Ocean Energy Harvesting from a Rotating Parametric Pendulum with Bounded Control Power

Abstract

Recently, energy harvesting from sea waves was studied using a controlled rotating pendulum. Consisting of a pendulum with a vertical motion induced by the sea waves, pendulum’s rotations generate energy to be extracted by an electrical generator attached to its axis. Following this ideas, a complete dynamic model in state-space variables can be written, with the control input given by the torque of a brush-less dc motor and the pendulum’s rotational energy is the object to be controlled. On the other hand, an optimal setup for this control problem is defined, so a user tuned function acts as a set-point (desired pendulum’s trajectory). Moreover, the harvested energy comes from the generator attached to the rotating pendulum, whereas the DC motor must be fed to provide the necessary control action. In this analysis, it is rather important to keep track the balance: output power vs input control power. To account for this balance, in this paper, besides the optimal control horizon in order to tune the rotating energy, an additional constraint is added to limit the amount of power used by the DC motor, ensuring a real energy harvesting. The Pontryagin’s principle can be used to solve this singular optimal control problem resulting in a classic sign function. This feedback control requires only angular position and velocity’s measurements, allowing this controller to be easily implemented in hardware. Implementing the obtained control law along with the complete mechanical model in Matlab/Simulink, some simulations will show the effectiveness of the energy harvesting principle. The tracking properties and effective harvesting form ocean sea waves will be shown.