To compensate for hysteresis, low damping vibration, and their coupling effects, this paper proposes a gated recurrent unit and convolutional neural network (GRU-CNN) model as a feedforward control model that maps desired displacement trajectories to driving voltages. The GRU-CNN integrates a gated recurrent unit (GRU) layer to capture long-term temporal dependencies, a multi-layer convolutional neural network (CNN) to extract local data features, and residual connections to mitigate information distortion. The GRU-CNN is then combined with transfer learning (TL) for feedforward control of cross-batch and cross-type piezoelectric actuators (PEAs), so as to reduce reliance on training datasets. The analysis focuses on the impacts of target PEA data volume and source-target similarity on transfer learning strategies. The GRU-CNN trained on PEA #1 achieves high control accuracy, with a mean absolute error (MAE) of 0.077, a root mean square error (RMSE) of 0.129, and a coefficient of determination (R2) of 0.997. When transferred to cross-batch PEA #2 and cross-type PEA #3, the GRU-CNN feedforward controller still delivers favorable performance; R2 values all exceed 0.98, representing at least a 27% improvement compared to training from scratch. These results indicate that the proposed transfer learning-based feedforward control method can effectively reduce retraining effort, suggesting its potential applicability to batch production scenarios.
Hu et al. (Tue,) studied this question.