Theory and Applications of Fractional Differential Equations, Volume 204 (North-Holland Mathematics Studies)
Functional Fractional Calculus for System Identification and Controls
Functional Fractional Calculus for System Identification and Controls
Fractional order control: a tutorial
ACC'09 Proceedings of the 2009 conference on American Control Conference
Calculation of all stabilizing fractional-order PD controllers for integrating time delay systems
Computers & Mathematics with Applications
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This paper discusses the application of a particular fractional-order control scheme, the PDD1/2, to the position control of a micrometric linear axis. The PDD1/2 scheme derives fromthe classical PDscheme with the introduction of the half-derivative term. The PD and PDD1/2 schemes are compared by adopting a nondimensional approach for the sake of generality. The linear model of the closed-loop system is discussed by analysing the pole location in the σ-plane. Then, different combinations of the derivative and half-derivative terms, characterized by the same settling energy in the step response, are experimentally compared in the real mechatronic application, with nonnegligible friction effects and a position set point with trapezoidal speed law. The experimental results are coherent with the nonlinear model of the controlled system and confirmthat the introduction of the half-derivative term is an interesting option for reducing the tracking error in the transient state.