Abstract
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.
Highlights
Hysteresis is the phenomenon that can be found in a wide variety of smart materials [1,2,3], such as piezoceramics [4,5,6], magnetostrictive materials [7], and shape memory alloys [8]
It brings considerable problems to the application of smart materials because the output of the system actuated by these materials cannot be predicted without the knowledge of the hysteresis behavior of the system
To simulate the observed hysteresis behavior, many phenomenological models have been developed in the literature, e.g., Bouc-Wen [9,10,11,12], Duhem, Preisach model [1], Maxwell [4], and Prandtl-Ishlinskii (PI) models [13]
Summary
Hysteresis is the phenomenon that can be found in a wide variety of smart materials [1,2,3], such as piezoceramics [4,5,6], magnetostrictive materials [7], and shape memory alloys [8]. German physicist Madelung presented three rules based on his observation of the hysteresis phenomenon in the early 20th century These rules are always used to validate hysteresis models [25], such as the Preisach model and the PI model [13]. Instead of considering Madelung’s rules as criteria, we propose a modeling method for the rate-independent and symmetric hysteresis based on these rules. We propose a modeling method to describe the symmetric hysteresis by directly constructing its trajectory based on Madelung’s rules rather than considering these rules as criteria. This method is translated into an algorithm that can be run by digital processors.
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