Adaptive simulation of hysteresis using neuro-Madelung model

Abstract

Hysteretic phenomena have been observed in different branches of engineering sciences. Although each of them has its own characteristics, Madelung’s rules are common among most of them. Based on Madelung’s rules, we propose a general approach to the simulation of both the rate-independent and rate-dependent hystereses with either congruent or non-congruent loops. In this approach, a static function accommodates different properties of the hystereses. Using the learning capability of the neural networks, an adaptive general model for hysteresis is introduced according to the proposed approach and it is called the neuro-Madelung model. Using various hystereses from different areas of engineering with different properties, the proposed model has been evaluated and the results show that the model is successful in the simulation of the considered hystereses. Comparison of the performance of the proposed model with different hysteresis models on experimental data indicates that the neuro-Madelung model has much better performance than them and its results are in excellent agreement with experimental data. In addition, an implicit inverse of the neuro-Madelung model is introduced. Its application in an open-loop control of a rate-dependent hysteresis is assessed and the results show its success.