Optimization of Magnet Angles for Three-Dimensional Position Control with Three Permanent Magnets

Abstract

  In the three-dimensional position control of a small permanent magnet using three base magnets, an advanced control method that incorporates feedforward and feedback control is required to extend the control range and increase speed. Feedforward control requires knowledge of the angles of the base magnets, such that when the controlled magnet is placed in a certain position, the force acting on it is zero. In this study, the covariance matrix adaptation evolution strategy is used to determine the angles of the three magnets at which the force acting on the controlled magnet is zero. As a result of the optimization, it was confirmed that, to lift the controlled magnet upward, the three magnets should be turned in the positive direction (N-pole facing outward), and to move the stable point of the controlled magnet away from a certain base magnet, the magnet should be turned in the negative direction. A comparison of the optimization results with the experimental results showed that the rotation directions of the three magnets matched, but the rotation angles were smaller in the experiment. One possible reason is the inclination of the controlled magnet.