Rotation Control of a Parametrically Forced Magnetic Pendulum

Abstract

A novel control strategy is proposed to induce and sustain stable rotational motion in a parametric pendulum. This approach is motivated by its potential application in pendulum-based wave energy converters. The control action consists of a small torque applied to the pendulum to conveniently increase its angular velocity. This torque arises from the magnetic interaction between a permanent magnet attached to the pendulum and an externally powered coil, eliminating the need for mechanical couplings which is an advantage for practical implementations. A comprehensive model is developed to describe the coupled system, incorporating the parametric pendulum, the coil, the magnet, and the control action. The resulting mathematical formulation integrates principles of electromagnetism, classical mechanics, and nonlinear dynamics, with all parameters derived directly from the physics of the system. The model is validated through experiments conducted on a custom-built test rig and supported by numerical simulations. Both experimental and computational results demonstrate that the proposed control technique effectively achieves and maintains rotations across a wide range of forcing conditions and initial states. Furthermore, its performance is shown to be comparable to more complex strategies, such as those based on Time-Delayed Feedback, while remaining considerably simpler to implement.

Keywords: parametric pendulum, magnetic pendulum, non-linear dynamics, rotation control, Energy harvesting