Nonlinear dynamics and control strategies: On a energy harvester vibrating system with a linear form to non-ideal motor torquet

¹ UNESP-São Paulo State University, Bauru, São Paulo, Brazil
² UNESP-São Paulo State University, Rio Claro, São Paulo, Brazil
³ UTFPR- Paraná Federal Technological University, Ponta Grossa, Paraná, Brazil
⁴ UNIPAMPA-Pampa Federal University, Bagé, Rio Grande do Sul, Brazil

Abstract

In this paper, we deal with the research of a vibrating model of an energy harvester device, including the nonlinearities in the model of the piezoelectric coupling and the non-ideal excitation. We show, using numerical simulations, in the analysis of the dynamic responses, that the harvested power is influenced by non-linear vibrations of the structure. Chaotic behavior was also observed, causing of the loss of energy throughout the simulation time. Using a perturbation technique, we find an approximate analytical solution for the non-ideal system. Then, we apply both two control techniques, to keep the considered system, into a stable condition. Both the State Dependent Ricatti Equation (SDRE) control as the feedback control by changing the energy of the oscillator, were efficient in controlling of the considered non-ideal system.