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Two direct Tustin discretization methods for fractional-order differentiator/integrator. (English) Zbl 1051.93031
The aim of this paper is to obtain discrete equivalents to the fractional integrodifferential operators in the Laplace domains \(s^{\pm r}\) with \((0< r< 1)\).
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.

MSC:
93B40 Computational methods in systems theory (MSC2010)
93C55 Discrete-time control/observation systems
93B17 Transformations
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