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Numerical simulation of the fractional-order control system

Cai, Xin & Liu, Fawang (2007) Numerical simulation of the fractional-order control system. Journal of Applied Mathematics and Computing, 23(1-2), pp. 229-241.

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Abstract

Multi-term fractional differential equations have been used to simulate fractional-order control system. It has been demonstrated the necessity of the such controllers for the more efficient control of fractionalorder dynamical system. In this paper, the multi-term fractional ordinary differential equations are transferred into equivalent a system of equations. The existence and uniqueness of the new system are proved. A fractional order difference approximation is constructed by a decoupled technique and fractional-order numerical techniques. The consistence, convergence and stability of the numerical approximation are proved. Finally, some numerical results are presented to demonstrate that the numerical approximation is a computationally efficient method. The new method can be applied to solve the fractional-order control system.

Impact and interest:

13 citations in Scopus
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ID Code: 14891
Item Type: Journal Article
Keywords: Multi, term, fractional control system, Caputo derivative, numerical approximation, consistence, convergence, stability
DOI: 10.1007/BF02831971
ISSN: 1865-2085
Subjects: Australian and New Zealand Standard Research Classification > MATHEMATICAL SCIENCES (010000) > NUMERICAL AND COMPUTATIONAL MATHEMATICS (010300) > Numerical Analysis (010301)
Australian and New Zealand Standard Research Classification > MATHEMATICAL SCIENCES (010000) > PURE MATHEMATICS (010100) > Ordinary Differential Equations Difference Equations and Dynamical Systems (010109)
Australian and New Zealand Standard Research Classification > ENGINEERING (090000) > CHEMICAL ENGINEERING (090400) > Process Control and Simulation (090407)
Divisions: Past > QUT Faculties & Divisions > Faculty of Science and Technology
Copyright Owner: Copyright 2007 Springer
Copyright Statement: The original publication is available at SpringerLink http://www.springerlink.com
Deposited On: 17 Sep 2008
Last Modified: 29 Feb 2012 23:37

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