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.