Impulsive control for nanopositioning: Stability and performance

In this paper, impulsive control is applied to a class of linear feedback systems and studied both theoretically and experimentally, with a particular focus on the usage in nanopositioning. By using impulsive control, improvements in tracking performance and tolerance to measurement noise can be achieved which are beyond the limits of conventional linear feedback. We derive sufficient conditions for bounded-input-bounded-state stability of the resulting hybrid systems, investigate their performance and unveil an inherent connection to the recently published signal transformation approach. It is demonstrated that for a triangular reference signal, impulsive control outperforms the signal transformation approach both in terms of performance and implementation complexity. Furthermore, we show that the measurement noise-induced positioning error of an impulsive feedback system is significantly lower than in case of a comparable, conventional linear feedback. The experimental results are obtained on a fast microelectromechanical nanopositioner. Copyright 2011 ACM.