Problems in solving fractional differential equations in a microcontroller implementation of an FOPID controller

• Autorzy: Matusiak Mariusz , Ostalczyk Piotr

Identyfikatory

DOI

10.24425/aee.2019.129342

• Języki publikacji: EN

Abstrakty

EN

The article focuses on the fractional-order backward difference, sum, linear time-invariant equation analysis, and difficulties of the fractional calculus microcontroller implementation with regard to designing a fractional-order proportional integral derivative (FOPID) controller. In opposite to the classic proportional integral derivative (PID), the FOPID controller is defined by five independent parameters. Hence, it is more customizable and, potentially, more precise on condition that the values of fractional integration and differentiation orders are properly selected. However, a number of operations and the time required to calculate the output signal continuously increase. This can be a significant problem considering the limitations of a microcontroller, including memory size and a constant sampling time of the set-up analog-to-digital (ADC) converters. In the article, three solutions are considered, and results obtained in the experiments are presented.

Słowa kluczowe

EN

fractional calculus; Grünwald-Letnikov fractional-order backward difference; FOPID; hardware implementation

• Wydawca: Polish Academy of Sciences, Committee on Electrical Engineering
• Czasopismo: Archives of Electrical Engineering
• Rocznik: 2019
• Tom: Vol. 68, nr 3
• Strony: 565--577
• Opis fizyczny: Bibliogr. 26 poz., rys., tab., wz.

Twórcy

autor

Matusiak Mariusz

• Lodz University of Technology Institute of Applied Computer Science Faculty of Electrical, Electronic, Computer and Control Engineering Stefanowskiego 18/22, 90-924 Łódź, Poland

autor

Ostalczyk Piotr

• Lodz University of Technology Institute of Applied Computer Science Faculty of Electrical, Electronic, Computer and Control Engineering Stefanowskiego 18/22, 90-924 Łódź, Poland

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Uwagi

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).