Position control of charged spherical particles suspended in laminar flow within a channel

In this paper, steering a set of charged particles suspended in fluid flow within a plane channel is considered. In this way, the linear-state feedback control methodology is used to determine the external electric field. In order to design the proposed controller, at first, the governing mathematical ordinary differential equations are derived by the combination of Newton's second law, Coulomb's law and Navier-Stokes equations. Then, a linear quadratic regulator, which is one of the optimal control methods, is used to design the state-feedback control gains. For this purpose, continuous-time and discrete-time control methods are utilized. Simulation studies demonstrate the efficiency of the implemented control strategy for controlling the particles position and also tracking desired trajectories within the fluid flow. These results can contribute substantially to the development of related industrial processes.