Linear Matrix Inequality Approach to Designing Damping and Tracking Control for Nanopositioning Application

Abstract

This paper presents a method to extend the eigenstructure assignment based design of the Positive Position Feedback (PPF) damping controller to the family of well-known second-order Positive Feedback Controllers (PFC) namely: (i) the Positive Velocity and Position Feedback (PVPF) and (ii) the Positive Acceleration Velocity and Position Feedback (PAVPF) using appropriate eigenstructure assignment. This design problem entails solving a set of linear equations in the controller parameters using Linear Matrix Inequalities (LMI) to specify a convex design constraint. These damping controllers are popularly used in tandem with a tracking controller (typically an integrator) to deliver high-bandwidth nanopositioning performance. Consequently, the closed-loop performance of all three controllers (PPF, PVPF and PAVPF) employed in tandem with suitably gained integral tracking loops is thoroughly quantified via relevant performance metrics, using measured frequency response data from one axis of a piezo-stack actuated x-y nanopositioner.

Keywords

• eigen-vector assignment
• nanopositioning
• linear matrix inequality
• damping