Optimal sliding mode control for atomic force microscope tip positioning during nano-manipulation process

This research presents two-dimensional controlled pushing-based nanomanipulation using an Atomic Force Microscope (AFM). A reliable control of the AFM tip position is crucial to AFM-based manipulation since the tip can jump over the target nanoparticle causing the process to fail. However, detailed modeling and an understanding of the interaction forces on the AFM tip have a central role in this process. In the proposed model, the Lund-Grenoble (LuGre) method is used to model the dynamic friction force between the nanoparticle and the substrate. This model leads to the stick-slip behavior of the nanoparticle, which is in agreement with the experimental behavior at nanoscale. Derjaguin interaction force, which includes both attractive and repulsive interactions, is used to model the contact between the tip and nanoparticle. AFM is modeled by the lumped-parameter model. A controller is designed based on the proposed dynamic model for positioning of the AFM tip during a desired nanomanipulation task. An optimal sliding mode approach is used to design the controller, and the performance of the controller is shown by the simulation.