Análise Multifractal de Movimentos Persistentes num Sistema de Controle de Atitude
DOI:
https://doi.org/10.5540/tema.2006.07.02.0307Abstract
O presente trabalho caracteriza movimentos persistentes num sistema de controle de atitude que possui atuadores sujeitos a atrasos e restrições de chaveamento e controlador de primeira ordem, como no caso de satélites ou do VLS (Veículo Lançador de Satélite) brasileiro. Através de simulações, e utilizando o método WTMM (wavelet transform modulus maxima) para calcular o espectro de singularidades dos atratores, foram obtidos diagramas de bifurcação no espaço de parâmetros do controlador (ℜ2), que permitiram discriminar e conhecer os possíveis atratores para cada conjunto de parâmetros. Os resultados foram comparados com a dimensão de Lyapunov.References
[1] A. Arneodo et al. Wavelet based fractal analysis of DNA sequences, Physica D 96 (1996), 291-320.
A. Arneodo et al., The thermodynamics of fractals revisited with wavelets, Physica A, 213 (1995), 232-275.
G. Avanzini, Bifurcation analysis of attitude dynamics in rigid spacecraft with switching control logics, J. Guid., Control, Dynamics, 24 (2001), 953-959.
I. Daubechies, “Ten Lectures on Wavelets”, SIAM, Philadelphia, 1992.
M. Degaudenzi, C. Arizmendi, Wavelet-based fractal analysis of electrical power demand, Fractals 8 (2000), 239-245.
G. F. Franklin, J.D. Powell, A. Emami-Naeini, “Feedback Control of Dynamic Systems”, Addison Wesley, Reading, 1994.
P. Frederickson et al., The liapunov dimension of strange attractors, Journal of Differential Equations, 49 (1983), 185-207.
P. Grassberger, I. Procaccia, Dimensions and entropies of strange attractors from a fluctuating dynamics approach, Physica D, 13 (1984), 34-54.
T. Halsey et al., Fractal measures and their singularities: the characterization of strange sets, Physical Review A, 33 (1986), 1141-1151.
S. Mallat,W. Hwang, Singularity detection and processing with wavelets, IEEE Trans. on Information Theory, 38 (1992), 617-643.
J. Mendel, On-off limit-cycle controllers for reaction-jet-controlled systems, IEEE Transactions on Automatic Control, 15 (1970), 285-299.
A. Mesquita, “Análise Paramétrica de um Sistema de Controle de Atitude com Atuadores Sujeitos a Restrições de Chaveamento”, Trabalho de Graduação. IEE, ITA, São José dos Campos, SP, 2004. Disponível em www.bibl.ita.br.
Downloads
Published
How to Cite
Issue
Section
License
Copyright
Authors of articles published in the journal Trends in Computational and Applied Mathematics retain the copyright of their work. The journal uses Creative Commons Attribution (CC-BY) in published articles. The authors grant the TCAM journal the right to first publish the article.
Intellectual Property and Terms of Use
The content of the articles is the exclusive responsibility of the authors. The journal uses Creative Commons Attribution (CC-BY) in published articles. This license allows published articles to be reused without permission for any purpose as long as the original work is correctly cited.
The journal encourages Authors to self-archive their accepted manuscripts, publishing them on personal blogs, institutional repositories, and social media, as long as the full citation is included in the journal's website version.