Flatness-based approach for the manipulation of a microscopic particle by optical tweezers

Abstract

Based on the fact that optical tweezers (OT) constitute a flat system, with flat outputs given by the horizontal and vertical position coordinates of the geometric centre of the laser beam, a flatness-based control strategy for the manipulation of a microscopical particle is presented in this article. The control strategy is derived under the assumption that the particle is suspended in a frictionless medium, obtaining a simple controller with a relatively simple stability analysis. The control strategy is tested by tracking a straight line, an elliptic curve, and carrying out the rest-to-rest transfer manoeuvre task by using a smooth trajectory.

Keywords:

• optical tweezers
• flatness-based control
• saturation function
• velocity observers
• numerical simulation

Acknowledgements

This article was supported by the Secretaría de Investigación y Postgrado of the Instituto Politécnico Nacional (SIP-IPN) under the research grant 20091430. A. Barrañón acknowledges financial support from CONACYT Grant/75722. L.I. Rosas-Soriano is a doctoral student at the Centro de Investigación en Computación of the Instituto Politécnico Nacional. He is also a scholarship holder of the Consejo Nacional de Ciencia y Tecnología of México.

Notes

Note

1. Recalling that e = 2.71828.