Two direct Tustin discretization methods for fractional-order differentiator/integrator.

*(English)*Zbl 1051.93031The 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 $D\left(s\right)={s}^{0\xb75}$ is used for a double integrator plant. Robustness properties of the closed-loop systems with unity negative feedback are illustrated.

Reviewer: Rudolf Tracht (Essen)

##### MSC:

93B40 | Computational methods in systems theory |

93C55 | Discrete-time control systems |

93B17 | System transformation |