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Journal of Vibration and Control
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Discretization of Complex-order Algorithms for Control Applications

Ramiro S. Barbosa

Institute of Engineering of Porto, Rua Dr Antonio Bernardino de Almeida, 431, 4200-072 Porto, Portugal, rsb{at}isep.ipp.pt

J.A. Tenreiro Machado

Institute of Engineering of Porto, Rua Dr Antonio Bernardino de Almeida, 431, 4200-072 Porto, Portugal

Manuel F. Silva

Institute of Engineering of Porto, Rua Dr Antonio Bernardino de Almeida, 431, 4200-072 Porto, Portugal

In this article we describe several methods for the discretization of the differintegral operator sa, where {alpha} = u + jv is a complex value. The concept of the conjugated-order differintegral is also introduced, which enables the use of complex-order differintegrals while still producing real-valued time responses and transfer functions. The performance of the resulting approximations is analysed in both the time and frequency domains. Several results are presented that demonstrate its utility in control system design.

Key Words: Fractional calculus • discretization • complex-order differintegrals • conjugated-order differintegrals • fractional-order control

Journal of Vibration and Control, Vol. 14, No. 9-10, 1349-1361 (2008)
DOI: 10.1177/1077546307087445
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