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Fuzzy modeling of a class of linear oscillators and its application to electric circuits

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Abstract

Modeling in physics is often faced with challenges in terms of measurement uncertainty. Oscillations are observed in many real-world systems, in particular, in electrical circuits. One of the ways to insert the uncertainty present in some elements of an electrical circuit is to use fuzzy sets. To get insight into this issue, in this work, a mathematical model describing an linear oscillator is considered by assuming its initials conditions has uncertainty in terms of fuzzy numbers linearly correlated. The system obtained is known as fuzzy initial value problem (FIVP). Solutions of the FIVP are obted using fuzzy Laplace transform for linearly correlated process. We propose to analyze the dynamics of an RLC-type electrical circuit with initial conditions given by linearly correlated fuzzy numbers. According to the oscillations described by the circuit three types of damped oscillators are considered comprising underdamped, critically damped, and overdamped. For the underdamped case, the formalism presented here allows a first approximation analysis of an RLC circuit in the transient phase and subjected to impulsive transients (pulse).

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Acknowledgements

This research was partially supported by National Council for Scientific and Technological Development (CNPq) under Grants no. 314464/2021-2 and 314885/2021-8. Thanks to Dr. Joaquim Paulo da Silva for his discussions on impulsive transients.

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Author notes

  1. Otávio José de Rezende Silveira, Sérgio Martins de Souza and Onofre Rojas Santos have contributed equally to this work.

Authors and Affiliations

  1. Institute of Applied Social Sciences, Federal University of Alfenas, Varginha, Minas Gerais, Brazil

    Sílvio Antônio Bueno Salgado

  2. Physics Department, Federal University of Lavras, Lavras, Minas Gerais, Brazil

    Otávio José de Rezende Silveira, Sérgio Martins de Souza & Onofre Rojas Santos

Authors
  1. Sílvio Antônio Bueno Salgado
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  2. Otávio José de Rezende Silveira
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  3. Sérgio Martins de Souza
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  4. Onofre Rojas Santos
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Correspondence to Sílvio Antônio Bueno Salgado.

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Communicated by Leonardo Tomazeli Duarte.

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Salgado, S.A.B., Silveira, O.J.d.R., Souza, S.M.d. et al. Fuzzy modeling of a class of linear oscillators and its application to electric circuits. Comp. Appl. Math. 43, 98 (2024). https://doi.org/10.1007/s40314-024-02604-x

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  • DOI: https://doi.org/10.1007/s40314-024-02604-x

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