[Show abstract][Hide abstract] ABSTRACT: In this paper, an integral representation of a class of Kapteyn series is proposed. Such a representation includes the most used series in practical applications. The approach uses the property of uniform convergence of the considered class and the integral representation of the Bessel functions. The usefulness of the proposed method is highlighted by providing an integral solution of Kepler’s equation and of some Kapteyn series arising in radiation problems. Moreover it allows us to generalize a result due to Meissel.
Full-text · Article · Nov 2010 · Applied Mathematics Letters
[Show abstract][Hide abstract] ABSTRACT: The number of equipments based on static converters such as uninterrupted power systems, series or shunt compensators and distributed generations systems is increasing in the actual power distribution systems. For a correct operation in grid connected condition, these equipments need the information about amplitude, phase angle and frequency of the grid fundamental voltages and currents. Since noise as harmonic pollution and frequency variations are common problems in the utility grid, then it is necessary to have systems able to extract information about the fundamental values from highly distorted signals. For these reasons, robust and accurate estimation and synchronization methods are necessary to obtain the above information also in noise environmental. In this paper, a simple and robust method for frequency estimation based on modulating functions is presented; moreover it is used in addition to an orthogonal system generation method based on the second order generalized integrator (SOGI). The combined use of the two methods has the advantages of a fast and accurate signal tracking capabilities and a good rejection to noise due to the low-pass filter properties of the modulating functions. The effectiveness of the proposed method is validated through simulated experiments and comparisons.
[Show abstract][Hide abstract] ABSTRACT: In this paper an identification method to estimate the parameters of a first order plus time delay model is proposed. Such a method directly obtains these parameters using a filtered equation and an optimization procedure without iterative calculations. A simple true/false criterion to establish if the hypothesis on the process type is correct can be easily derived. The proposed method shows an acceptable robustness to disturbances and measurement noise as it is confirmed by several simulated experiments.
[Show abstract][Hide abstract] ABSTRACT: Presented in this paper is a Prony-like polynomial-based method to identify reduced-order linear models using response-matching technique. Impulse and step inputs have been considered. The poles configuration is automatically chosen by the solution of a new regression equation which uses modified signals obtained directly from the responses. The approach uses the algebraic derivatives method in the frequency domain yielding exact formula in terms of multiple integrals of the signal, when placed in the time domain. The effectiveness of the proposed method is shown by simulated experiments.
[Show abstract][Hide abstract] ABSTRACT: In this paper the authors propose a novel method in order to identify the Hammerstein model where the nonlinear process is approximated by a static nonlinear element followed by a linear dynamic second or third-order model. The method is able to determine the parameters of the linear plant and two point of the nonlinear element in a unique step by using a filtered equation and the least-squares method. One of the most significant simulation example applied to the identification of a dc-engine is reported; it demonstrates the effectiveness of the proposed method and its acceptable robustness to disturbance and to measurements noise.
[Show abstract][Hide abstract] ABSTRACT: The aim of this paper is to give explicit formulas for the discrete orthogonal polynomials and the Moore-Penrose pseudoinverse on Gauss-Lobatto nodes. The expression of the orthogonal polynomials is proved by using some facts about the hypergeometric functions. Moreover some properties of the normal matrix on Gauss-Lobatto nodes are investigated: it can be factorized as the sum of a full rank matrix which admits a Cholesky factorization and a 2-rank matrix. Explicit formula for its inverse is also provided. Finally many numerical experiments are presented to support the theoretical results and they are provided to demonstrate the efficacy of the proposed approach.
No preview · Article · Feb 2007 · WSEAS Transactions on Mathematics
[Show abstract][Hide abstract] ABSTRACT: The inversion of the Vandermonde matrix has received much attention for its role in the solution of some problems of numerical analysis and control theory. This work deals with the problem of getting an explicit formula for the generic element of the inverse. We derive two algorithms in O(n2) and O(n3) and compare them with the Parker–Traub and the Björck–Pereyra algorithms.
Full-text · Article · Mar 2006 · Applied Mathematics and Computation
[Show abstract][Hide abstract] ABSTRACT: A simple closed-loop identification method for a first-order plus time delay is proposed. The approach directly obtains model parameters using a filtered equation and a least-squares method. Implicit in this method is a simple true/false criterion to establish whether the hypothesis on the process type is correct. Using simulations, robustness to acceptable disturbance and measurement noise is investigated.
[Show abstract][Hide abstract] ABSTRACT: This paper discusses the application of the dual-input describing function method to the analysis of closed loop pulse width modulated systems. Such method is here considered based on the use of the Kapteyn series, which allow to obtain a simple stability criterion that gives sufficient conditions for the absence of limit cycles of period multiple of that characteristic of the modulator. Some simulation results confirm the validity of the proposed criterion which can be considered a useful design tool for the selection of some parameters of the modulator although, in some cases, the result could be conservative.
[Show abstract][Hide abstract] ABSTRACT: We exhibit a simple relation concerning the elementary symmetric functions and present two applications concerning the inverse of a Vandermonde matrix and the spectral properties of square matrices.
[Show abstract][Hide abstract] ABSTRACT: Properties of Lebesgue function for Lagrange interpolation on equidistant nodes are investigated. It is proved that Lebesgue
function can be formulated both in terms of a hypergeometric function,2F1 and Jacobi polynomials. Moreover, an integral expression of Lebesgue function is also obtained and the asymptotic behavior
of Lebesgue constant is studied.
Full-text · Article · Dec 2004 · Analysis in Theory and Applications
[Show abstract][Hide abstract] ABSTRACT: Properties of Landau constant are investigated in this note. A new representation in terms of a hypergeometric function 3F2 is given and a property defining the family of asymptotic sequences of Landau constant is formalized. Moreover, we give an other asymptotic expansion of Landau constant by using asymptotic expansion of the ratio of gamma functions in the sense of Poincaré due to Tricomi and Erdélyi.
Full-text · Article · Dec 2001 · Approximation Theory and Its Applications
[Show abstract][Hide abstract] ABSTRACT: The pole placement problem for linear MIMO systems with p outputs
and m inputs is faced from the algebraic point of view. A formulation is
proposed, that allows us to analyze both theoretical and numerical
aspects of the case min(sn,p)=2 with more sharpness
[Show abstract][Hide abstract] ABSTRACT: This note discusses the problem of pole placement by static output
feedback from a geometric point of view. It is shown, without any
assumption on the system, that the pole placement can be solved by
choosing the closed-loop eigenvectors “almost freely”.
Theoretical results are derived and a numerical procedure is proposed