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Dynamical friction modelling and adaptive compensation on the nanometer scale

The presented work concerns the modelling and compensation of highly nonlinear friction effects on nanometer scale. Experiments in the pre-rolling and rolling friction regimes are conducted on a high precision positioning stage. Two selected dynamical friction models were identified as well as validated and this analysis shows, that the system behaviour of the experimental set-up is highly position dependent. Hence the identified models are not valid over the whole operating range and online parameter adaption mechanisms are presented, which ensure precise friction estimations over the positioning range of 200 mm. Finally, the models are utilized as an adaptive feed-forward friction compensator in a trajectory tracking control scheme. Using this adaptive control approach the tracking error is reduced significantly. Both adaptive models showed a similar performance but differ noticeably relating to consumption of calculating time.