IEEE Transactions on Automatic Control, Vol.56, No.3, 697-702, 2011
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(v), 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.
Keywords:Delta-domain;delta operator;differential operator;discretization;fractional calculus;fractional-order control (FOC)