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Fractional-order systems and PI/sup /spl lambda//D/sup /spl mu//-controllers

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1 Author(s)
I. Podlubny ; Dept. of Manage. & Control Eng., Tech. Univ. of Kosice, Slovakia

Dynamic systems of an arbitrary real order (fractional-order systems) are considered. The concept of a fractional-order PI λD μ-controller, involving fractional-order integrator and fractional-order differentiator, is proposed. The Laplace transform formula for a new function of the Mittag-Leffler-type made it possible to obtain explicit analytical expressions for the unit-step and unit-impulse response of a linear fractional-order system with fractional-order controller for both open- and closed-loops. An example demonstrating the use of the obtained formulas and the advantages of the proposed PI λD μ-controllers is given.

Published in:

IEEE Transactions on Automatic Control  (Volume:44 ,  Issue: 1 )