The typical characteristic of a magnetic shape memory alloy (MSMA)-based actuator is rate-dependent and stress-dependent hysteresis. In addition, the hysteresis in an MSMA-based actuator includes memory, multivalued mapping, and asymmetry properties, which seriously degrade the positioning accuracy. In this article, a feedforward neural network (FNN)-based nonlinear autoregressive moving average with exogenous inputs (NARMAX) model is employed to describe the hysteresis in an MSMA-based actuator. Through a Taylor expansion, it is revealed how the FNN constructs the nonlinear function of the NARMAX model. For the controller implementation, an FNN-based iterative learning control (ILC) strategy is proposed to achieve the desired tracking performance. The contributions of this study include exploring the update rule of the FNN-based ILC and analyzing the convergence properties of the proposed controller when the initial state of the system varies. To verify the effectiveness of the proposed method, experiments on an MSMA-based actuator were conducted. The results illustrate that the proposed modeling and control methods achieve an excellent performance and that the theoretical results are correct.

Magnetic shape memory alloy (MSMA) based actuators are extensively applied in the fields of precision manufacturing and micro/nano technology. Nevertheless, the inherent hysteresis in the MSMA-based actuator severely hinders its further application. In this study, the characteristics of hysteresis behavior under different input signals are investigated. Then, a nonlinear auto-regressive moving average with exogenous inputs (NARMAX) model based on a diagonal recurrent neural network (DRNN) is used to construct the rate-dependent hysteresis model. To improve the capability of characterizing the multi-valued mapping of the hysteresis loop, the play operator is adopted as the exogenous variable function of the NARMAX model. To verify the effectiveness of the proposed model, a series of comparisons are implemented. The experimental results show that the proposed NARMAX model based on the DRNN exhibits excellent modeling performance.

A Bouc–Wen model is presented and identified based on the bat‐inspired algorithm to describe the hysteresis of the piezo‐actuated stage. Based on the established Bouc–Wen model, a sliding mode controller is proposed to suppress the hysteresis non‐linearity of the piezo‐actuated stages. In order to solve the buffeting problem in the process of control, the sign function is replaced by the sigmoid function. Experiment is performed to validate the effectiveness of the proposed sliding mode controller, and the results show that the maximum error of the motion tracking control of the piezo‐actuated stage is 0.3264 μm.

Piezo-actuated stages are widely applied in the field of high-precision positioning. However, piezo-actuated stages produce hysteresis between the input voltage and the output displacement that negatively influences the positioning accuracy. In this study, the Bouc-Wen model is established and identified using the bat-inspired optimization algorithm. Subsequently, based on the established hysteresis model, we propose a sliding mode control method with a new reaching law to suppress the hysteresis nonlinearity and achieve high-precision tracking control for the piezo-actuated stages. In additon, the proposed control method contains the perturbation estimation part, which can estimate online the modeling uncertainty and the unknown external disturbances. The stability of the proposed control method is demonstrated through the Lyapunov theory. Finally, to validate the effectiveness of the proposed control method, experiments are conducted on the piezo-actuated stages. Experimental results demonstrate that the proposed control method is superior to the feed-forward control and the conventional sliding mode control method.