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Mathematical Problems in Engineering
Volume 2009 (2009), Article ID 969714, 16 pages
Research Article

On the Positioning Problem of a Microscopic Particle Trapped in Optical Tweezers

CIC-IPN, Avenida Juan de Dios Bátiz s/n, Esq. M. Othón de Mendizabal, U.P.A.L., Col. San Pedro Zacatenco, A.P. 75476, México DF 07700, Mexico

Received 1 July 2009; Revised 30 November 2009; Accepted 17 December 2009

Academic Editor: Oded Gottlieb

Copyright © 2009 Carlos Aguilar-Ibañez and Luis I. Rosas-Soriano. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We solve the positioning problem of a spherical microparticle trapped by Optical Tweezers, under the assumption that the drag viscous force is presented. To do it, we develop two control strategies for the manipulation of this kind of optical trap. The first control strategy is developed assuming that the damping coefficient is known, while in the second strategy this parameter value is only partially known, which in practice it is more realistic due to the difficulty to estimate it. Both strategies are based on the traditional Lyapunov method in conjunction with the use of a saturation function. The stability analysis of both strategies was carried out by using the standard Lyapunov stability theory. Finally, numerical simulations validate the effectiveness of both control approaches in reducing the random position fluctuations produced by the inherent thermal noise.