Modeling of Rate-Dependent Butterfly Hysteresis in Dielectric Elastomer Actuators

The rate-dependent butterfly hysteretic nonlinearity deteriorates the positioning performance of smart material-based actuators, such as dielectric elastomer actuators (DEAs). In comparison with modeling of the single loop hysteresis effect, the rate-dependent butterfly hysteresis is more complicated to represent. In this paper, a rate-dependent butterfly hysteresis structure is proposed for describing the rate-dependent butterfly hysteresis behavior in DEAs. The structure is composed of a rate-dependent butterfly operators and neural networks for weight prediction and rate-dependent hysteresis. In particular, the rate-dependent hysteresis operator is constructed by considering the rate change of the input to the model. Two neural networks are used for predicting the weights of operators and improving the prediction performance of the rate-dependent butterfly hysteresis model. Experiment results indicate that the developed model can effectively predict the rate-dependent hysteresis effect in DEAs.