The Microcontroller Implementation of the Basic Fractional-Order Element

eng Article in English DOI: 10.14313/PAR_238/19

Krzysztof Oprzędkiewicz , Maciej Rosół , send Jakub Żegleń-Włodarczyk AGH University of Science and Technology, Faculty of Electrical Engineering Automatics, Computer Science and Biomedical Engineering

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Abstract

The paper presents the implementation of the basic fractional order element sγ on the STM32 microcontroller platform. The implementation employs the typical CFE and FOBD approximations, the accuracy of approximation as well as duration of calculations are experimentally tested. Microcontroller implementation of fractional order elements is known; however, real-time tests of such implementations have been not presented yet. Results of experiments show that both methods can be implemented at the considered platform. The FOBD approximation is more accurate, but the CFE one is faster. The presented experimental results prove that the STM32F7 family processor could be used to develop the embedded fractional-order control systems for a broad class of linear and nonlinear dynamic systems. This is crucial during the implementation of the fractional-order control in the hard real-time or embedded systems.

Keywords

CFE approximation, FOBD, fractional-order systems, microcontroller, STM32

Implementacja podstawowego elementu ułamkowego na mikrokontrolerze

Streszczenie

W pracy przedstawiono implementację podstawowego układu ułamkowego rzędu sγ na platformie mikrokontrolera STM32. Implementacja wykorzystuje typowe aproksymacje CFE oraz FOBD. Dokładność aproksymacji oraz czas trwania obliczeń testowane są eksperymentalnie. Implementacja układów ułamkowych na mikrokontroler jest znana, jednak ich testy w czasie rzeczywistym nie były jak dotąd omawiane w literaturze. Wyniki wskazują, że obie metody można wdrożyć na rozważanej platformie. Aproksymacja FOBD jest dokładniejsza, z kolei CFE jest szybsza. Przedstawione rezultaty eksperymentów dowodzą, że procesor z rodziny STM32F7 może zostać wykorzystany do opracowania wbudowanych ułamkowych układów sterowania dla szerokiej klasy liniowych i nieliniowych układów dynamicznych. Zaprezentowane wyniki są istotne z punktu widzenia implementacji algorytmów ułamkowych w twardych systemach czasu rzeczywistego lub w systemach wbudowanych.

Słowa kluczowe

aproksymacja CFE, FOBD, mikrokontroler, STM32, układy ułamkowe

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