Elliptical modelling of hysteresis operating characteristics in a dielectric elastomer tubular actuator

A dielectric elastomer (DE) tubular actuator, based on compliant metal electrode technology, exhibits hysteresis-like characteristics when driven with a low power rated high voltage power supply (HVPS). This behavior occurs mainly because the DE actuator acts as a capacitive load compromising the 'slew rate' of the HVPS during the actuator's operation. The motivation of this contribution is to investigate the use of elliptical modelling approaches for capturing the hysteresis characteristics exhibited by the DE tubular actuator when it is driven by a low cost low power rated HVPS. The DE tubular actuator considered in this work demonstrates asymmetric hysteresis behaviour due to the nonlinear voltage-strain behaviour of the actuator. A linearization filter placed in series with the actuator (during its operation) ensures a symmetric hysteresis characteristic that can then be modelled using an ellipse-based approach. Elliptical models come in many forms with the two most popular being the constrained general conic form and the general parametric form. Elliptical-based hysteresis model fits are carried out on experimental data obtained from the application of periodic input voltages, at a number of different low-frequencies, to the tubular actuator. The range of frequencies used is related to the possible use of the tubular actuator for attenuating low frequency vibration during DE actuator-based load positioning applications. Constrained conic and general parametric forms of elliptical model are used for modelling the hysteresis characteristics of the DE actuator and rate dependent models developed based on both approaches. The sensitivity of both of these rate dependent models to small inaccuracies in model parameters was then investigated. The general parametric form was found to be more robust in this respect.