The Moments in Control: a tool for Analysis, Reduction and Design
Keywords:
Moments, model reduction, optimization.Abstract
In this paper we present a new method of model reduction via the moments. The reduction technique is composed of two steps, the first one consists on using the Least Squares linear optimization algorithm to minimize a cost function representing the norm 2 of the error between different moments of the full order function and the reduced model. This solution represents an initialization of the second step algorithm which is based a Non Linear Programming minimizing a new criterion composed of the cost function of the first step and an equality constraint.References
K.Astöm and B.Wittenmark "Computer Controlled Systems, Theory and Design", Prenctice Hall (1984)
A.Bentayeb, N.Maamri and D.Mehdi "Moments Based Synthesis Approach Comparison with HÂ¥ Design",IFAC DECOM-TT "Istanbul, Turkey" (2003).
S.Boyd and C.Barratt "Linear Controller Design-Limits of Performance". Prentice Hall (1991).
K.V.Fernando and H.Nicholson "Singular perturbational model reduction of balanced systems", IEEE Transactions on Automatic Control, AC-27:2:466-468 (1982). http://dx.doi.org/10.1109/TAC.1982.1102932
N.Maamri and J.C.Trigeassou "PID design for time delayed systems by the method of moments", European Control Conference, Groningen Holland (1993).
F.Monroux. "Méthodologie Générale de Synthèse de Correcteurs par la Méthode des Moments, Approche Mixte: Fréquentielle et Temporelle", Thèse de doctorat, Université de Poitiers, 1999.
N.Maamri, A.Bentayeb and J-C.Trigeassou "Design and Iterative Optimization of Reduced Robust Controllers with Equality-Constraints" ROCOND-Milan (2003).
D.W.Marquardt "An Algorithm for Least-Squares Estimation of Non Linear Parameters" Journal of Soc. Indust. Appl. Math V(11-2) (1963).
M.G.Safonov and R.Y.Chiang "A schur method for balanced truncation model reduction". IEEE Transactions on Automatic Control AC-34:729-733, (1989). http://dx.doi.org/10.1109/9.29399
S.Skogested and I.Postlethwaite "Multivariable Feedback Control", JW (1996).
M.S.Tombs and I.Postlethwaite "Truncated balanced realization of a stable non-minimal statespace system",International Journal of Control:46:1319-1330. http://dx.doi.org/10.1080/00207178708933971
J.C.Trigeassou "La méthode des moments en automatique". CIFA, Lille (2000).
Published
Issue
Section
License
ONLINE OPEN ACCES: Acces to full text of each article and each issue are allowed for free in respect of Attribution-NonCommercial 4.0 International (CC BY-NC 4.0.
You are free to:
-Share: copy and redistribute the material in any medium or format;
-Adapt: remix, transform, and build upon the material.
The licensor cannot revoke these freedoms as long as you follow the license terms.
DISCLAIMER: The author(s) of each article appearing in International Journal of Computers Communications & Control is/are solely responsible for the content thereof; the publication of an article shall not constitute or be deemed to constitute any representation by the Editors or Agora University Press that the data presented therein are original, correct or sufficient to support the conclusions reached or that the experiment design or methodology is adequate.