Control of frictional dynamics of a one-dimensional particle array

Authors:
Yi Guo;Zhihua Qu
Affiliations:
Department of Electrical and Computer Engineering, Stevens Institute of Technology, Hoboken, NJ 07030, USA;School of Electrical Engineering and Computer Science, University of Central Florida, Orlando, FL 32816, USA
Venue:
Automatica (Journal of IFAC)
Year:
2008

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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.