Fast and robust control of nanopositioning systems: Performance limits enabled by field programmable analog arrays

Abstract

This paper aims at control design and its implementation for robust high-bandwidth precision (nanoscale) positioning systems. Even though modern model-based control theoretic designs for robust broadband high-resolution positioning have enabled orders of magnitude improvement in performance over existing model independent designs, their scope is severely limited by the inefficacies of digital implementation of the control designs. High-order control laws that result from model-based designs typically have to be approximated with reduced-order systems to facilitate digital implementation. Digital systems, even those that have very high sampling frequencies, provide low effective control bandwidth when implementing high-order systems. In this context, field programmable analog arrays (FPAAs) provide a good alternative to the use of digital-logic based processors since they enable very high implementation speeds, moreover with cheaper resources. The superior flexibility of digital systems in terms of the implementable mathematical and logical functions does not give significant edge over FPAAs when implementing linear dynamic control laws. In this paper, we pose the control design objectives for positioning systems in different configurations as optimal control problems and demonstrate significant improvements in performance when the resulting control laws are applied using FPAAs as opposed to their digital counterparts. An improvement of over 200% in positioning bandwidth is achieved over an earlier digital signal processor (DSP) based implementation for the same system and same control design, even when for the DSP-based system, the sampling frequency is about 100 times the desired positioning bandwidth.