A Digital Observer-Based Repetitive Learning Composite Control Method for Large Range Piezo-Driven Nanopositioning Systems

In this study, a novel digital compound compensation method is proposed to compensate for the hysteresis nonlinearity and the drift disturbance of a piezoelectric nanopositioning system with a large range. The overall hysteresis behaviors can be divided into the static amplitude-dependent behavior and the dynamic rate-dependent behavior, where the static hysteresis is compensated for by a novel discrete feedforward controller, while the dynamic hysteresis and the drift disturbance are compensated for by a novel discrete composite feedback controller composed of a drift observer-based state feedback controller and a repetitive learning controller. Compared with traditional control strategies, the proposed compound control strategy, including feedforward and feedback components, can eliminate system errors more effectively when tracking large range signals with obvious hysteresis. Moreover, the proposed online drift observer is superior over a traditional offline drift compensator both in response speed and compensation accuracy. Sufficient simulation tests and convincing tracking experiments, with large range periodic signals up to 90 $\mathsf{\mu }$m, are carried out. And comparisons with the two classical control algorithms are performed. The tracking results show that the mean absolute error of the proposed control method is minor compared with the other two algorithms, which validates that the proposed strategy can efficiently compensate for the hysteresis nonlinearity and the drift disturbance.