Semi-Analytical Lorentz Actuator Model for a Superconductor-Based 6-Degrees-of-Freedom Levitation System Exploiting Magnetization Periodicity

Abstract Lorentz actuators use magnetic interactions between coils and magnets to create forces and torques for actuation. Especially for applications that enable actively controlled 6-DoF levitation, it is necessary to model these Lorentz forces and torques and evaluate these models in real-time. Generally, Lorentz forces are evaluated using numerical integration of the Lorentz force integrals. These calculations become computationally expensive for an increasing number of magnets and, therefore, deriving analytical or semi-analytical (SA) models for the integrals is important to reduce computation time while maintaining model accuracy. For the studied superconductor-based 6-DoF levitation system, a semi-analytical model of the Lorentz actuators' forces/torques is derived by exploiting the periodicity of the actuator magnets' magnetization. Using Fourier series, an analytical expression of the magnetic flux density of the actuator magnets is found by solving Maxwell's equations under magnetostatic conditions. Using this analytical expression, a semi-analytical formulation of the Lorentz force integrals is given. In this publication, the model derivation is presented, and the model is validated and discussed based on single coil experiments and compared to the fully numeric surface charge model. It was possible to show that the semi-analytical model can closely match the measured forces and torques, even with a reduced set of approximation elements to reduce computational effort by over 70% with respect to a fully numeric implementation.