A generalized power series and its application in the inversion of transfer functions

Ortigueira, Manuel Duarte; Trujillo, Juan J.; Martynyuk, Valeriy; Coito, Fernando

doi:10.1016/j.sigpro.2014.04.018

Cited by 20 publications

(18 citation statements)

References 11 publications

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“…6 we can conclude that the small semicircle is substantially deformed by the loss of electric energy and is under the influence of noise obstruction. Such a character of the Nyquist plot corresponds to the fractional capacitor with significant losses of electric energy [7,8].…”

Section: Solar Cell Diagnostics Systemmentioning

confidence: 98%

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Diagnostics of Solar Cells

et al. 2019

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The paper represents the mathematical model for diagnostics of solar cell. The research objectives are the problem of determining a solar cell technical condition during its operation. The solar cell diagnostics is based on the mathematical model of solar cells. The single-diode solar cell model is characterized by a slight deviation of the theoretically calculated characteristics from the characteristics of the real solar cell, one of the reasons being the complexity of the accurate measurement of the series resistance. The single-diode solar cell model uses the current and voltage ratio in the form of an implicit function and it cannot be solved directly. For its solution it is necessary to use numerical methods. This is main disadvantage of the single-diode solar cell model. The methodological approach to increasing the reliability of the solar cell diagnostic has been proposed, in terms of multi-parameter the solar cell diagnostic by applying the solar cell impedance model.

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Section: Solar Cell Diagnostics Systemmentioning

confidence: 98%

“…Paper [6] is devoted to the development of a solar cell model in the Matlab/Simulink software environment. Paper [7] presents a method for calculating series and parallel resistances of single-diode solar cell model on the basis of I-V curve analysis.…”

Section: Solar Cell Mathematical Modelmentioning

confidence: 99%

Diagnostics of Solar Cells

et al. 2019

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“…This approach has been applied to describe spatial dispersion in electrodynamics and continuum mechanics. Then, this approach has been considered in several papers [56,57], where the fractional Taylor series has been used for Laplace transform of the kernels, i.e., in the s-domain. This representation has been applied for the signal processing.…”

Section: Introductionmentioning

confidence: 99%

Generalized Memory: Fractional Calculus Approach

Tarasov

2018

Fractal Fract

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The memory means an existence of output (response, endogenous variable) at the present time that depends on the history of the change of the input (impact, exogenous variable) on a finite (or infinite) time interval. The memory can be described by the function that is called the memory function, which is a kernel of the integro-differential operator. The main purpose of the paper is to answer the question of the possibility of using the fractional calculus, when the memory function does not have a power-law form. Using the generalized Taylor series in the Trujillo-Rivero-Bonilla (TRB) form for the memory function, we represent the integro-differential equations with memory functions by fractional integral and differential equations with derivatives and integrals of non-integer orders. This allows us to describe general economic dynamics with memory by the methods of fractional calculus. We prove that equation of the generalized accelerator with the TRB memory function can be represented by as a composition of actions of the accelerator with simplest power-law memory and the multi-parametric power-law multiplier. As an example of application of the suggested approach, we consider a generalization of the Harrod-Domar growth model with continuous time.

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“…Introduction of the fractional calculus concepts and theories in the field of signals and systems, i.e., fractional signal processing (FrSP) belongs to Ortigurea and his team [26][27][28][29], and later on FrSP strategies have been used effectively for various problems such as robust design of finite impulse response filters and differintegrators [30,31], fractional-order describing functions [32], feedback control in DC motor [33] and generalization of power series for transfer function inversion [34]. Recently, FrSP adaptive algorithmbased fractional least mean square (FrLMS) method and its variant are developed by exploiting strong mathematical foundations of fractional calculus in internal optimization structure of the algorithms [35,36].…”

Section: Introductionmentioning

confidence: 99%

Design of modified fractional adaptive strategies for Hammerstein nonlinear control autoregressive systems

2015

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In this study, modified fractional least mean square (FrLMS) algorithms are formulated for parameter estimation of Hammerstein nonlinear control autoregressive system (HNCAR) by exploiting the fractional calculus concepts in weight adaptation mechanism of the algorithm. In modified FrLMS (MFrLMS) of first kind, forgetting factor is applied to exploit the strength of both standard LMS and FrLMS algorithms. The MFrLMS algorithm of second kind is based on single fractional weight adaptation term in cost function for finding the optimal values instead of considering both fractional and first derivative terms as in FrLMS approach. Performance analysis of the proposed methods are carried out on the basis of optimization ability to the true values of HNCAR system, and comparison is made in terms of accuracy, convergence and complexity. Reliability and effectiveness of the proposed scheme is validated through performance indices based on mean square error, variance account for and Nash Sutcliffe efficiency for sufficient large number of independent runs.

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A generalized power series and its application in the inversion of transfer functions

Cited by 20 publications

References 11 publications

Diagnostics of Solar Cells

Diagnostics of Solar Cells

Generalized Memory: Fractional Calculus Approach

Design of modified fractional adaptive strategies for Hammerstein nonlinear control autoregressive systems

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