TY - JOUR
N2 - 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.
L1 - http://so.czasopisma.pan.pl/Content/112886/PDF/08_AEE-2019-3_INTERNET.pdf
L2 - http://so.czasopisma.pan.pl/Content/112886
PY - 2019
IS - No 3
EP - 565–577
DO - 10.24425/aee.2019.129342
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
DA - 2019.09.09
T1 - Problems in solving fractional differential equations in a microcontroller implementation of an FOPID controller
SP - 565–577
UR - http://so.czasopisma.pan.pl/dlibra/publication/edition/112886
T2 - Archives of Electrical Engineering
ER -