Computation of All Robustly Stabilizing PID Controllers Based on H-∞ Robust Stability Condition

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dc.contributor.authorMenak, Ramazan
dc.contributor.authorTan, Nusret
dc.date.accessioned2026-04-04T13:33:24Z
dc.date.available2026-04-04T13:33:24Z
dc.date.issued2024
dc.departmentİnönü Üniversitesi
dc.description.abstractIn this paper, the computation of all robustly stabilizing Proportional-Integral-Derivative (PID) controllers for Single-Input-Single-Output (SISO) Linear Time Invariant (LTI) systems with/without time delay and unstructured uncertainty is presented. The study proposes a graphical technique to plot the regions of all robustly stabilizing PID controllers that satisfy the H-infinity based robust stability condition. These regions are formed by the Real Root Boundary (RRB), the Complex Root Boundary (CRB), and the Infinite Root Boundary (IRB), which represent the transitions of the roots of the characteristic equation from the left half-plane to the right half-plane (or vice versa), based on Hurwitz stability criteria. The regions are depicted in the (k(i)-k(d)), (k(p)- k(i)), and (k(p)- k(d)) 2-D planes for fixed values of k(p), k(d), and k(i), respectively. The methodology is detailed step by step and demonstrated through various examples. Additionally, stability analyses are visually performed using Nyquist envelopes and uncertainty discs.
dc.description.sponsorshipTurkish Academy of Sciences (TUBA)
dc.description.sponsorshipWe thank Turkish Academy of Sciences (TUBA) for supporting this work.
dc.identifier.doi10.1109/ACCESS.2024.3461315
dc.identifier.endpage140593
dc.identifier.issn2169-3536
dc.identifier.orcid0000-0003-3223-4808
dc.identifier.orcid0000-0002-1285-1991
dc.identifier.scopus2-s2.0-85204521876
dc.identifier.scopusqualityQ1
dc.identifier.startpage140556
dc.identifier.urihttps://doi.org/10.1109/ACCESS.2024.3461315
dc.identifier.urihttps://hdl.handle.net/11616/109142
dc.identifier.volume12
dc.identifier.wosWOS:001329028700001
dc.identifier.wosqualityQ2
dc.indekslendigikaynakWeb of Science
dc.indekslendigikaynakScopus
dc.language.isoen
dc.publisherIeee-Inst Electrical Electronics Engineers Inc
dc.relation.ispartofIEEE Access
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanı
dc.rightsinfo:eu-repo/semantics/openAccess
dc.snmzKA_WOS_20250329
dc.subjectPID controller
dc.subjectH-infinity norm
dc.subjectrobust control
dc.subjectrobust control
dc.subjectrobust stability
dc.subjectrobust stability
dc.subjectstability boundary locus
dc.subjectstability boundary locus
dc.subjectunstructured uncertainty
dc.subjectunstructured uncertainty
dc.subjectunstructured uncertainty
dc.titleComputation of All Robustly Stabilizing PID Controllers Based on H-∞ Robust Stability Condition
dc.typeArticle

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