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Design of Fractional Order Controllers Using the PM Diagram

Author

Listed:
  • Santiago Garrido

    (RoboticsLab, Carlos III University of Madrid, Getafe, 28903 Madrid, Spain)

  • Concepción A. Monje

    (RoboticsLab, Carlos III University of Madrid, Getafe, 28903 Madrid, Spain)

  • Fernando Martín

    (RoboticsLab, Carlos III University of Madrid, Getafe, 28903 Madrid, Spain)

  • Luis Moreno

    (RoboticsLab, Carlos III University of Madrid, Getafe, 28903 Madrid, Spain)

Abstract

This work presents a modeling and controller tuning method for non-rational systems. First, a graphical tool is proposed where transfer functions are represented in a four-dimensional space. The magnitude is represented in decibels as the third dimension and a color code is applied to represent the phase in a fourth dimension. This tool, which is called Phase Magnitude (PM) diagram, allows the user to visually obtain the phase and the magnitude that have to be added to a system to meet some control design specifications. The application of the PM diagram to systems with non-rational transfer functions is discussed in this paper. A fractional order Proportional Integral Derivative (PID) controller is computed to control different non-rational systems. The tuning method, based on evolutionary computation concepts, relies on a cost function that defines the behavior in the frequency domain. The cost value is read in the PM diagram to estimate the optimum controller. To validate the contribution of this research, four different non-rational reference systems have been considered. The method proposed here contributes first to a simpler and graphical modeling of these complex systems, and second to provide an effective tool to face the unsolved control problem of these systems.

Suggested Citation

  • Santiago Garrido & Concepción A. Monje & Fernando Martín & Luis Moreno, 2020. "Design of Fractional Order Controllers Using the PM Diagram," Mathematics, MDPI, vol. 8(11), pages 1-18, November.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:11:p:2022-:d:444520
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    References listed on IDEAS

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    1. João Clímaco & João Paulo Costa & Gregory Kersten, 2015. "Introduction," Group Decision and Negotiation, Springer, vol. 24(4), pages 563-566, July.
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    Cited by:

    1. Cristina I. Muresan & Iulia Bunescu & Isabela Birs & Robin De Keyser, 2023. "A Novel Toolbox for Automatic Design of Fractional Order PI Controllers Based on Automatic System Identification from Step Response Data," Mathematics, MDPI, vol. 11(5), pages 1-17, February.

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