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Fractional-Order in RC, RL and RLC Circuits

  • Yang Chen
  • Guang-yuan Zhao
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 891)

Abstract

In mathematics, differential equations with fractional-order derivatives have a long history, for example, the “one in third” derivative, but haven’t gotten tremendous use in applied science and engineering. While applications do exist in several modeling specific phenomena, such as semi-infinite lossy transmission, which are difficult to model, and there exist some extensions of control in fractional-order PID, everyday use of fractional order modeling is more and more common. In this paper, the basic principles of the conventional RC and RL circuits in fractional-order way and a fractional differential equation are studied in the electrical RLC circuit. We consider the order of the derivative (0 < γ ≤ 1). In order to keep the dimensionality of the physical quantities R, L and C, an auxiliary parameter σ is introduced.

Keywords

Fractional calculus Caputo derivative Fractional-Order circuit Simulation of Fractional-Order response 

Notes

Acknowledgments

Yang Chen acknowledges fruitful discussion with Prof. Zhao and Hao-yu Li and has been supported by Graduate Innovation Fundation (Key No. 114-602080146).

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.School of AutomationXi’an University of Posts and TelecommunicationsXi’anChina

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