Fast Robust Nanopositioning—A Linear-Matrix-Inequalities-Based Optimal Control Approach

Abstract

This paper proposes a 2-DOF robust optimal control design method for achieving multiple objectives of resolution, bandwidth, and robustness to modeling uncertainties in nanopositioning systems. The main theoretical contribution of this paper is the formulation of a multiobjective 2-DOF optimal control problem in terms of linear matrix inequalities, which are then solved using standard convex optimization tools. The main distinguishing feature of this approach is the flexibility this method provides in formulating and solving the optimization problems that results in achieving a larger set of performance specifications. It facilitates solving of a certain class of mixed-norm optimization and pole-placement problems that arise naturally in nanopositioning systems. This methodology is demonstrated through experiments on a nanopositioning system that archives performance specifications, which are impossible with 1-DOF designs. Experimental results also demonstrate over 200% improvement in bandwidth of the resulting nanopositioning system over the optimal 1-DOF control designed for the same resolution and robustness specifications.