Abstract

Hysteresis is a nonlinear phenomenon which may cause inaccuracies and delay in control applications. Shape memory alloys (SMAs) have an asymmetric saturated hysteresis. In addition, the excitation frequency changes the hysteresis behavior of SMA-driven systems and makes them challenging to track reference inputs at different frequencies. In this study, a rate-dependent Prandtl–Ishlinskii model coupled with a deadband function is proposed to characterize the asymmetric and saturated hysteresis behavior as well as its rate-dependency. Unknown parameters of the model are identified using genetic optimization algorithm in MATLAB Toolbox based on measured data. The identified model is validated to consider the excitation frequency effect with a different measured data set. The inverse model is also proposed as a compensator to mitigate hysteresis nonlinearity effects especially the frequency effect in tracking control. Although the proposed compensator cannot fully compensate for hysteresis effects, it can reduce the input–output hysteresis. The proposed rate-dependent compensator as a feedforward controller combined with a proportional–integral–derivative (PID) controller as a feedback mitigates hysteresis effects. The PID controller is used to improve the accuracy of compensated system and remove the steady-state error. Experimental results illustrate that the proposed controller has a great accuracy in tracking control to consider the excitation frequency effect as well as the asymmetric saturated hysteresis.

Graphic abstract

中文翻译：

---

使用磁滞逆模型对具有速率相关行为的SMA驱动执行器进行跟踪控制

摘要

磁滞是一种非线性现象，可能会导致控制应用中的误差和延迟。形状记忆合金（SMA）具有不对称的饱和磁滞。此外，激励频率改变了SMA驱动系统的磁滞行为，并使其难以跟踪不同频率下的参考输入。在这项研究中，提出了速率依赖的Prandtl–Ishlinskii模型和死区函数，以描述非对称和饱和磁滞行为及其速率依赖。使用MATLAB优化工具箱中的遗传优化算法，基于测得的数据识别模型的未知参数。验证所识别的模型以考虑具有不同测量数据集的激励频率效应。还提出了逆模型作为补偿器，以减轻磁滞非线性效应，尤其是跟踪控制中的频率效应。尽管建议的补偿器不能完全补偿磁滞效应，但可以减少输入输出磁滞。提议的速率相关补偿器作为前馈控制器，与比例积分微分（PID）控制器作为反馈相结合，可以减轻磁滞效应。PID控制器用于提高补偿系统的精度并消除稳态误差。实验结果表明，该控制器在考虑励磁频率效应以及非对称饱和磁滞的跟踪控制中具有很高的精度。尽管建议的补偿器不能完全补偿磁滞效应，但可以减少输入输出磁滞。提议的速率相关补偿器作为前馈控制器，与比例积分微分（PID）控制器作为反馈相结合，可以减轻磁滞效应。PID控制器用于提高补偿系统的精度并消除稳态误差。实验结果表明，该控制器在考虑励磁频率效应以及非对称饱和磁滞的跟踪控制中具有很高的精度。尽管建议的补偿器不能完全补偿磁滞效应，但可以减小输入输出磁滞。提议的速率相关补偿器作为前馈控制器，与比例积分微分（PID）控制器作为反馈相结合，可以减轻磁滞效应。PID控制器用于提高补偿系统的精度并消除稳态误差。实验结果表明，该控制器在考虑励磁频率效应以及非对称饱和磁滞的跟踪控制中具有很高的精度。提议的速率相关补偿器作为前馈控制器，与比例积分微分（PID）控制器作为反馈相结合，可以减轻磁滞效应。PID控制器用于提高补偿系统的精度并消除稳态误差。实验结果表明，该控制器在考虑励磁频率效应以及非对称饱和磁滞的跟踪控制中具有很高的精度。提议的速率相关补偿器作为前馈控制器，与比例积分微分（PID）控制器作为反馈相结合，可以减轻磁滞效应。PID控制器用于提高补偿系统的精度并消除稳态误差。实验结果表明，该控制器在考虑励磁频率效应以及非对称饱和磁滞的跟踪控制中具有很高的精度。

图形摘要