Reachability and controllability of a particle in a dielectrophoretic system

Dielectrophoretic (DEP) force is a result of the interaction between a nonuniform electric field and a particle. As the electric field is dominant at the micro/nano scale, this force can be effectively used to manipulate and control particles on this scale. We consider the motion of a particle on an invariant line with the suspending medium being a fluid with low Reynolds number. This DEP system has two states and two parameters: the two states are indicative of the particle position and the induced dipole moment, the two parameters are a and c which depend upon the electric properties of the particle and the medium. The system is described by a set of ordinary differential equations with a quadratic term in the control variable (control being the applied voltage on the electrodes which induces the electric field) making the system non-affine. For this system, we address the issues of reachability, accessibility and controllability.