Characterizing Hysteresis Nonlinearity Behavior of SMA Actuators by Krasnosel’skii-Pokrovskii Model

Abstract

Krasnosel’skii-Pokrovskii (KP) model is one of the great operator-based phenomenological models which is used in modeling hysteretic nonlinear behavior in smart actuators. The time continuity and the parametric continuity of this operator are important and valuable factors for physical considerations as well as designing well-posed identification methodologies. In most of the researches conducted about the modeling of smart actuators by KP model, especially SMA actuators, only the ability of the KP model in characterizing the hysteretic behavior of the actuators is demonstrated with respect to some specified experimental data and the accuracy of the developed model with respect to other data is not validated. Therefore, it is not clear whether the developed model is capable of predicting hysteresis minor loops of those actuators or not and how accurate it is in this prediction task. In this paper the accuracy of the KP model in predicting SMA hysteresis minor loops as well as first order ascending curves attached to the major hysteresis loop are experimentally validated, while the parameters of the KP model has been identified only with some first order descending reversal curves attached to the major loop. The results show that, in the worst case, the maximum of prediction error is less than 18.2% of the maximum output and this demonstrates the powerful capability of the KP model in characterizing the hysteresis nonlinearity of SMA actuators.In order to have continuous operator rather than jump discontinuities like the Preisach operator, Krasnosel’skii- Pokrovskii[12] allows the Preisach operators to be any reasonable functions. The elementary operator of the KP model which is referred to as the KP kernel, a special case of a so called generalized play operator, is a continuous function on the Preisach plane and has minor loops within its major loop. Let <i>P</i> be the Preisach plane over which hysteresis occurs: