Geometrical error compensation and control of an XY table using neural networks

This paper presents extended results for geometrical error compensation and control, addressing several issues beyond the approach in Tan, Huang, and Seet (2000) (IEEE Transactions on Instrumentation and Measurement, 49, 984–991). It is a key objective to attain more efficient compensation performance with less or comparable memory using this approach. Three new features are associated with this proposed approach. Firstly, the geometrical error of an industrial XY table is considered and modeled in the overall control structure. Secondly, multilayer NNs are used to approximate the components of geometrical errors, resulting in a significantly less number of neurons compared to the use of radial basis functions (RBFs). Thirdly, the direction of motion is considered in the compensator in details, i.e., a separate compensator is used when compensating for motion in the forward and reverse direction. This is important as the geometrical errors can be quite distinct depending on the direction of motion due to backlash and other nonlinearities in the servo systems. The overall geometrical error is computed from these NNs based on a kinetic equation for the machine in point. Finally, the stability issue when considering the overall control system with the geometrical error compensation is discussed. Full results on the application of the proposed method to an XY   table are presented, and the evaluation tests show that the overall geometrical errors can be reduced to about 96μm from 324μm.