Design of an Optimal Input Signal for Parameter Estimation of Linear Fractional-Order Systems

Wiktor Jakowluk

Abstract

The optimal input signal design is a procedure of generating an informative excitation signal to extract the model parameters with maximum accuracy during the estimation process. Non-integer order calculus is a very useful tool, which is often utilized for modeling and control purposes. In the paper, we present a novel optimal input formulation and a numerical scheme for fractional order LTI system identification. The Oustaloup recursive approximation (ORA) method is used to determine the fractional order differentiation in an integer order state-space form. Then, the presented methodology is adopted to obtain an optimal input signal for fractional order system identification from the order interval 0.5≤α≤2.0 . The fundamental step in the presented method was to reformulate the problem into a similar fractional optimal input design problem described by Lagrange formula with the set of constraints. The methodology presented in the paper was verified using a numerical example, and the computational results were discussed.
Author Wiktor Jakowluk (FCS / DDMCG)
Wiktor Jakowluk,,
- Department of Digital Media and Computer Graphics
Pages128-141
Publication size in sheets0.65
Book Malinowska Agnieszka, Mozyrska Dorota, Sajewski Łukasz (eds.): Advances in Non-Integer Order Calculus and Its Applications, Lecture Notes in Electrical Engineering, vol. 559, 2020, Springer, ISBN 978-3-030-17344-9, 307 p., DOI:10.1007/978-3-030-17344-9
Keywords in EnglishFractional calculus, Optimal inputs, Oustaloup filter, Parameter identification
ASJC Classification2209 Industrial and Manufacturing Engineering
DOIDOI:10.1007/978-3-030-17344-9_10
Internal identifierROC 19-20
Languageen angielski
Score (nominal)20
Score sourcepublisherList
ScoreMinisterial score = 20.0, 26-03-2020, MonographChapterAuthor
Publication indicators Scopus SNIP (Source Normalised Impact per Paper): 2018 = 0.216
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