Estimation of the Shear Force in Transverse Dynamic Force Microscopy using a Sliding Mode Observer

This paper concerns the application of a sliding mode observer to the problem of estimation of the shear force affecting the cantilever dynamics of a Transverse Dynamic Force Microscope (TDFM). The oscillated cantilever in proximity to a specimen permits the investigation of the specimen topography at nano-metre precision. The oscillation amplitude, but also in particular the shear forces, are a measure of distance to the specimen, and therefore the estimation of the shear force is of significance when attempting to construct TDFM images at submolecular accuracy. For estimation of the shear forces, an approximate model of the cantilever is derived using the method of lines. Model order reduction and sliding mode techniques are employed to reconstruct the unknown shear force affecting the cantilever dynamics based on only tip position measurements. Simulations are presented to illustrate the proposed scheme, which is to be implemented on the TDFM set up at the Centre for NSQI at Bristol.