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

Abstract

In this paper, we proposed a neural network-based model predictive control of piezoelectric motion stages for autofocus. Rather than using an internal controller to account for the problematic hysteresis effects of the piezoelectric motion stage, we use the long short-term memory unit to integrate the hysteresis effects and the focus measurement into a single learning-based model. Subsequently, a model predictive control method is developed based on this long short-term memory 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 model predictive control, an optimized backpropagation algorithm is proposed that optimizes the model predictive control cost function. Experiments verified our proposed method reduces at minimum 30&#x0025; regarding autofocus time when compared to well-known ruled-based autofocus methods and other learning-based methods. Videos of the experiments are available at https:&#x002F;&#x002F; youtu.be&#x002F;AyvnMIq48Vc and <uri>https://youtu.be/SQN3ETbuf2g</uri>.