Hartman-Grobman decomposition when in presence of jumps in the relative degree of the dynamics in an energy harvesting device

• Autor(a) principal: Barbanti, Luciano [UNESP]
• Data de Publicação: 2012
• Outros Autores: Damasceno, Berenice Camargo [UNESP], dos Reis, Celia Aparecida [UNESP], Pereira da Silva, Neusa A. [UNESP]
• Tipo de documento: Artigo de conferência
• Idioma: eng
• Título da fonte: Repositório Institucional da UNESP
• Texto Completo: http://dx.doi.org/10.1063/1.4765473; http://hdl.handle.net/11449/10398
• topic: Energy Harvesting System; Internal Dynamic; Zero Dynamic; Input-Output Linearization; Asymptotic Stability

This work deals with the nonlinear piezoelectric coupling in vibration-based energy harvesting, done by A. Triplett and D.D. Quinn in J. of Intelligent Material Syst. and Structures (2009). In that paper the first order nonlinear fundamental equation has a three dimensional state variable. Introducing both observable and control variables in such a way the controlled system became a SISO system, we can obtain as a corollary that for a particular choice of the observable variable it is possible to present an explicit functional relation between this variable one, and the variable representing the charge harvested. After-by observing that the structure in the Input-Output decomposition essentially changes depending on the relative degree changes, presenting bifurcation branches in its zero dynamics-we are able in to identify this type of bifurcation indicating its close relation with the Hartman - Grobman theorem telling about decomposition into stable and the unstable manifolds for hyperbolic points.