The Frequency and Real-Time Properties of the Microcontroller Implementation of Fractional-Order PID Controller

Krzysztof Oprzędkiewicz,Jakub Żegleń-Włodarczyk,Maciej Rosół

doi:10.3390/electronics10050524

Krzysztof Oprzędkiewicz, Jakub Żegleń-Włodarczyk + Show 1 more

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https://doi.org/10.3390/electronics10050524

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Journal: Electronics	Publication Date: Feb 24, 2021
Citations: 9	License type: CC BY 4.0

Affiliation: AGH University of Krakow

Abstract

The paper presents time, frequency, and real-time properties of a fractional-order PID controller (FOPID) implemented at a STM 32 platform. The implementation uses CFE approximation and discrete version of a Grünwald–Letnikov operator (FOBD). For these implementations, experimental step responses and Bode frequency responses were measured. Real-time properties of the approximations are also examined and analyzed. Results of tests show that the use of CFE approximation allows to better keep the soft real-time requirements with an accuracy level a bit worse than when using the FOBD. The presented results can be employed in construction-embedded fractional control systems implemented at platforms with limited resources.

Highlights

The fractional-order PID controller (FOPID) control is one of the main areas of application of fractional calculus in automatic control
This paper presents the analysis of real-time and frequency properties of the FOPID controller implemented at the typical microcontroller platform
The FOPID controller using fractional-order Backward Difference (FOBD) and CFE approximations can be implemented at a STM-32 platform with respect to soft real-time requirements

Summary

Introduction

The FOPID control is one of the main areas of application of fractional calculus in automatic control. The book [1] describes the issue of fractional-order systems very well, from theory to practice. A good extension is the book [2] presenting further applications, including, for example, electrochemistry. It is known that fractional calculus is not a new idea. It has been analysed by mathematicians since the XVII century, but later it was forgotten due to difficulties in its application in solving real problems in physics and engineering. Fractional calculus is the main topic of the fundamental book [3]. The book [4] describes many uses of fractional-order control, such as coupled tank systems or MAGLEV

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