Development of a butterfly hysteresis structure for dielectric elastomer-actuated systems

Butterfly hysteresis behaviors show more complicated characteristics than single-loop hysteresis behaviors, which include two crossed single loops in opposite orientation. Most available hysteresis models used for describing the single-loop hysteresis behavior fail to predict the butterfly hysteresis. Therefore, it is a great challenge to build a hysteresis model to describe the butterfly hysteresis behavior. To this end, butterfly hysteresis operators including the butterfly play operator, the butterfly Krasnosel'skii-Pokrovskii kernel, and the butterfly asymmetric shift operator, are proposed to describe butterfly hysteresis effects. To further improve the modeling accuracy, a butterfly hysteresis structure containing the butterfly hysteresis operator and the neural networks for weight prediction and unmodeled dynamics is developed. The validation of the proposed structure is carried out on a dielectric elastomer-actuated system.