Control of an Energy-Harvesting System Using Sinha’s Theory for the Purpose of Energy Production

Abstract

The goal of this study was to develop a linear feedback control method to increase the energy produced for a parametrically excited energy-harvesting system. The chosen control design uses state feedback based on the Lyapunov–Floquet transformation to direct the system dynamics toward a previously chosen trajectory. The methodology of this work was based on the studies of Sinha and Butcher. They developed stability and control analysis techniques based on Floquet theory and the approximation of the state transition matrix of systems that have periodic coefficients in time. It was observed that the stability and instability conditions of the system were obtained from the choice of physical parameters related to the parametric excitation force. When the control technique was applied to the system, it was found that the suggested control effectively directed the system’s trajectory in the direction of the predetermined trajectory. The application of control significantly increased the energy generation compared with the uncontrolled system, which was seen when comparing the energy generated by the uncontrolled system and the net energy generated by the controlled system.