Abstract: To describe the rate-dependent hysteresis behavior of the piezoelectric actuators, a cascade block-based model is proposed in this paper, i.e., a rate-independent hysteresis block cascading with a rate-dependent block. For the approximation of the hysteresis block, a hysteresis operator is introduced into the input space to represent the changing tendency of the gradient with the hysteresis. Then a neural hysteresis sub-model is constructed based on a one-to-one mapping. Meanwhile, to describe the rate-dependent characteristics of the dynamic hysteresis, a NARX (nonlinear autoregressive model with exogenous inputs) model is adopted. And a recursive stochastic Newton approximation algorithm is derived for the optimization of the model. The validation results have shown the effectiveness of the proposed model for characterizing the dynamic hysteresis.

Key words: Piezoelectric actuators, dynamic hysteresis, neural networks, NARX, stochastic Newton approximation algorithm

摘要： 为了准确描述压电陶瓷执行器中存在的速率依赖性迟滞，给出了一种由迟滞环节和动态环节构成的串联块模型。迟滞环节的数学模型通过引入描述梯度变化的迟滞算子，将多值映射转化为扩展输入空间上的一一映射，使用前向神经网络来逼近。基于迟滞模型，引入线性动态模型描述压电陶瓷迟滞输出的速率依赖性，构造神经网络NARX（nonlinear autoregressive model with exogenous inputs）模型。进一步，给出了模型参数优化的递推随机牛顿算法。实验结果验证了所提出的模型和估计算法的有效性。

关键词: 压电陶瓷执行器, 动态迟滞, 神经网络, NARX, 随机牛顿算法