Signal-Transformation-Based Repetitive Control of Spiral Trajectory for Piezoelectric Nanopositioning Stages

In this article, a novel signal-transformation-based repetitive controller (STBRC) dedicated to the accurate and fast tracking of spiral trajectory with a time-variant amplitude is proposed and tested. To overcome the requirement of strictly periodic references of conventional repetitive controller, a mapping between spiral trajectory and constant amplitude sinusoid is developed to provide multiple lower gains at the fundamental frequency and its harmonics of the spiral trajectory to ensure zero steady-state errors. The stability of the control method and convergence of steady-state errors are analyzed with a lifted-system representation, respectively, for its time-variant property. Compared with internal model-based controllers for this trajectory, STBRC has the advantages of a simpler structure, fewer parameters, and better performance. The application to a piezoelectric nanopositioning stage verifies the effectiveness of the proposed control method on suppression of cross-coupling errors and improving the tracking performance of high-speed spiral trajectory in comparison with other controllers.