Title

Control Of Frictional Dynamics Of A One-Dimensional Particle Array

Keywords

Frictional dynamics; Interconnected systems; Lyapunov stability; Nanoscale systems; Nonlinear control systems

Abstract

Control of frictional forces is required in many applications of tribology. While the problem is approached by chemical means traditionally, a recent approach was proposed to control the system mechanically to tune frictional responses. We design feedback control laws for a one-dimensional particle array sliding on a surface subject to friction. The Frenkel-Kontorova model describing the dynamics is a nonlinear interconnected system and the accessible control elements are average quantities only. We prove local stability of equilibrium points of the un-controlled system in the presence of linear and nonlinear particle interactions, respectively. We then formulate a tracking control problem, whose control objective is for the average system to reach a designated targeted velocity using accessible elements. Sufficient stabilization conditions are explicitly derived for the closed-loop error systems using the Lyapunov theory based methods. Simulation results show satisfactory performances. The results can be applied to other physical systems whose dynamics is described by the Frenkel-Kontorova model. © 2008 Elsevier Ltd. All rights reserved.

Publication Date

10-1-2008

Publication Title

Automatica

Volume

44

Issue

10

Number of Pages

2560-2569

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1016/j.automatica.2008.03.012

Socpus ID

52949092390 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/52949092390

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