Optimal-control methods for design of two-degree-freedom systems for nanopositioning

This paper presents, reviews, compares, and analyzes 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. In this context, we study fundamental trade-offs between these performance objectives in 2DOF control designs for nanopositioning systems. In particular, in terms of the trade-offs, our 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.