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Modeling of hysteresis in piezoelectric actuators using neural networks

机译：使用神经网络对压电执行器中的磁滞进行建模

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摘要

For the application of neural networks to the approximation of hysteresis which is characterized of multi-valued mapping and non-smooth nonlinearities, a novel modeling technique based on a transformation of one-to-one mapping is proposed in this paper. In this method, a special hysteretic operator is introduced to describe the change tendency of the hysteresis with regard to its input. Then an expanded input space is constructed for hysteresis with the introduction of such hysteretic operator, on which the multi-valued hysteresis is decomposed into a one-to-one mapping. Thus, neural networks model for hysteresis is derived, avoiding the calculation of the gradient of hysteresis. Subsequently, for approximation of rate-dependent hysteresis in piezoelectric actuators which is caused by the dynamic voltage excitations, a hybrid model, i.e. the dynamic extension of the proposed neural hysteresis submodel is developed. In the model, a linear dynamic block is introduced in series with the proposed neural model to allow for rate-dependent dynamics of the piezoelectric actuator simultaneously. Also the corresponding optimization algorithm by use of the modified Levenberg-Marquarqt (MLM) method is given. Finally, the experimental validation results of applying both the proposed neural hysteresis model and hybrid model to a piezoelectric actuator are presented.
机译：为了将神经网络应用于具有多值映射和非光滑非线性特征的滞后逼近，提出了一种基于一对一映射变换的新型建模技术。在这种方法中，引入了一种特殊的磁滞算子来描述磁滞相对于其输入的变化趋势。然后，通过引入这种滞后算子，构造用于滞后的扩展输入空间，在该滞后算子上，多值滞后被分解为一对一映射。因此，导出了用于滞后的神经网络模型，从而避免了计算滞后的梯度。随后，为了近似由动态电压激励引起的压电致动器中的速率相关磁滞，建立了一个混合模型，即所提出的神经磁滞子模型的动态扩展。在模型中，线性动力学模块与所提出的神经模型串联引入，以允许压电致动器同时具有速率相关的动力学特性。还给出了使用改进的Levenberg-Marquarqt（MLM）方法的相应优化算法。最后，给出了将所提出的神经滞后模型和混合模型应用于压电致动器的实验验证结果。

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