A Flexible Magnetic Field Mapping Model For Calibration of Magnetic Manipulation System

Abstract

Magnetic manipulation provides a versatile, remote, noninvasive, and cost-effective strategy in a variety of applications. Till now, many different configurations of magnetic manipulation systems have been developed to address different needs on force, torque, accuracy, and accessibilities. Magnetic field mapping can help to explore the exact map of the magnetic field in the working space and guarantee the homogeneity of the magnetic field. In this paper, a flexible mapping method is employed to solve the scalar potential of the magnetic source by using the separation of variables in Cartesian coordinates. Levenberg-Marquardt Algorithm (LMA) and Whale Optimization Algorithm (WOA) are set to the solver of the model. The work is evaluated in the mapping of an eight-pole magnetic manipulation system. The result of numerical simulation shows that the coefficient of determination R <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> of the model reaches99.81%, and the actual system mapping obtains R <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> value of 99.57%. This technique can directly be used to calculate the magnetic flux density and gradient field in a short period (≈1ms). Finally, the manipulation of a permanent magnet under the control magnetic field mapping and PID controller demonstrates the effectiveness of the proposed method.