Optimal Digital Implementation of Fractional-Order Models in a Microcontroller

The growing number of operations in implementations of the non-local fractional differentiation operator is cumbersome for real applications with strict performance and memory storage requirements. This demands use of one of the available approximation methods. In this paper, the analysis of the cla...

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Bibliographic Details
Main Authors: Mariusz Matusiak, Marcin Bąkała, Rafał Wojciechowski
Format: Article
Language:English
Published: MDPI AG 2020-03-01
Series:Entropy
Subjects:
Online Access:https://www.mdpi.com/1099-4300/22/3/366
Description
Summary:The growing number of operations in implementations of the non-local fractional differentiation operator is cumbersome for real applications with strict performance and memory storage requirements. This demands use of one of the available approximation methods. In this paper, the analysis of the classic integer- (IO) and fractional-order (FO) models of the brushless DC (BLDC) micromotor mounted on a steel rotating arms, and next, the discretization and efficient implementation of the models in a microcontroller (MCU) is performed. Two different methods for the FO model are examined, including the approximation of the fractional-order operator <inline-formula> <math display="inline"> <semantics> <msup> <mi>s</mi> <mi>&#957;</mi> </msup> </semantics> </math> </inline-formula> (<inline-formula> <math display="inline"> <semantics> <mrow> <mi>&#957;</mi> <mo>&#8712;</mo> <mi mathvariant="double-struck">R</mi> </mrow> </semantics> </math> </inline-formula>) using the Oustaloup Recursive filter and the numerical evaluation of the fractional differintegral operator based on the Gr&#252;nwald&#8722;Letnikov definition and Short Memory Principle. The models are verified against the results of several experiments conducted on an ARM Cortex-M7-based STM32F746ZG unit. Additionally, some software optimization techniques for the Cortex-M microcontroller family are discussed. The described steps are universal and can also be easily adapted to any other microcontroller. The values for integral absolute error (IAE) and integral square error (ISE) performance indices, calculated on the basis of simulations performed in MATLAB, are used to evaluate accuracy.
ISSN:1099-4300