Friction compensation for Nanopositioning and Nanomeasuring Machines

The presented work concerns the modeling and experimental verification of the highly nonlinear behavior in positioning on the nanometer scale. The main goal of this work is to identify and extend a simple dynamic friction model, which allows a model-based estimation of the friction force including the system inertia only based on a displacement input. Experiments in the pre-sliding and sliding friction regimes are conducted on a high precision positioning stage. A hybrid parameter estimation algorithm is used offline to fit the model parameters based on the experimental data. Extensive experiments show, that the system behavior of the experimental setup is highly position dependent and hence the inverse system model is not valid over the whole operating range of the positioning stage. To solve this problem the parameters of the friction model are adjusted online to ensure precise friction estimation over the positioning range of 200 mm. Finally, an adaptive model is utilized as a model-based friction compensator in a trajectory tracking control scheme. With this adaptive control approach the tracking error is reduced significantly.