Synchronization in the Frenkel-Kontorova Model with Application to Control of Nanoscale Friction

TitleSynchronization in the Frenkel-Kontorova Model with Application to Control of Nanoscale Friction
Publication TypeConference Paper
Year of Publication2021
AuthorsDo, Loi, and Zdeněk Hurák
MonthSeptember
Conference LocationTokyo, Japan
Abstract

This paper tailors synchronization of multi-agent systems to motion control of the Frenkel-Kontorova (FK) model, a one-dimensional chain of harmonically coupled identical particles in a spatially periodic potential field. In particular, the goal is to drive all particles in the FK model to the desired trajectory by controlling only a single—boundary—particle. The proposed solution augments harmonic coupling in the FK model with dissipative inter-particle interactions, allowing all particles in the chain to synchronize to a particular reference trajectory. The boundary control represents a special case of pinning control. Moreover, as the FK model describes the frictional dynamics of a nanosheet sliding over a surface, we use its synchronization for controlling the nanoscale sliding friction. The key idea is to introduce a sliding reference trajectory that allows particles to move near synchrony. Synchronization effectively increases the system’s stiffness, so less energy ends up dissipated through inter-particle relative motion, thus reducing the frictional force. We validate the proposed solution through numerical simulations.

URLhttps://www.sciencedirect.com/science/article/pii/S2405896321017948?via%3Dihub
DOIhttps://doi.org/10.1016/j.ifacol.2021.10.388
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