High-Speed, Ultra-High-Precision Nanopositioning: A Signal Transformation Approach

Signal transformation is a novel strategy employed in feedback control to reduce the impact of measurement noise on positioning accuracy. This chapter addresses robustness issues of the method with respect to output disturbance and uncertainty in plant low frequency gain. The robustness problems can be solved by an inner loop with integral action before incorporating the signal transformation mappings. Feedback controllers are designed for two-dimensional positioning of a novel 12-electrode piezoelectric tube used for scanning probe microscopy. The closed-loop bandwidths are intentionally limited to set the standard deviation of the projected noise around 0.1 nm. For triangular waveform tracking and a general class of plants and compensators, necessary and almost sufficient conditions are derived for stability and convergence of tracking error. Effectiveness of the proposed method, regarding tracking and robust performances, is shown by simulations and experiments.