Discretization schemes for fractional-order differentiators and integrators

Abstract

Abstract—For fractional-order differentiator where is a real number, its discretization is a key step in digital implementation. Two discretization methods are presented. The first scheme is a direct re-cursive discretization of the Tustin operator. The second one is a direct discretization method using the Al-Alaoui operator via continued fraction expansion (CFE). The approximate discretization is minimum phase and stable. Detailed discretization procedures and short MATLAB scripts are given. Examples are included for illustration. Index Terms—Al-Alaoui operator, discretization, fractional differen-tiator, fractional-order differentiator, fractional-order dynamic systems, recursive, Tustin operator. I