Modeling of Rate-Independent and Symmetric Hysteresis Based on Madelung's Rules

Hysteresis is a kind of nonlinearity with memory, which is usually unwanted in practice. Many phenomenological models have been proposed to describe the observed hysteresis. For instance, the Prandtl-Ishlinskii (PI) model, which consists of several backlash operators, is the most widely used. On the other hand, the well-known Madelung's rules are always used to validate hysteresis models. It is worth pointing out that the PI model obeys Madelung's rules. In this paper, instead of considering these rules as criteria, we propose a modeling method for symmetric hysteresis by directly constructing the trajectory based on Madelung's rules. In the proposed method, turning points are recorded and wiped out according to the input value. After the implementation of the recording and wiping-out mechanisms, the curve which the current trajectory moves along can be determined and then the trajectory can be described. Furthermore, the relationship between the proposed method and the PI model is also investigated. The effectiveness of the presented method is validated by simulation and experimental results.