Modelling of hysteresis in smart actuators using the generalised Prandtl-Ishlinskii operator

Hysteresis poses a significant challenge for the modelling and control of smart material-based actuators. The Prandtl-Ishlinskii (PI) operator-based model has been a popular choice for characterising the symmetric hysteresis properties of piezoceramic actuators. Various modified PI operators have also been suggested to extend the modelling technique to (a) asymmetric hysteresis and (b) input rate dependent hysteresis characteristics. A major advantage of using PI or modified PI operators is that they have an analytical inverse which allows the straightforward implementation of the inverse model to provide hysteresis compensation as part of a control scheme. The generalised PI operator, a type of modified PI operator, has the potential to model both asymmetric and constrained hysteresis characteristics. In this contribution the ability of the generalized PI operator-based model to approximate the hysteresis characteristics of two smart actuators; a tubular Dielectric Elastomer (DE) actuator with both saturated and unsaturated asymmetric hysteresis behaviour, and a Magnetorheological (MR) Damper with saturated and approximately symmetric hysteresis behaviour is investigated.