Generalized method for rational approximation of SISO/MIMO fractional-order systems using squared magnitude function

A new method for the rational approximation of stable/unstable single-input, single-output (SISO)/multiple-input, multiple-output (MIMO) fractional-order systems is proposed. The objective of the proposed algorithm is to obtain an integer-order approximant of an SISO/MIMO fractional-order system. Th...

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Bibliographic Details
Published in:Transactions of the Institute of Measurement and Control 2024-01, Vol.46 (2), p.207-222
Main Authors: Damodaran, Suraj, Sunil Kumar, TK, Sudheer, AP
Format: Article
Language:English
Subjects:
Algorithms
Approximation
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Summary:A new method for the rational approximation of stable/unstable single-input, single-output (SISO)/multiple-input, multiple-output (MIMO) fractional-order systems is proposed. The objective of the proposed algorithm is to obtain an integer-order approximant of an SISO/MIMO fractional-order system. The developed method utilizes the concept of matching of an appropriate number of approximate generalized time moments and approximate generalized Markov parameters of squared magnitude function of fractional-order system to those of approximant. The proposed method preserves the stability/instability property and minimum phase/non-minimum phase characteristics of fractional-order system in the approximant. The method also incorporates a provision for matching the steady-state response of the approximant to that of fractional-order system. Numerical examples consider three cases of approximation, while fractional-order system has the characteristics of (a) stable non-minimum phase SISO, (b) stable non-minimum phase MIMO, and (c) unstable SISO which are presented to validate the efficiency of the proposed method.
ISSN:0142-3312
1477-0369
DOI:10.1177/01423312231175996