Neural Networks Based Learning Control for a Piezoelectric Nanopositioning System

In this article, approximation model-based control and neural networks-based adaptive control are investigated for obtaining the solution to the motion tracking of a piezoelectric nanopositioning system, respectively. In order to reduce the effect of unknown hysteresis nonlinearity, a disturbance observer is introduced to estimate it. By considering nominal parts of an unknown piezoelectric nanopositioning system, approximation model-based control is obtained. The unknown parts corresponding to nominal parts are dealt with by the online learning ability of neural networks, and an adaptive neural network control is proposed to improve control accuracy. Compared with existing works, a great benefit of the proposed control method is that the neural networks-based learning algorithm is developed to deal with uncertainty of a piezoelectric nanopositioning system in an online way such that the closed-loop system can be governed automatically, obtaining satisfactory motion tracking. With Lyapunov stability theory, it is proved that all error signals are semiglobally uniformly ultimately bounded. Experiment is carried out to verify the effectiveness of the proposed control.