Hybrid Identification of Electromagnetic Interaction Forces in a Magnetically Actuated Pendulum Using Physics-Based and Neural Approaches

This study addresses the identification of electromagnetic interaction forces in a pendulum system equipped with a permanent magnet (PM) and an electromagnet (EM), based on the proof-of-concept of a contactless motion control method for suspended offshore loads. The objective is to experimentally characterise the nonlinear PM–EM coupling and compare direct force measurements from a load cell with physics-based and data-driven estimations. A dedicated test rig excites the pendulum under steady and dynamic electromagnetic fields for multiple configurations, varying payload mass, PM strength, and the presence of a thin steel plate on the actuator-facing side. The magnetic coupling coefficient is first derived analytically from equilibrium data using an inverse-cubic magnetic force law. A physics-informed neural network is then trained on the experimental dataset to predict the interaction law as a function of gap, excitation, and configuration parameters. Results show close agreement between load-cell data, analytical predictions, and neural estimates, demonstrating the value of combining physical insight and machine learning for accurate, interpretable modelling of contactless actuators. The approach forms a basis for model-based control of electromagnetically actuated pendulums and scalable non-contact manipulation systems in offshore engineering.