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.

JO - Archives of Electrical Engineering L1 - http://sp.czasopisma.pan.pl/Content/112886/PDF/08_AEE-2019-3_INTERNET.pdf L2 - http://sp.czasopisma.pan.pl/Content/112886 PY - 2019 IS - No 3 EP - 565–577 KW - fractional calculus KW - Grünwald-Letnikov fractional-order backward difference/sum KW - FOPID KW - hardware implementation A1 - Matusiak, Mariusz A1 - Ostalczyk, Piotr PB - Polish Academy of Sciences VL - vol. 68 JF - Archives of Electrical Engineering DA - 2019.09.09 T1 - Problems in solving fractional differential equations in a microcontroller implementation of an FOPID controller SP - 565–577 UR - http://sp.czasopisma.pan.pl/dlibra/docmetadata?id=112886 DOI - 10.24425/aee.2019.129342 ER -