Magnetic microfibers are fibers that behave as a flexible paramagnetic body, for example, polymer fibers filled with superparamagnetic particles. A cantilevered magnetic microfiber will bend in response to an applied magnetic field. In a nonuniform field, generated for example by a single electromagnet or by a magnetic dipole, a magnetic microfiber displays position hysteresis as the field strength increases and decreases. This paper presents a model for determining stable shapes of a cantilevered magnetic microfiber in a nonuniform magnetic field. The model determines stable shapes by finding local minima of the potential energy using a Rayleigh-Ritz method. The model predicts the position hysteresis behavior observed in magnetic microfibers. Experimental data ware collected using two electromagnets with different geometries. The model simulation and experimental data compare well both qualitatively and quantitatively. The model will be useful for designing actuators based on magnetic microfibers and for characterizing the magnetic properties of fabricated fibers. A rigid bar model is also introduced, which captures the qualitative behavior of the fiber and illustrates the source of the position hysteresis behavior.

Polymer fibers embedded with paramagnetic particles bend when placed in a magnetic field. The fiber can be manipulated by varying the coil current in an electromagnet. The operating range of the fiber is divided into one region with stable equilibria and one region with unstable equilibria. In this paper, fiber dynamics are modeled as a rigid bar. This model is used to develop a nonlinear controller for the position of the fiber over the whole operating range. An experimental platform for sensing and controlling fiber position was developed. The controller is tested experimentally and results are presented. The results show that the controller can control the position of the fiber in the unstable region despite model uncertainty.

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