种情况。在第一种情况下，PI模型用于表征马氏体体积分数（MVF），称为混合模型。在第二种情况下，该模型被用作本构模型的输出中的调节器，称为基于 PI 的输出 (PIO) 调节器。由于 Liang-Rogers (LR) 模型在转换阶段的简单性和能力，它被认为是原始本构模型中的 MVF。将两种建议模型的性能与原始的基于 LR 的本构模型进行了比较。使用 MATLAB Toolbox 中的遗传算法识别所有三个模型的未知参数。三种模型的性能在三个不同的频率下进行了研究 \[\frac{{2\pi }}{8}\] , \[\frac{{2\pi }}{{15}}\] ， 和 \[\frac{{2\pi }}{{30}}\] Hz，因为激励频率会改变滞后行为。结果表明，所提出的混合模型在不同频率下保持了原始本构模型的精度。此外，所提出的 PIO 模型显示了预测不同频率下滞后行为的最佳性能。