Infinite Dimensional Design Approach of Robust Disturbance Observer for a Piezo-Actuated Nano-Positioner With Measurement Delays

Abstract

In this article, we consider the disturbance observer (DOB) design supporting high performance nano-positioning with sensor-induced time delays, where the standard robust disturbance observer design methodology is extended to time-delay systems by employing an infinite dimensional approach. In particular, the dynamic model including the piezo-induced hysteresis and the measurement delays are investigated and the infinite dimensional <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathcal {H}^\infty$</tex-math></inline-formula> optimization problem is formulated to achieve an optimal Q-filter design in the DOB control framework. The fragility resulting from unstable pole-zero cancellations in the infinite dimensional Q-filter is further discussed and the direct-moment-matching-based rational approximation is developed for stable digital implementations of the proposed method. Comprehensive experimental studies are conducted on a piezo-actuated stage, where the proposed method successfully demonstrates excellent performances on hysteresis compensation, disturbance suppression, and trajectory tracking, significantly outperforming existing approaches.