Modeling of butterfly-shaped hysteresis in dielectric elastomer actuators

Dielectric elastomer actuators exhibit butterfly-shaped hysteresis effects under unbiased periodic input signals. In comparison with single hysteresis effects, butterfly-shaped hysteresis effects are more complicated, which include two single hysteresis loops, and the directions of both loops are different. Hence, it is a great challenge to build a hysteresis model to describe the butterfly-shaped behavior. To this end, a butterfly-shaped relay operator is newly proposed as an elementary operator to construct the butterfly-shaped Preisach model, and the weighting functions/weights of the developed model are positively defined, which facilitates the construction of the unique inverse model and the controller design. To further improve the modeling accuracy, a piecewise-defined butterfly-shaped Preisach model considering the variation of asymmetric nonlinear hysteresis effects with different input amplitudes is proposed. Experiments with the fabricated elastomer actuator-actuated system are conducted to validate the effectiveness of the developed modeling approach.