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Fractional-Order Approximation and Synthesis of a PID Controller for a Buck Converter

Author

Listed:
  • Allan G. Soriano-Sánchez

    (CONACYT–Instituto Tecnológico de Celaya, Antonio García Cubas Pte. 600, Celaya 38010, Gto., Mexico)

  • Martín A. Rodríguez-Licea

    (CONACYT–Instituto Tecnológico de Celaya, Antonio García Cubas Pte. 600, Celaya 38010, Gto., Mexico)

  • Francisco J. Pérez-Pinal

    (Tecnológico Nacional de México, Instituto Tecnológico de Celaya, Antonio García Cubas Pte. 600, Celaya 38010, Gto., Mexico)

  • José A. Vázquez-López

    (Tecnológico Nacional de México, Instituto Tecnológico de Celaya, Antonio García Cubas Pte. 600, Celaya 38010, Gto., Mexico)

Abstract

In this paper, the approximation of a fractional-order PIDcontroller is proposed to control a DC–DC converter. The synthesis and tuning process of the non-integer PID controller is described step by step. A biquadratic approximation is used to produce a flat phase response in a band-limited frequency spectrum. The proposed method takes into consideration both robustness and desired closed-loop characteristics, keeping the tuning process simple. The transfer function of the fractional-order PID controller and its time domain representation are described and analyzed. The step response of the fractional-order PID approximation shows a faster and stable regulation capacity. The comparison between typical PID controllers and the non-integer PID controller is provided to quantify the regulation speed introduced by the fractional-order PID approximation. Numerical simulations are provided to corroborate the effectiveness of the non-integer PID controller.

Suggested Citation

  • Allan G. Soriano-Sánchez & Martín A. Rodríguez-Licea & Francisco J. Pérez-Pinal & José A. Vázquez-López, 2020. "Fractional-Order Approximation and Synthesis of a PID Controller for a Buck Converter," Energies, MDPI, vol. 13(3), pages 1-17, February.
    • Handle: RePEc:gam:jeners:v:13:y:2020:i:3:p:629-:d:315665
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    References listed on IDEAS

    as
    1. A.G., Soriano–Sánchez & C., Posadas–Castillo & M.A., Platas–Garza & A., Arellano–Delgado, 2018. "Synchronization and FPGA realization of complex networks with fractional–order Liu chaotic oscillators," Applied Mathematics and Computation, Elsevier, vol. 332(C), pages 250-262.
    2. Arthi, G. & Park, Ju H. & Suganya, K., 2019. "Controllability of fractional order damped dynamical systems with distributed delays," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 165(C), pages 74-91.
    3. Muñoz-Vázquez, Aldo Jonathan & Ortiz-Moctezuma, Manuel Benjamín & Sánchez-Orta, Anand & Parra-Vega, Vicente, 2019. "Adaptive robust control of fractional-order systems with matched and mismatched disturbances," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 162(C), pages 85-96.
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