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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 ±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.

93B40Computational methods in systems theory
93C55Discrete-time control systems
93B17System transformation