Fractional calculus application in control systems

Axtell, Michael; Bise, M.E.

doi:10.1109/naecon.1990.112826

Cited by 197 publications

(115 citation statements)

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“…Thus, our objective is to apply the fractional order control (FOC) to enhance the integer order dynamic system control performance. Pioneering works in applying fractional calculus in dynamic systems and controls and the recent developments can be found in research works of Manabe, Oustaloup, and Axtell et al [14][15][16][17].…”

Section: Introductionmentioning

confidence: 99%

Optimal Fractional Order Proportional Integral Controller for Varying Time-Delay Systems

Bhambhani

Chen

Xue

2008

IFAC Proceedings Volumes

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Section: Introductionmentioning

confidence: 99%

Optimal Fractional Order Proportional Integral Controller for Varying Time-Delay Systems

Bhambhani

Chen

Xue

2008

IFAC Proceedings Volumes

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“…Their analysis requires familiarity with fractional-order derivatives and integrals [7,8,9]. In the last decades there has been, besides the theoretical research of FO derivatives and integrals [10,11,12,13], a growing number of applications of FO calculus in many different areas such as, for example, long electrical lines, electrochemical processes, dielectric polarization, colored noise, viscoelastic materials, chaos and of course in control theory as well [8,14,15,16,17,18,19,20]. This is a confirmation of the statement that real objects are generally fractional-order, however, for many of them the fractionality is very low.…”

Section: Introductionmentioning

confidence: 99%

Identification of Fractional-Order Dynamical Systems Based on Nonlinear Function Optimization

'ak¹,

Gonzalez²,

'ak³

et al. 2013

Int. J. of Pure and Appl. Math.

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In general, real objects are fractional-order systems and also dynamical processes taking place in them are fractional-order processes, although in some types of systems the order is very close to an integer order. So we consider dynamical system whose mathematical description is a differential equation in which the orders of derivatives can be real numbers. With regard to this, in the task of identification, it is necessary to consider also the fractional order of the dynamical system. In this paper we give suitable numerical solutions of differential equations of this type and subsequently an experimental method of identification in the time domain is given. We will concentrate mainly on the identification of parameters, including the orders of derivatives, for a chosen structure of the dynamical model of the system. Under mentioned assump- tions, we would obtain a system of nonlinear equations to identify the system. More suitable than to solve the system of nonlinear equations is to formulate the identification task as an optimization problem for nonlinear function minimization. As a criterion we have considered the sum of squares of the vertical deviations of experimental and theoretical data and the sum of squares of the corresponding orthogonal distances. The verification was performed on systems with known parameters and also on a laboratory object.

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“…The corresponding system representations are of the types of infinite-dimensional or distributed-parameter systems, enriched by diverse approximating non-integer-order models, indifferently called fractional-order models. There are abundant successful examples in the literature and one can see some for example in [15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30].…”

Section: Introductionmentioning

confidence: 99%