Control of frictional dynamics of a one-dimensional particle array

    Authors

    Y. Guo;Z. H. Qu

    Comments

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    Abbreviated Journal Title

    Automatica

    Keywords

    Frictional dynamics; Lyapunov stability; Interconnected systems; Nanoscale systems; Nonlinear control systems; SCALE NONLINEAR-SYSTEMS; STABILIZATION; MOTION; Automation & Control Systems; Engineering, Electrical & Electronic

    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. (C) 2008 Elsevier Ltd. All rights reserved.

    Journal Title

    Automatica

    Volume

    44

    Issue/Number

    10

    Publication Date

    1-1-2008

    Document Type

    Article

    Language

    English

    First Page

    2560

    Last Page

    2569

    WOS Identifier

    WOS:000260728400010

    ISSN

    0005-1098

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