LSTM-Based Model Predictive Control of Piezoelectric Motion Stages for High-Speed Autofocus

In this article, we proposed a neural network-based model predictive control (MPC) of piezoelectric motion stages (PEMAs) for autofocus (AF). Rather than using an internal controller to account for the problematic hysteresis effects of the PEMA, we use the long short-term memory (LSTM) unit to integrate the hysteresis effects and the focus measurement into a single learning-based model. Subsequently, a MPC method is developed based on this LSTM model that successfully finds the optimal focus position using a series of focus measurements derived from a sequence of images. To further improve the speed of the long short-term based MPC, an optimized backpropagation algorithm is proposed that optimizes the MPC cost function. Experiments verified our proposed method reduces at minimum 30% regarding AF time when compared to well-known ruled-based AF methods and other learning-based methods.