Dynamics and control of an energy harvesting system using the Lyapunov-Floquet transformation and sensitivity analysis using Sobol indices

Luiz Oreste Cauz; Fábio Roberto  Chavarette; Lakshmi Narayan Mishra; Laxmi Rathour

doi:10.4025/actascitechnol.v48i1.71579

Authors

Luiz Oreste Cauz Universidade Estadual de Mato Grosso do Sul / Universidade Estadual Paulista https://orcid.org/0009-0006-5105-4027
Fábio Roberto Chavarette Universidade Estadual Paulista https://orcid.org/0000-0002-1203-7586
Lakshmi Narayan Mishra Vellore Institute of Technology https://orcid.org/0000-0001-7774-7290
Laxmi Rathour National Institute of Technology https://orcid.org/0000-0002-2659-7568

DOI:

https://doi.org/10.4025/actascitechnol.v48i1.71579

Keywords:

: Stability analysis; global sensitivity analysis; lyapunov-floquet transformation; linear feedback control.

Abstract

This study aimed to design a linear feedback control approach for a parametrically excited energy harvesting system utilizing a piezoelectric material as the transduction element. The purpose was to significantly increase the amount of energy produced compared to that produced by the original system. To do so, firstly, it is necessary to analyze the stability of the system and perform a global sensitivity analysis to determine the physical parameters of the system that most contribute to energy production. The sensitivity analysis is done by calculating the Sobol indices, which are statistical indices that measure the relative contribution of each input variable (in this case, the physical parameters of the system) to the contribution of all input variables. In the stability analysis, the state transition matrix approximation techniques created by Sinha and Butcher and the results of the Floquet Theory for periodic systems were used. Stability analysis and global sensitivity analysis are methodologically complementary techniques for a better understanding of the dynamics of a system. In the case of this work, they are applied to an energy-harvesting system based on mechanical vibrations, providing important information to design a more efficient controller. The control technique used was proposed by Sinha and Butcher (1997), and is known as Linear Feedback Controller Design via the Lyapunov-Floquet Transform.

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