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Time optimal control of 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 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 α 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 α can have either sign. We solve the time optimal control problem for this system when α≥0 and y(0) is arbitrarily prescribed.