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

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Tarih

2024

Dergi Başlığı

Dergi ISSN

Cilt Başlığı

Yayıncı

IEEE-Inst Electrical Electronics Engineers Inc

Erişim Hakkı

info:eu-repo/semantics/openAccess

Özet

In 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.

Açıklama

Anahtar Kelimeler

PID controller, H-infinity norm, robust control, robust control, robust stability, robust stability, stability boundary locus, stability boundary locus, unstructured uncertainty, unstructured uncertainty, unstructured uncertainty

Kaynak

Ieee Access

WoS Q Değeri

N/A

Scopus Q Değeri

Q1

Cilt

12

Sayı

Künye