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In this paper, controversial views on the use of an integer- and fractional-order derivatives in the theory and practice of electric circuits are discussed. Maxwell's equations are definitely useful in classical circuit analyses but empirical, fractional-order modeling is advocated in specific applications, including an exemplary supercapacitor charging circuit. Thus, both methodologies can be employed...
This paper introduces a method for modeling and identification of a simple dynamical system described by fractional-order differential equation. The Grünwald-Letnikov fractional-order derivative is approximated by a discrete-time Laguerre-based model, giving rise to a new discrete-time integerorder equation modeling the considered system. An application example involves a supercapacitor charging circuit...
This paper presents a new method for modeling and identification of a simple electric circuit described by fractional-order differential equation. The Grunwald-Letnikov fractional-order derivative is approximated by its effective discrete-time model based on Laguerre filters, giving rise to a new discrete-time integer-order equation modeling the considered electric circuit. High accuracy of modeling...
This paper presents a general, modified framework for various time-domain approximations to the Grünwald-Letnikov fractional difference, namely finite fractional and Laguerre-based differences. The approximations are applied in the modeling problem for linear fractional-order state space systems, with two different implementation schemes presented.
This paper presents a new implementable strategy for modeling and identification of a fractional-order discrete-time nonlinear block-oriented SISO Wiener system. The concept of modeling of a linear dynamics by means of orthonormal basis functions (OBF) is employed to separate linear and nonlinear submodels, which enables a linear regression formulation of the parameter estimation problem. Finally,...
This paper presents a new simple form of a polynomial matrix σ-inverse introduced as a result of research works on minimum variance control (MVC) for LTI MIMO nonsquare systems. A new approach to construction of a σ-inverse of a nonsquare polynomial matrix can result in e.g. pole-free design of MVC, which is provided by specially selected degrees of freedom of the σ-inverse. A simulation example in...
This paper presents a new concept of modeling of LTI SISO discrete-time fractional-order systems, in which the Laguerre filters are employed to model both 1) the Grünwald-Letnikov fractional difference and 2) a dynamics of the LTI SISO fractional-order system. Such a ‘double-Laguerre’ concept yields original accuracy and computational results at both modeling stages, illustrated with a series of simulation...
This paper presents new results in finite-memory modeling of a discrete-time fractional derivative. The introduced normalized finite fractional derivative is shown to properly approximate its fractional derivative original, in particular in terms of the steady-state properties. A stability analysis is also presented as well as a recursive computation algorithm is offered for finite fractional derivatives.
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