Modeling for Simulation and Control of a X-Y High Precision Positioning Table

The production of micro-scale objects with nano-scale properties demands for appropriate measurement and test equipment for quality control. This work is motivated by an experimental setup to proof nano-positioning capabilities with 200 mm traveling range. This paper is about the modeling of an x-y high precision positioning table, with double-H-configuration and driven by direct linear DC motors, using the Lagrange method. Furthermore the elasto-plastic friction model was extended, based on system parameters and former experiments with nano-positioning guides. The influence of the normal force on the friction force is essential for creating a connection between the macroscopic and microscopic models. A simplified model for control purposes was derived and applied to a PI-state regulator with additional feedforward of the system dynamics. Simulation results show the effectiveness of the approach.