Recurrent-neural-network-based Predictive Control of Piezo Actuators for Precision Trajectory Tracking

Precise real-time trajectory tracking of piezo actuators (PEAs) is essential to high-precision systems and applications. However, most current real-time control techniques for PEAs are based on linear models and suffer significantly from modeling uncertainty. In this paper, we propose a network (RNN)-based predictive control technique for real-time PEA trajectory tracking. Specifically, a RNN is trained to model the nonlinear dynamics of the PEA system. Considering the length of the RNN training set is limited, a second order linear model embedded with an error term (LME) is proposed to model the PEA low frequency dynamics. Moreover, an unscented Kalman filter is designed to estimate the states of the nonlinear model. Then the nonlinear model consisting of the RNN and the LME are used for nonlinear predictive control based on gradient descent algorithm. To solve the optimization problem in the nonlinear predictive control, a method for analytically calculating the gradient of the cost function is developed as well. To verify the effectiveness of the proposed approach, experiments were conducted on a nano piezo actuator. The results demonstrated that the proposed method can achieve high precision output tracking of PEAs in real time.