Development of a Butterfly Fractional-Order Backlash-Like Hysteresis Model for Dielectric Elastomer Actuators

Differential equation-based hysteresis model is an efficient approach to predict the hysteresis effect with less modeling parameters. Available differential equation-based hysteresis models mainly focus on describing the single-loop hysteresis effect and fail to describe the butterfly hysteresis effect. In this article, a butterfly fractional-order backlash-like hysteresis model is proposed to describe the butterfly hysteretic behavior. To this end, a twist mechanism is developed to transform the single-loop backlash-like hysteresis model into the one that is capable of representing the butterfly hysteresis. To further improve the modeling accuracy, a fractional-order expression is integrated into the butterfly backlash-like hysteresis model. In addition, considering the buckling threshold characteristic of the elastomer membrane in dielectric elastomer actuators, a buckling threshold selector is designed and incorporated into the model as well. Experiments are conducted to validate the effectiveness of the proposed model.