Comparison of two non-linear control approaches to fast nanopositioning: Impulsive control and signal transformation

Non-linear approaches to feedback control for nanopositioning have recently attracted renewed interest thanks to their superior performance in the presence of measurement noise. In this article, we investigate two recent non-linear control schemes, namely signal transformation and impulsive control, and show that in the context of triangular waveform tracking, they are inherently related. This rather surprising result not only fosters further theoretical studies but also has a significant impact on implementation. We demonstrate that for the tracking of triangular reference signals, impulsive control drastically improves the transient tracking error while providing the same steady state performance. Both methods are compared in theory, simulation and experiments.