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Design of Fractional Order Controllers Using the PM Diagram

RoboticsLab, Carlos III University of Madrid, Getafe, 28903 Madrid, Spain
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Mathematics 2020, 8(11), 2022; https://doi.org/10.3390/math8112022
Received: 15 October 2020 / Revised: 7 November 2020 / Accepted: 9 November 2020 / Published: 13 November 2020
(This article belongs to the Special Issue Fractional Calculus and Nonlinear Systems)
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. View Full-Text
Keywords: non-rational systems; phase magnitude diagram; optimal control; differential evolution; fractional order control non-rational systems; phase magnitude diagram; optimal control; differential evolution; fractional order control
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MDPI and ACS Style

Garrido, S.; Monje, C.A.; Martín, F.; Moreno, L. Design of Fractional Order Controllers Using the PM Diagram. Mathematics 2020, 8, 2022. https://doi.org/10.3390/math8112022

AMA Style

Garrido S, Monje CA, Martín F, Moreno L. Design of Fractional Order Controllers Using the PM Diagram. Mathematics. 2020; 8(11):2022. https://doi.org/10.3390/math8112022

Chicago/Turabian Style

Garrido, Santiago; Monje, Concepción A.; Martín, Fernando; Moreno, Luis. 2020. "Design of Fractional Order Controllers Using the PM Diagram" Mathematics 8, no. 11: 2022. https://doi.org/10.3390/math8112022

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