Recurrent-Neural-Network-Based Predictive Control of Piezo Actuators for Trajectory Tracking

Precise trajectory tracking of piezo actuators (PEAs) in real time is essential to high-precision systems and applications. However, the real-time tracking accuracy is rather limited as the PEA cannot be accurately modeled over large bandwidth and displacement range due to its nonlinearities. In this article, we propose to use recurrent-neural-network (RNN) to model the PEA system and develop a nonlinear predictive controller for PEA trajectory tracking. Considering the computation efficiency, first, an RNN is trained to model the nonlinear dynamics of the PEA system at high-frequency range. Then, a second-order linear model is proposed to account for the PEA low-frequency dynamics. Therefore, the PEA dynamics is modeled by the nonlinear model consisting of the RNN and the linear model, which is further used for nonlinear predictive control of the displacement. To increase the prediction accuracy, an unscented Kalman filter is designed to estimate the states of the nonlinear model. The nonlinear predictive control problem is solved based on a gradient descent algorithm, in which a method for analytically calculating the gradient of the cost function is developed. The proposed technique was experimentally implemented on a nano piezo stage for demonstration and its performance was compared with that of a PID controller. The accuracy of an iterative learning control approach was used as a benchmark for comparison as well. The results showed that high precision trajectory tracking of PEAs in real time can be achieved using the proposed technique.