Dual-Stage Repetitive Control for High-Speed Nanopositioning

This paper studies an enhanced dual-stage repetitive controller (RC) for improved robustness and tracking of periodic reference trajectories in piezo-based nanopositioning systems. The dual-stage RC system consists of a signal generator designed to provide high gain at the fundamental and all the harmonic frequencies of the reference trajectory and another that offers high gain only at the odd harmonics. The stability of the dual-RC system is analyzed, and simulation and experimental results are presented to demonstrate their performance compared to PID control and standard RC. The proposed controller is implemented using FPGA hardware (with closed-loop sample rate of 100 kHz), and then applied to a custom-built three-axis serialkinematic nanopositioning stage. Measured tracking results at 1 kHz and 2 kHz show that the enhanced dual-RC minimizes the maximum steady state error to approximately 2.71% and 5.05%, respectively. The improvement in tracking precision compared to (1) traditionally-used PID control is over 88%, nearly one order of magnitude reduction in the tracking error, and (2) standard RC is over 35%, underscoring the benefits of the controller.