The atomic force microscope (AFM) system has evolved into a useful tool for direct measurements of intermolecular forces with atomic-resolution characterization that can be employed in a broad spectrum of applications such as electronics, semi-conductors, materials, manufacturing, polymers, biological analysis, and biomaterials. The noncontact AFM offers unique advantages over other contemporary scanning probe techniques such as contact AFM and scanning tunneling microscopy. Current AFM imaging techniques are often based on a lumped-parameters model and ordinary differential equation (ODE) representation of the micro-cantilevers coupled with an ad-hoc method for atomic interaction force estimation (especially in non-contact mode). Since the magnitude of the interaction force lies within the range of nano-Newtons to pica-Newtons, precise estimation of the atomic force is crucial for accurate topographical imaging. In contrast to the previously utilized lumped modeling methods, this paper aims at improving current AFM measurement technique through developing a general distributed-parameters base modeling approach that reveals greater insight into the fundamental characteristics of the microcantilever-sample interaction. For this, the governing equations of motion are derived in the global coordinates via the Hamilton’s Extended Principle. By properly selecting a set of general coordinates, the resulting non-homogenous boundary value problem is then converted to a homogenous one, and hence, analytically solvable. The AFM controller can then be designed based on the original infinite dimensional distributed-parameters system which, in turn, removes some of the disadvantages associated with the truncated-model base controllers such as control spillovers, residual oscillations and increased order of the control. Numerical simulations are provided to support these claims.

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