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Zbl 1051.93031
Vinagre, Blas M.; Chen, Yang Quan; Petráš, Ivo
Two direct Tustin discretization methods for fractional-order differentiator/integrator. (English)
[J] J. Franklin Inst. 340, No. 5, 349-362 (2003). ISSN 0016-0032; ISSN 1879-2693/e

The aim of this paper is to obtain discrete equivalents to the fractional integrodifferential operators in the Laplace domains $s^{\pm r}$ with $(0< r< 1)$.\par Two direct discretization methods based on the Tustin transformation are presented. For the first method a recursion scheme is derived. In the second method, continued fraction expansion is used. The methods are illustrated and compared by an application example. A fractional order controller with $D(s)= s^{0.5}$ is used for a double integrator plant. Robustness properties of the closed-loop systems with unity negative feedback are illustrated.
[Rudolf Tracht (Essen)]

MSC 2000:: *93B40 Computational methods in systems theory
93C55 Discrete-time control systems
93B17 System transformation

Keywords: Fractional differentiator; Fractional-order controllers; Tustin operator; Power series expansion; Continued fraction expansion; Discretization

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