Robustness analysis of control systems with mixed perturbations

Tan N., Atherton D.

TRANSACTIONS OF THE INSTITUTE OF MEASUREMENT AND CONTROL, cilt.25, sa.2, ss.163-184, 2003 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 25 Sayı: 2
  • Basım Tarihi: 2003
  • Doi Numarası: 10.1191/0142331203tm081oa
  • Dergi Adı: TRANSACTIONS OF THE INSTITUTE OF MEASUREMENT AND CONTROL
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.163-184
  • Anahtar Kelimeler: circle criterion, Lur'e criterion, Nyquist envelope, Popov criterion, robust performance, robust stability, small gain theorem, strict positive realness, uncertain systems, POPOV CRITERION, STABILITY
  • İnönü Üniversitesi Adresli: Evet

Özet

The paper considers control systems with parametric as well as unstructured uncertainty. Parametric uncertainty is modelled by a transfer function whose numerator and denominator polynomials are independent uncertain polynomials of the form of P (s, q) = l(0) (q) + l(1) (q) s +... + l(n) (q)s(n) where the coefficients depend linearly on q = [q(1), q(2),., q(q)](T) and the uncertainty box is Q = {q: q(i)is an element of[(q(i)) under bar, (q(i)) over bar], i = 1, 2,., q}. The unstructured uncertainty is modelled as H-infinity norm bounded perturbations and perturbations consisting of a family of nonlinear sector bounded feedback gains. Using the geometric structure of the value set of P(s, q), some results are presented for determination of the robust small gain theorem, robust performance, strict positive realness and absolute stability problem of control systems with parametric as well as unstructured uncertainty. Numerical examples are given to illustrate application of the proposed methods.