Open AccessFractional‐order controllers for irrational systems
Author(s) -
GuelCortez AdrianJosue,
MéndezBarrios CésarFernando,
Kim Eunjin,
Sen Mihir
Publication year - 2021
Publication title -
iet control theory and applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.059
H-Index - 108
eISSN - 1751-8652
pISSN - 1751-8644
DOI - 10.1049/cth2.12095
Subject(s) - control theory (sociology) , transfer function , robustness (evolution) , laplace transform , fractional order system , irrational number , mathematics , controller (irrigation) , robust control , computer science , fractional calculus , control system , mathematical analysis , engineering , control (management) , artificial intelligence , agronomy , biochemistry , chemistry , geometry , electrical engineering , biology , gene
In this contribution, fractional‐order controllers of the type PD μ and PI λ are applied to a class of irrational transfer function models that appear in large‐scale systems, such as networks of mechanical/electrical elements and distributed parameter systems. More precisely, by considering the fractional‐order controllerk p + k η s αin the Laplace domain with − 1 ≤ α ≤ 1 , a stability analysis in the parameter‐space ( k p , k η , α ) is presented. Furthermore, as a way to measure the controller robustness, the controller's fragility analysis using the parameter‐space ( k p , k η , α ) is derived. Finally, several applications that demonstrate the utility of our results are included.