H∞ loop shaping design for nano-positioning

This article presents the identification and control of a nano-positioning device. The device consists of two stages, which enable two-dimensional positioning. Each stage is actuated by piezo-electric stacks and its motion is sensed by a linear variable differential transformer (LVDT). A 2 × 2 transfer function has been identified to describe the device. In this paper the main limitations to nano-positioning have been overcome through control. Feedback laws have been designed to address the undesirable effects of hysteresis and creep, which are significant in the open loop implementation, and to meet the steady state tracking and bandwidth requirements of nano-positioning. Great emphasis has been placed on robustness, which leads to a system that can withstand the diverse conditions where it will be used and does not necessitate tuning, as is the case with the existing designs. Accordingly, Glover-McFarlane H_∞ loop shaping controllers have been employed to robustify existing non-model based designs. The merits of these designs along with the experimental results obtained by using them have been presented.