Abstract - This article is devoted to the identification of an arctangent hysteresis model, using the particle swarm optimization method. Results obtained from simulated and measured curves are compared and analyzed.

Introduction

Swarm intelligence-based algorithms are widely used to solve difficult optimization problems. Scientists and researchers are particularly interested in the PSO approach, as it needs few parameters, it is adapted to nonlinear functions, and it is easy to implement.

Describing mathematical hysteresis loops is one of the most challenging aspects of ferromagnetism. Mathematical models are characterized by their simplicity of implementation.

This paper suggests the use of PSO method in order to identify the parameters of the arctangent hysteresis model that will be presented in the coming section.

Methodology

For a given magnetic field H, the magnetic induction B in the arctangent model hysteresis curve is represented by the following equations.

For the upward curve:

B=arctan(b(H-d)cH (1)

For the downward curve:

B=arctan(b(H+d)cH (2)

Generally, the parameters a, b, c, and d are calculated from analytical expressions. The particle swarm optimization method is used to identify them too. This method is based on the definition of a search space, which includes a set number of particles and the function to be optimized. Each particle is identified by its present location, speed, and best position.

Results

It is obvious that the hysteresis curve generated by the PSO method leads to a better fit of the measured loop than the one obtained using the analytical approach. The convergence of the PSO method is very fast and can be reached in a few iterations.

Conclusion

From the obtained results, it is evident that the identification of the set of parameters (a, b, c, and d) using the PSO method gives a better approximation of the measured curve than those obtained when they are analytically identified.