An Approach for Hysteresis Modeling Based on Shape Function and Memory Mechanism

Abstract

This paper presents a shape function and memory mechanism based approach to design the hysteresis models which are related to the behaviors of smart materials, such as magnetorheological (MR) fluids, electrorheological fluids, piezoelectric materials, and friction forces. The proposed approach is inspired from two general properties of the existing hysteresis models, like Bouc–Wen, Dahl, and LuGre models. The memory mechanism originating from the charging and discharging processes of the resistor-capacitor circuit is constructed by adopting a virtual displacement variable and updating laws for the reference points. The shape function is achieved and generalized from analytical solutions of a simple semilinear Duhem model. Using the proposed approach, the memory mechanism reveals the essence of specific Duhem hysteresis and the general shape function provides a direct and clear means to fit the hysteresis loops. In addition, the proposed approach has a potential capability to formulate the inverse hysteresis model by estimating the virtual displacement. Eventually, as an example within a predefined format of the shape function, the feasibility of the proposed approach is verified through modeling the hysteresis behaviors of a commercial MR damper. A comparative work with Bouc–Wen model is further undertaken to demonstrate superior performances of high computational efficiency and comparable accuracy of the developed model based on the proposed approach.