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.

中文翻译：

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一种耦合 Duhem 型迟滞双轴压电平台的系统辨识方法

目的

由于存在滞后、动力学和交叉轴耦合，双轴压电平台的参数识别问题仍然是一项具有挑战性的任务。本研究旨在找到一种准确和系统的方法来解决这个问题。

设计/方法/方法

首先，提出了具有 Duhem 型迟滞的双输入双输出 (DIDO) 模型来描述双轴压电级的动态行为。然后，提出了一种基于改进差分进化 (DE) 算法的系统识别方法，用于识别双轴压电级 Duhem 型 DIDO 模型的未知参数。改进的DE算法的随机性和并行性保证了其高效率。

发现

实验结果表明，基于输入-输出数据可以准确识别双轴压电平台的特性，峰谷误差在 X 方向占全范围的 2.8%，在 Y 方向占 1.5%方向。得到的结果验证了所提出的识别方法的正确性和有效性。

原创性/价值

经典的DE算法调整参数较多，增加了实际使用的不便和难度。Duhem 型 DIDO 压电模型的参数识别很少被详细研究，其基于 DE 算法在双轴压电平台上的成功应用迄今尚未探索。为了弥补这一差距，这项工作提出了一种改进的基于 DE 的系统识别方法。它不仅可以识别这种参数较多的复杂模型，而且调整参数很少，因此易于使用。