TIME OPTIMAL CONTROL OF A DIELECTROPHORETIC SYSTEM

Abstract

This paper examines a time optimal control problem for a dielectrophoretic system. The system consists of a neutrally buoyant and neutrally charged particle in a chamber filled with a fluid flowing with a low Reynolds number. At the bottom of this chamber is a series of parallel electrodes with a controlled time-varying voltage. The voltage on the electrodes creates a time-varying nonuniform electric field inducing a dipole moment in the particle. This induced dipole moment interacts with the electric field to generate a force on the particle. There are two state variables x and y, where x is the position of the particle and y is the induced dipole moment in the particle. The system has two parameters alpha and c which depend on the electric characteristics of the particle and the ambient fluid. The parameter c is always positive by the laws of physics, but alpha can have either sign. We solve the time optimal control problem for this system when alpha >= 0 and y( 0) is arbitrarily prescribed.