Fractional Order Modeling of Large Three-Dimensional RC Networks

Autor(es)

Harrop Galvao, Roberto Kawakami ^[1] ; Hadjiloucas, Sillas ^[2] ; Kienitz, Karl Heinz ^[1] ; Paiva, Henrique Mohallem ^[3] ; Magalhaes Afonso, Rubens Junqueira ^[1]

Afiliação do(s) autor(es)

^[1] Inst Tecnol Aeronaut, Dept Elect Engn, BR-12228900 Sao Jose Dos Campos, SP - Brazil

^[2] Univ Reading, Sch Syst Engn, Reading RG6 6AY, Berks - England

^[3] Mectron Odebrecht Org, BR-12227000 Sao Jose Dos Campos, SP - Brazil

• Tipo de documento: Artigo Científico
• Fonte: IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS I-REGULAR PAPERS; v. 60, n. 3, p. 624-637, MAR 2013.
• Citações Web of Science: 58

Resumo

An incidence matrix analysis is used to model a three-dimensional network consisting of resistive and capacitive elements distributed across several interconnected layers. A systematic methodology for deriving a descriptor representation of the network with random allocation of the resistors and capacitors is proposed. Using a transformation of the descriptor representation into standard state-space form, amplitude and phase admittance responses of three-dimensional random RC networks are obtained. Such networks display an emergent behavior with a characteristic Jonscher-like response over a wide range of frequencies. A model approximation study of these networks is performed to infer the admittance response using integral and fractional order models. It was found that a fractional order model with only seven parameters can accurately describe the responses of networks composed of more than 70 nodes and 200 branches with 100 resistors and 100 capacitors. The proposed analysis can be used to model charge migration in amorphous materials, which may be associated to specific macroscopic or microscopic scale fractal geometrical structures in composites displaying a viscoelastic electromechanical response, as well as to model the collective responses of processes governed by random events described using statistical mechanics. (AU)

• Processo FAPESP: 11/13777-8 - Espectroscopia terahertz no domínio do tempo: desenvolvimento de métodos analíticos, técnicas de processamento de sinais, estudos bioquímicos e fundamentais
• Beneficiário: Celio Pasquini
• Modalidade de apoio: Auxílio à Pesquisa - Temático
• Processo FAPESP: 11/17610-0 - Monitoramento e controle de sistemas dinâmicos sujeitos a falhas
• Beneficiário: Roberto Kawakami Harrop Galvão
• Modalidade de apoio: Auxílio à Pesquisa - Temático
• Processo FAPESP: 11/18632-8 - Controle Preditivo tolerante a falhas com planejamento de trajetórias na presença de obstáculos
• Beneficiário: Rubens Junqueira Magalhães Afonso
• Modalidade de apoio: Bolsas no Brasil - Doutorado