Classical Preisach Model Based on Polynomial Approximation and Applied to Micro-Piezoelectric Actuators

Abstract

In engineering applications, where we demand more and more precision, the modeling of systems with hysteretic nonlinearity has received considerable attention. The classical Preisach model (CPM) is currently the most popular for characterizing systems with hysteresis, and this model can represent the hysteresis with an infinite but countable first-order inversion curve (FORC). The table method is a method used to realize CPM in practice. The data in the table corresponds to a limited number of FORC samples. There are two problems with this approach: First, in order to reflect the timing effects of elements with hysteresis, it needs to consume a lot of memory space to obtain accurate data table. Second, it is difficult to come up with an efficient way to modify the data table to reflect the timing effects of elements with hysteresis. To overcome these shortcomings, this paper proposes to use a set of polynomials instead of the table method to implement the CPM. The proposed method only needs to store a small number of polynomial coefficients, and thus it reduces the required memory usage. In addition, to obtain polynomial coefficients, we can use least squares approximation or adaptive identification algorithms, which can track hysteresis model parameters. We developed an adaptive algorithm for the identification of polynomial coefficients of micro-piezoelectric actuators by applying the least mean method, which not only reduces the required memory size compared to the table method implementation, but also achieves a significantly improved model accuracy, and the proposed method was successfully verified for displacement prediction and tracking control of micro-piezoelectric actuators.