The fractional order, inertial discrete transfer function using Atangana-Baleanu and FOBD operators [PDF]
Archives of Control SciencesIn the paper a new, fractional order, discrete transfer function model of an elementary inertial plant is proposed. The model uses Atangana-Baleanu and discrete Fractional Order Backward Difference operators to describe of the fractional derivative. Such
Krzysztof Oprzędkiewicz
semanticscholar +2 more sources
Adaptive Control of Milling Forces under Fractional Order Holds [PDF]
, 2007 This paper introduces a novel discrete-time modelreference based control of the tool-work-piece interaction force in a milling process. The novelty of the scheme relies on the use of a fractional order hold (FROH) instead of a traditional zero order hold
De la Sen Parte, Manuel +1 more
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Fractional transformations of generalised functions [PDF]
, 2009 A distributional theory of fractional transformations is developed. A constructive approach, based on the eigenfunction expansion method pioneered by A. H.
Lamb, Wilson +2 more
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Analysis of discrete time schemes for milling forces control under fractional order holds [PDF]
, 2013 In this paper, discrete time model reference control schemes for practical milling using different discretization of the continuous-time plant are presented. First, a basic controller scheme is addressed where a fractional order hold with pre-fixed value
De la Sen, Manuel +11 more
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Diffusive representations for fractional Laplacian: systems theory framework and numerical issues [PDF]
, 2009 Bridging the gap between an abstract definition of pseudo-differential operators, such as (-\Delta)^{\gamma} for - 1/2 < \gamma < 1/2, and a concrete way to represent them has proved difficult; deriving stable numerical schemes for such operators is not ...
Matignon, Denis
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Stabilization of a fractional-order chain of integrators: a contraction-based approach [PDF]
, 2013 In this paper, stabilization of a chain of fractional-order integrators is attempted. The stability is proved using contraction analysis.
SPURGEON, S +8 more
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Fractional power NARX model identification using a harmony search algorithm [PDF]
, 2012 A novel type of discrete-time fractional-powernonlinear autoregressive with exogenous input (FPNARX) modelis introduced for system identification, modeling and prediction.Parameter estimation of such a model is a nonlinear optimizationproblem.
Zhao, Yifan +7 more
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Fractional Exponential Function and Its Application
, 2022 : In this paper, we obtain the limit representation of fractional exponential function. The application of fractional exponential function is illustrated.
Chii-Huei Yu
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Fractional variational problems depending on indefinite integrals [PDF]
, 2012 We obtain necessary optimality conditions for variational problems with a Lagrangian depending on a Caputo fractional derivative, a fractional and an indefinite integral.
Pooseh, Shakoor +8 more
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Stability of closed-loop fractional-order systems and definition of damping contours for the design of controllers [PDF]
, 2012 Fractional complex order integrator has been used since 1991 for the design of robust control-systems. In the CRONE control methodology, it permits the parameterization of open loop transfer function which is optimized in a robustness context.
Oustaloup, Alain +2 more
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