Shear force reconstruction in a vertically oriented probe microscope using a super-twisting observer

In this paper, a scheme employing a super-twisting sliding mode observer is proposed to reconstruct the unknown shear forces at the tip of the vertically oriented cantilever (VOC) which is the key component of Bristol University's Vertically Oriented Probe Microscope (VOPM). The VOPM is unique in the sense that the distance of the VOC tip from the specimen can be measured using the known amplitude of the horizontal excitation of the cantilever. This amplitude is directly influenced by the interaction of the VOC with the fluid layer above the biological specimen. The shear forces caused by the fluid interaction increase with the proximity of the tip to the specimen. Thus, knowledge of the shear forces is another important measure of the closeness of the VOC tip to the specimen. Simulation examples show the feasibility of its eventual real-time application.