Modeling piezoelectric actuators with Hysteretic Recurrent Neural Networks

This paper describes the application of Hysteretic Recurrent Neural Networks (HRNNs) to the modeling of polycrystalline piezoelectric actuators. Because piezoelectric materials exhibit voltage/strain relationships that are hysteretic and rate-dependent, the HRNN is composed of neurons with activation functions that incorporate these characteristics. Individual neurons are shown to agree with existing models of ideal single-crystal piezoelectric behavior. The combination of many such neurons into a network allows prediction of the heterogeneous behavior of polycrystalline materials. This model is shown to approximate the strain and polarization of an unloaded commercial stack actuator at multiple loading rates. A comparison is made to a recurrent Radial Basis Function Network model, and the HRNN is demonstrated to more accurately generalize across data sets. The model is further shown to execute on a PC platform at rates over 100 Hz, fast enough to support its application to real-time control.