Robust damping PI repetitive control for nanopositioning

In many applications of nanopositioning, such as scanning probe microscopy, tracking fast periodic reference trajectories with high accuracy is highly desirable. Repetitive control (RC) is a simple and effective scheme to obtain good tracking of such reference trajectories. However, the highly resonant dynamics of the positioning stage combined with hysteresis and creep behavior in the piezoelectric actuator can degrade performance and even make creating a stable RC system difficult. In this paper, a damping proportional-integral (PI) controller is combined with a repetitive controller for robustness and high performance. Compared to a regular PI controller, the modified PI controller introduces damping, increases the bandwidth, and reduces the overall noise level due to feedback. Also, due to the integral action, the hysteresis and creep nonlinearities inherent in the piezoelectric actuator is minimized. A novel method for tuning the PI controller is proposed. The control approach is applied to a custom-design flexure-guided nanopositioning system with a dominant resonance of approximately 725 Hz. Experimental results demonstrate the effectiveness of the overall control scheme, and the maximum tracking error for scanning at 100 Hz and 400 Hz is measured at 0.27% and 2.7%, respectively, of the total positioning range.