High-Speed Digital Realizations of Fractional Operators in the Delta Domain

The realization of fractional-order controllers is based on the approximation of the irrational operators by continuous or discrete transfer functions. However, at high sampling frequencies, discrete z-transfer functions approximations can be very sensitive even to small changes in coefficient values. This technical note proposes a realization of s
^ν
, in terms of transfer functions in the complex delta-domain, which improves considerably the robustness of the approximation to parameter changes and then to truncation in transfer function coefficients applied for implementation with finite word length.