This is the author accepted manuscript. The final version is available from Wiley via the DOI in this record.This paper describes a sliding mode observer scheme for estimation of the
shear force affecting the cantilever in a Transverse Dynamic Force Microscope
(TDFM). The vertically oriented cantilever is oscillated in proximity to the
specimen under investigation. The amplitude of oscillation of the cantilever
tip is affected by these shear forces. They are created by the ordered-water
layer above the specimen. The oscillation amplitude is therefore a measure
of distance between the tip and the surface of the specimen. Consequently,
the estimation of the shear forces provides useful information about the
specimen characteristics. For estimating the shear forces, an approximate
finite dimensional model of the cantilever is created using the method of
lines. This model is subsequently reduced for its model order. An unknown
input sliding mode observer has been used to reconstruct the unknown shear
forces using only tip position measurements and the cantilever excitation. This
paper describes the development of the sliding mode scheme and presents
experimental results from the TDFM set up at the Centre for Nanoscience and
Quantum Information (NSQI) at Bristol University
