The inherent hysteresis nonlinearity of piezoelectric actuator degrades the positioning accuracy of the micro-positioning stage. Prandtl–Ishlinskii model is widely used for piezoelectric hysteresis modeling, yet it is a rate-independent model with weak generalization ability. To overcome this problem, we proposed a convolutional neural network model based on the Prandtl–Ishlinskii model, which consists of a rate-dependent Prandtl–Ishlinskii model layer and convolutional network layer. The rate-dependent Prandtl–Ishlinskii model layer extends the traditional Prandtl–Ishlinskii model to describe the rate-dependent hysteresis behavior. The convolutional network layer with deep learning ability extracts the deep features of the input signal to improve the generalization ability of the hysteresis model. The experiment results indicate that the standard error of the proposed hysteresis model to predict displacement at unmodeled frequencies has been reduced by 18.74%–36.75% in comparison with the Prandtl–Ishlinskii model, which verifies that the proposed hysteresis model has not only higher accuracy but also stronger generalization ability.

中文翻译：

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基于卷积神经网络的压电微定位平台迟滞建模

压电致动器固有的滞后非线性降低了微定位平台的定位精度。Prandtl-Ishlinskii 模型广泛用于压电迟滞建模，但它是一个与速率无关的模型，泛化能力弱。为了克服这个问题，我们提出了一种基于 Prandtl-Ishlinskii 模型的卷积神经网络模型，该模型由速率相关的 Prandtl-Ishlinskii 模型层和卷积网络层组成。速率相关的 Prandtl-Ishlinskii 模型层扩展了传统的 Prandtl-Ishlinskii 模型来描述速率相关的滞后行为。具有深度学习能力的卷积网络层提取输入信号的深层特征，提高滞后模型的泛化能力。