Open AccessDiscrete-time realization of fractional-order proportional integral controller for a class of fractional-order system
Author(s) -
Jaydeep Swarnakar
Publication year - 2022
Publication title -
numerical algebra, control and optimization
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.303
H-Index - 20
eISSN - 2155-3289
pISSN - 2155-3297
DOI - 10.3934/naco.2021007
Subject(s) - delta operator , discrete time and continuous time , control theory (sociology) , robustness (evolution) , mathematics , transfer function , limit (mathematics) , representation (politics) , controller (irrigation) , time domain , realization (probability) , computer science , mathematical analysis , shift operator , control (management) , artificial intelligence , law , compact operator , chemistry , engineering , biology , biochemistry , political science , agronomy , computer vision , programming language , statistics , politics , electrical engineering , extension (predicate logic) , gene
The approximation of the fractional-order controller (FOC) has already been recognized as a distinguished field of research in the literature of system and control. In this paper, a two-step design approach is presented to realize a fractional-order proportional integral controller (FOPI) for a class of fractional-order plant model. The design goals are based on some frequency domain specifications. The first stage of the work is focused on developing the pure continuous-time FOC, while the second stage actually realizes the FOPI controller in discrete-time representation. The presented approach is fundamentally dissimilar with respect to the conventional approaches of z -domain. In the process of realizing the FOC, the delta operator has been involved as a generating function due to its exclusive competency to unify the discrete-time system and its continuous-time counterpart at low sampling time limit. The well-known continued fraction expansion (CFE) method has been employed to approximate the FOPI controller in delta-domain. Simulation outcomes exhibit that the discrete-time FOPI controller merges to its continuous-time counterpart at the low sampling time limit. The robustness of the overall system is also investigated in delta-domain.