A systematic identification approach for biaxial piezoelectric stage with coupled Duhem-type hysteresis

Abstract

Purpose The problem of parameter identification for biaxial piezoelectric stages is still a challenging task because of the existing hysteresis, dynamics and cross-axis coupling. This study aims to find an accurate and systematic approach to tackle this problem. Design/methodology/approach First, a dual-input and dual-output (DIDO) model with Duhem-type hysteresis is proposed to depict the dynamic behavior of the biaxial piezoelectric stage. Then, a systematic identification approach based on a modified differential evolution (DE) algorithm is proposed to identify the unknown parameters of the Duhem-type DIDO model for a biaxial piezostage. The randomness and parallelism of the modified DE algorithm guarantee its high efficiency. Findings The experimental results show that the characteristics of the biaxial piezoelectric stage can be identified with adequate accuracy based on the input–output data, and the peak-valley errors account for 2.8% of the full range in the X direction and 1.5% in the Y direction. The attained results validated the correctness and effectiveness of the presented identification method. Originality/value The classical DE algorithm has many adjustment parameters, which increases the inconvenience and difficulty of using in practice. The parameter identification of Duhem-type DIDO piezoelectric model is rarely studied in detail and its successful application based on DE algorithm on a biaxial piezostage is hitherto unexplored. To close this gap, this work proposed a modified DE-based systematic identification approach. It not only can identify this complicated model with more parameters, but also has little tuning parameters and thus is easy to use.

A fractional-order Duhem model of rate-dependent hysteresis for piezoelectric actuators

“…The vector V G i is compared with the vector X G i , and the one with the higher fitness is selected as the evolved new individual, and the selection operation is as in (13).…”

“…At the end of the 19th century, physicists P. Duhem and Stefanini proposed the Duhem hysteresis model, which assumes that each state is in equilibrium under a constant input and its output characteristics change when and only when the input signal changes direction, the greatest advantage of this model is that it has a clear mathematical expression, and appropriate adjustment of the model parameters can accurately reflect the different Hysteresis nonlinearity, 11 Duhem model is a hysteresis model described by differential equations with explicit functional expressions, which provides convenience for establishing its inverse function. 12,13 Under high-frequency input excitation, Duhem has a large error, especially at the special point u · ( t ) = 0 . To compensate for this Gan et al 14 introduced a trigonometric function based on the Duhem model to compensate for the error at this point by using the special point where the trigonometric function has a derivative of zero.…”

Modeling and Control of a Linear Piezoelectric Actuator

“…Physical models include the Duhem and Bouc-Wen models, which are modeled based on material characteristics. For example, Chen et al proposed a dual-input dualoutput (DIDO) model based on the Duhem hysteresis model to describe the dynamic behavior of biaxial piezoelectricity [11]. Kim et al combined the Bouc-Wen model with a piecewise linear function to fit the hysteresis phenomenon with asymmetric strength degradation [12].…”