Reachability and controllability of a particle in a dielectrophoretic system

A dielectrophoretic (DEP) force is a result of the interaction between a nonuniform electric field and a polarizable 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 a low Reynolds number. This DEP system has two states and two parameters: the two states are indicative of the particle’s position and the induced dipole moment and the two parameters are αα and cc 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 in control. In the existing literature, the controllability studies of the DEP system have been restricted to reachability issues in the context of the time-optimal control problem. Here we present a comprehensive study of reachability, accessibility and controllability.