Steering a Ferromagnetic Particle by Optimal Magnetic Feedback Control

A class of feedback control policies for steering a magnetic particle in a viscous fluid and actuated by a magnetic field is presented. The magnetic field which is generated by an array of electromagnets can be adequately shaped by controlling the voltages of the electromagnets. Control design relies on a dynamical model which exploits the low-pass character of the electromagnets, the opposing viscous drag on the magnetic particle, and the nonlinear (quadratic) nature of the dependence of the magnetic force on the electrical currents passing through the electromagnets. It is shown that under a set of practically achievable conditions, the nonlinearity of the model can be canceled by incorporating an inverse nonlinear map in the controller so that the closed-loop system operates like a linear system. A systematic framework for determining an optimal inverse map and investigating its properties is developed and two important cases of minimum control effort and maximum robustness are discussed. The ability to control the magnetic particle along arbitrary trajectories is verified both in simulations and in an experiment.