Hysteresis Simulation Using Least-Squares Support Vector Machine

Abstract

Hysteresis is a highly nonlinear phenomenon, which is observed in different branches of sciences. The behavior of the hysteretic systems is usually controlled by some nonmeasurable internal states. It makes hysteresis be a nonunique nonlinearity, and therefore hysteresis identification is a cumbersome task. In this paper, which uses the capability of the least-squares support vector machine (LS-SVM) in static function approximation, a new rate-dependent hysteresis model is proposed. First, the model converts the hysteresis’ nonunique nonlinearity into a one-to-one mapping by means of classical hysteresis operators. Second, the mapping is learned by an LS-SVM. The training algorithm of the model is introduced and how the model can be applied in different situations is discussed. The proposed model is assessed with different hystereses with different properties. The generalization capability of the proposed model is compared with a neural-based hysteresis model. Finally, the application of the proposal is investigated in the feed-forward control of the hysteretic systems with an example. The results show the high accuracy of the proposed model in hysteresis simulation and control even for the experimental data.