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.

Type-2 fuzzy logic controller for position control of shape memory alloy wire actuator

“…However, type-2 controller works faster for decreasing values. In the case of SMA wires (used also in the actuator’s construction), the problem with controlling the displacement is due to the hysteresis of heating and cooling processes which are necessary for a martensite transformation responsible for a wire contraction (Zakerzadeh et al, 2011). The problem is especially important when the intermediate displacement values are required, for example, during a step sequence task (Figure 16).…”

Iterative Learning and Fractional Order PID Hybrid Control for a Piezoelectric Micro-Positioning Platform

“…The element operator of KP model overcome the drawback of the jump discontinuities of Preisach operators. Moreover, it includes minor loops within its major loop which makes it more closed to the actual behaviors of the hysteresis nonlinearity [21].…”

Modeling and Compensation for Asymmetrical and Dynamic Hysteresis of Piezoelectric Actuators Using a Dynamic Delay Prandtl–Ishlinskii Model

“…Many rate-independent hysteresis models have been proposed to describe the static hysteresis of piezoelectric actuators. These hysteresis models include Jiles–Atherton model [ 24 ], Preisach model [ 25 , 26 , 27 ], Prandtl–Ishlinskii (PI) model [ 28 , 29 , 30 ], Krasnosel’skii–Pokrovskii (KP) model [ 31 ], etc. The Jiles–Atherton model is a mechanistic model, which is formed by an ordinary differential equation formulation.…”