Optimal Sliding Mode Control of AFM Tip Vibration and Position During Manipulation of a Nanoparticle

Abstract

This research regards to a two-dimensional lateral pushing nanomanipulation using Atomic Force Microscope (AFM). Yet a reliable control of the AFM tip position during the AFM-based manipulation process is a chief issue since the tip can jump over the target nanoparticle and then the process can fail. However, a detailed Modeling and understanding of the interaction forces on the AFM tip is important for prosperous manipulation control and a nanometer resolution tip positioning. In the proposed model, Lund-Grenoble (LuGre) dynamic friction model is used as friction force on the contact surface between the nanoparticle and the substrate. This model leads to a stick-slip behavior of the nanoparticle that is so similar to the experimental behavior in nanoscale. Derjaguin interaction force is applied between the AFM tip and the nanoparticle which considers both attractive and repulsive interactions. The AFM is modeled by lumped-parameters model. A controller is designed based on the proposed dynamic model in order for positioning the AFM tip during a desired nanomanipulation task. Optimal sliding mode approach is used to design the controller. In this approach sliding surface which is used in the sliding mode approach is selected optimally based on the linear quadratic (LQ) method.