Real-Time Sliding Mode Observer Scheme for Shear Force Estimation in a Transverse Dynamic Force Microscope

Abstract

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 the 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 in terms of its 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.