Modeling of butterfly-shaped hysteresis in dielectric elastomer actuators

Abstract

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.

Energy-based modeling of rate-independent hysteresis and viscoelastic effects in dielectric elastomer actuators

“…The result (34) implies that η pj k −1 pj can be interpreted as a characteristic length of the Lion arm. For stretch variations from the large reversal point, which are much smaller than η pj k −1 pj the behavior of σ pj is approximately linear, whereas a saturation to ±η pj occurs whenever the stretch variation from the last reversal point is much larger than η pj k −1 pj .…”

“…Together, assumptions 2 and 3 imply that ∆ pj > 0 always holds true, so that the set of admissible values for σ pj (0) never degenerates into a single point. By recalling the general solution for the trajectory of σ pj given by ( 33) and (34), it can be deduced that the largest value of σ pj is achieved when starting from the largest admissible initial condition σ pj (0) = ∆ pj η pj and traveling from λ 1 (0) = 1 to λ 1 = λ1 with λ1 > 0. Similarly, it can be deduced that the smallest value of σ pj is achieved when starting from the smallest admissible initial condition σ pj (0) = −∆ pj η pj and traveling from λ 1 (0) = λ1 to λ 1 = 1 with λ1 < 0.…”

“…Despite their physical interpretability, such models are generally too complex to be used in real-time control applications. Other authors have investigated phenomenological DE models based on mathematical hysteresis operators [33][34][35][36]. Despite being generally accurate, these models lacked physical interpretation and, thus, are only able to reproduce the overall input-output behavior of DE actuator (DEA) systems in a black-box fashion.…”

An energy-based model for both rate-dependent and rate-independent hysteretic effects in uniaxially-loaded dielectric elastomer actuators

“…[5][6][7] A far less studied topic in the DEA modeling literature concerns the rate-independent hysteretic effects, which are experimentally observed when deforming some materials (e.g., silicone) in the sub-Hz regime, 8 and cannot be described by means of commonly adopted viscoelastic models. In this context, some authors investigated phenomenological models for rate-independent hysteretic effects observed in the voltage-displacement characteristics of DEA devices, [9][10][11][12] while few others focused on the physics-based description of stress-stretch hysteresis of elastomers, 13 or dielectric elastomers 14,15 specifically. On the one hand, phenomenological modeling approaches provide a description of the DEA system based on an input-output black box perspective.…”