The magnetic shape memory alloy based actuator (MSMA-BA) is an indispensable component mechanism for high-precision positioning systems as it possesses the advantages of high precision, low energy consumption, and large stroke. However, hysteresis is an intrinsic property of MSMA material, which seriously affects the positioning accuracy of MSMA-BA. In this study, we propose a multi meta-model approach incorporating the nonlinear auto-regressive moving average with exogenous inputs (NARMAX) and Bouc–Wen (BW) models to describe the complex dynamic hysteresis of MSMA-BA. In particular, the BW model is introduced into the NARMAX model as an exogenous variable function, and a wavelet neural network (WNN) is adopted to construct the nonlinear function of the multi meta-model. In addition, iterative learning control is combined with a WNN to improve its convergence speed. A two-valued function is employed in the controller design process, so as to make use of history iteration information in updating control input. The main contribution of this study is the convergence analysis of the proposed iteration learning controller with iteration-dependent uncertainties (non-strict repetition of the initial state and varying iteration length). The experiments conducted on the MSMA-BA illustrate the validity of the proposed control scheme.

磁性形状记忆合金驱动器（MSMA-BA）具有高精度、低能耗、大行程等优点，是高精度定位系统不可或缺的组成机构。然而，滞后现象是MSMA材料的固有特性，严重影响MSMA-BA的定位精度。在这项研究中，我们提出了一种多元模型方法，将非线性自回归移动平均线与外生输入 (NARMAX) 和 Bouc–Wen (BW) 模型相结合，以描述 MSMA-BA 的复杂动态滞后现象。特别地，将BW模型作为外生变量函数引入到NARMAX模型中，并采用小波神经网络（WNN）构建多元模型的非线性函数。此外，迭代学习控制与 WNN 相结合以提高其收敛速度。控制器设计过程中采用二值函数，利用历史迭代信息更新控制输入。本研究的主要贡献是对所提出的具有迭代相关不确定性（初始状态的非严格重复和不同的迭代长度）的迭代学习控制器的收敛性分析。在 MSMA-BA 上进行的实验说明了所提出的控制方案的有效性。本研究的主要贡献是对所提出的具有迭代相关不确定性（初始状态的非严格重复和不同的迭代长度）的迭代学习控制器的收敛性分析。在 MSMA-BA 上进行的实验说明了所提出的控制方案的有效性。本研究的主要贡献是对所提出的具有迭代相关不确定性（初始状态的非严格重复和不同的迭代长度）的迭代学习控制器的收敛性分析。在 MSMA-BA 上进行的实验说明了所提出的控制方案的有效性。