School of Astronautics, Harbin Institute of Technology, Harbin 150001, China.
Sensors (Basel). 2019 Jan 16;19(2):352. doi: 10.3390/s19020352.
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.
滞后是一种具有记忆的非线性，在实际中通常是不希望出现的。已经提出了许多现象学模型来描述观察到的滞后。例如，由几个滞后运算符组成的 Prandtl-Ishlinskii (PI) 模型是最广泛使用的模型。另一方面，著名的 Madelung 规则通常用于验证滞后模型。值得指出的是，PI 模型遵守 Madelung 规则。在本文中，我们不是将这些规则视为标准，而是通过直接基于 Madelung 规则构建轨迹来提出一种对称滞后的建模方法。在所提出的方法中，根据输入值记录和消除转折点。在实施记录和消除机制后，可以确定当前轨迹所沿曲线，然后可以描述轨迹。此外，还研究了所提出的方法与 PI 模型之间的关系。通过仿真和实验结果验证了所提出方法的有效性。
