Abstract
A compact model representing the dynamics between piezoelectric voltage inputs and cantilever probe positioning, including nonlinear surface interaction forces, for atomic force microscopes (AFM) is considered. By considering relatively large cantilever stiffness, singular perturbation methods reduce complexity in the model and allows for faster responses to Van der Waals interaction forces. In this study, we outline a near-optimal feedback control approach for non-contact mode imaging designed to maintain the cantilever tip about the equilibrium point of the attraction and repulsion forces. The tracking control problem for AFM raster scanning along the lateral directions is also addressed.
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