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

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Barbanti, Luciano [UNESP]
Damasceno, Berenice Camargo [UNESP]
dos Reis, Celia Aparecida [UNESP]
Pereira da Silva, Neusa A. [UNESP]
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Amer Inst Physics
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.
Energy Harvesting System, Internal Dynamic, Zero Dynamic, Input-Output Linearization, Asymptotic Stability
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9th International Conference on Mathematical Problems In Engineering, Aerospace and Sciences (icnpaa 2012). Melville: Amer Inst Physics, v. 1493, p. 84-87, 2012.