On the manipulation of microscopic particles by optical tweezers: Flatness based approach

In this paper we present a control strategy based on a combination of the flatness approach and saturation functions to manipulate the optical tweezers system, which is a flat system, with flat outputs given by the horizontal and vertical positions. The strategy allows the optical tweezers to steer a microscopic particle from an initial position to a final desired position, following a suitable trajectory. The control strategy is proposed under the assumption that the particle is suspended in a frictionless medium. Due to the fact that the particle horizontal and vertical velocities cannot be measurable, a high-gain observer is used. The resulting controller has a relatively simple stability analysis. The control strategy performance is tested by numerical simulations.