Hysteresis Nonlinearity Modeling for Magnetics Shape Mem-ory Alloy Actuator Based on a Novel Black-box Model with Least Squares Support Vector Machines

With the rapid development of micro-nano manufacturing technology, there are more and more fields need nano-driven control technology, such as the high-precision positioning systems [1]. Magnetically controlled shape memory (MSM)-alloy actuators serve as the core part of high-precision positioning system on account of their high precision, large energy density, and small volume. The hysteresis nonlinearity of the MSM-alloy actuator, however, severely damages the positional accuracy of the positioning system. In order to research the hysteresis nonlinearity in the MSM-alloy actuator, hysteresis nonlinearity modeling has become a significant hot spot of research [2] [3]. The purpose of this study is to structure an excellent hysteresis nonlinearity model to capture the hysteresis nonlinearity in MSM-alloy actuators. The criterion for evaluating modeling performance is that the established hysteresis model can embody the actual characteristic of the actuator. In this study, a novel black-box model composed of the hysteresis-like structure and a nonlinear function is proposed to capture the hysteresis nonlinearity of the MSM-alloy actuator. The proposed black-box hysteresis nonlinearity modeling approach has the advantages of requiring no prior knowledge and internal physical mechanism. The hysteresis-like structure solves the multi-value mapping problem and accurately depicts the major and minor hysteresis loops of the MSM-alloy actuator. The nonlinear function represents the nonlinearity part of the MSM-alloy actuator, which is identified using least squares support vector machines (LS-SVM) on account of its strong approximation capability, high generalization ability, less parameters, and great computing power. The schematic diagram of black-box model is shown in Fig. 1. u(k) is the input current at k time, y(k) is the output displacement at k time, F[⋅] is the nonlinear function, H
u
[⋅] is the hysteresis-like part of the black-box model. In the procedure of modeling, u(k) and y(k) are the input values of hysteresis-like part; u(k), y(k), and H
u
[⋅] are the input values of nonlinear function, which is obtained by the LS-SVM. To certify the effectiveness of the black-box model, the simulations are implemented using the obtained experimental data. The simulations show that the modeling error rate of the novel black-box model based on the LS-SVM is 1.37%, which is improved 73.97% in compared with the results in [4]. It is obvious that the modeling precision of the proposed hysteresis model is within the allowable range. The simulation results are shown in Fig.2. The blue solid line is the obtained experimental data, and the red dotted line is the output of the proposed black-box model. As shown in Fig.2(a), the proposed black-box model based on the LS-SVM can accurately describe the major and minor hysteresis loops of the MSM-alloy actuator. The modeling error curve is shown in Fig.2(b). In the future, the proposed black-box model can lay a foundation for designing an adaptive controller to eliminate the hysteresis nonlinearity in the MSM-alloy actuator.