Modeling and Implicit Inversion of Butterfly Hysteresis in Dielectric Elastomer Actuated System

Butterfly hysteresis nonlinearity is a unique type of hysteresis characteristic that is distinct from the traditional single-loop hysteresis characteristic, demonstrating non-monotonic and multi-peak features between input and output. In this paper, we analyze the causes of butterfly hysteresis non-linearity in dielectric elastomer actuated systems and propose a butterfly hysteresis model based on the classical relay operator. To compensate for the butterfly non-monotonic hysteresis nonlinearity in the dielectric elastomer actuated systems, an novel implicit inverse compensation algorithm is proposed. Experimental results demonstrate the effectiveness of the established model and the inverse compensation algorithm.