Further studies of time optimal control for a dielectrophoretic system

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 low Reynolds number. At the bottom of this chamber is a series of parallel electrodes with a controlled 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. The system has two parameters ¿ 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 ¿ can have either sign. The time-optimal control problem for this system with ¿ < 0 and y(0) = 0 was studied. In this article, we solve the time-optimal control problem when ¿ ¿ 0 and y(0) is arbitrarily pre-specified.