Model Predictive Control of a Piezoelectric Vortex-Induced Vibrations Energy Harvester

Abstract

In this paper, an optimal control method is proposed for a piezoelectric vortex-induced vibrations (VIV) energy harvester. The harvester comprises a blunt cylinder attached to the tip of a flexible beam. The beam is a composite cantilever that is partially covered by piezoelectric plates. A nonlinear model is derived for the VIV of the harvester by using the Euler–Lagrange principle with the unsteady aerodynamic force due to vortex shedding. To achieve the maximum energy production, an optimal controller is designed using the model predictive control (MPC) method. The MPC design problem turned out to be a linear quadratic optimization problem that is solved by efficient numerical methods. The closed-loop response of the MPC scheme is studied through extensive numerical simulation for several working conditions. The results showed that, compared with the conventional methods, the MPC scheme significantly increases the output electrical power of the VIV harvester.