2DOF control design for nanopositioning

Abstract

This chapter will focus on control systems theoretic analysis and synthesis that significantly expand the range of performance specifications and positioning capabilities of scanning probe microscopes (SPMs).We will present a systems theory framework to study fundamental limitations on the performance of one and two degree-of-freedom (DOF) control designs for nanopositioning systems. In particular, this chapter will present, compare, and analyze optimal-control methods for designing two-degree-of-freedom (2DOF) control laws for nanopositioning. The different methods are motivated by various practical scenarios and difficulty in achieving simultaneously multiple performance objectives of resolution, bandwidth, and robustness by tuning-based or shaping of open-loop-plants based designs. The analysis shows that the primary role of feedback is providing robustness to the closed-loop device whereas the feedforward component is mainly effective in overcoming fundamental algebraic constraints that limit the feedback-only designs. Experimental results indicate substantial improvements (over 200% in bandwidth) when compared to optimal feedback-only controllers. © 2011 Springer-Verlag Berlin Heidelberg.