Parameter identification of a class of time-varying systems via orthogonal shifted legendre polynomials

Hwang, Chyi; Guo, Tong‐Yi

doi:10.1016/0016-0032(84)90066-8

Cited by 22 publications

(7 citation statements)

References 23 publications

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“…By regression method, the parameters and their time-dependence can be evaluated (see Chang, R. Y, et al 1988;Hwang, C., and Guo, T. Y, 1984). Expanding the single-input and single-output of a process into generalized orthogonal polynomials yields a set of linear algebraic equations.…”

Section: Parameter Estimation In Linear Systemsmentioning

confidence: 99%

Uncertain Models and Robust Control

Weinmann¹

1991

311

126

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PrefaceControl system analysis and design are important fields in the engineering sciences. Process identification and optimum design have developed rapidly over the past decades and resulted in great engineering progress. However, many results have suffered from considerable dependence on uncertainties, mainly incorporated in the plant, in actuators and sensors, and released by other internal disturbances.More and more, methods tackling uncertainties form a central and important issue in designing feedback control systems. Choosing appropriate design methods, the influence of uncertainties on the closed-loop behaviour can be reduced to a large extent. Control systems particularly designed to manage uncertainties are called robust control systems. Robust control theory provides a design philosophy with respect to perturbed or uncertain parts of the system. This monograph is devoted to plants and their approximate models and to the discussion of their uncertainties. The thrust of the book is on systematic representation of methods for robust control.Most of the important areas of robust control are covered. The aim is to provide an introduction to the theory and methods of robust control system design, to present a coherent body of knowledge, to clarify and unify presentation, and to streamline derivations and proofs in the field of uncertainties and robust control. The book contains a thorough treatment of important material which is scattered throughout the literature.The primary goal of the text is to present significant derivations and proofs. As far as less significant proofs or lengthy derivations are concerned, only the results are outlined and the reader is referred to the literature relevant to this subject. In a few cases, some topics are set forth only as a suggestion for further reading.Some important problems treated in this book are:• How is uncertainty described and bounded when applying methods of differential equations, transfer functions or transfer matrices, state-space algorithms or some approximating calculus?• Which uncertainty or which perturbation in some special system description forces the system to instability? This question arises both for open-loop and for closed-loop systems.• Which kind of controller is able to tolerate maximum uncertainty?2In most cases stability robustness is applied but performance robustness is also a very important subject, e.g., determining the regions in the parameter space of controllers which place all the closed-loop eigenvalues into a desired region, thus satisfying the design specifications in the face of uncertain but bounded plant parameters.The book is intended specifically for practicing but mathematically inclined engineers, for postgraduate students and engineers on master's level. Moreover, the book is intended for those readers who wish to apply robust design principles and theories to real-life applications and problems.Emphasis is put on practical considerations and on applicability at the expense of extensive proofs and mathematical rigor.The ...

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Section: Parameter Estimation In Linear Systemsmentioning

confidence: 99%

Uncertain Models and Robust Control

Weinmann¹

1991

311

126

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“…A great variety of orthogonal series has been used, depending on the specific class of systems examined. Typical examples are the Walsh series (Chen and Hsiao 1975, Rao and Sivakumar 1975, Tzafestas 1978, block-pulse series (Palanisamy and Bhattacharya 1981, Kwong and Chen 198\), Laguerre series Shih 1982, Clement 1982), Chebyshev series (Paraskevopoulos and Kekkeris 1983 a), Fourier series (Paraskevopoulos et al 1983), Legendre series (Hwang and Guo 1984), and Hermite series (Paraskevopoulos and Kekkeris 1983 b). It is clear that other types of orthogonal series, such as the Jacobi, the Gegenbauer, the hypergeometric or the Bessel series, may also be used following similar procedures.…”

Section: Introductionmentioning

confidence: 98%

Parameter identification of a class of time-varying linear systems via polynomial series

Mouroutsos

Sparis

1986

International Journal of Systems Science

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A class of time-varying linear systems is identified with the use of polynomial series following a new approach. The main characteristic of this approach is the use of the operational matrix of differentiation for the derivation of the system of algebraic equations that determines the unknown coefficients of the system, instead of the operational matrix of integration. In this way, the initial or boundary conditions of the system identified need not enter the computation, and the resulting algorithm is considerably simpler. Several characteristic examples are considered.

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“…These series may also be used to establish algebraic methods for the solution of problems described by diOE erential equations, such as analysis of linear time-invariant and time-varying systems, model reduction, optimal control, and system identi cation. The problem of parameter identi cation using orthogonal includes linear time-invariant lumped and distributed systems [1], linear time-varying lumped and distributed systems [2][3], and nonlinear systems [4][5].…”

Section: Introductionmentioning

confidence: 99%

“…Also, error introduced in the solution may be diOE erent. Typical examples are the applications of Laguerre polynomials [6][7], Legendre polynomials [1][2], Chebyshev polynomials of the rst [8] and second kind [9], Fourier series [4], Walsh series [5], block-pulse series [10], Haar series [11], and Hartley series [12].…”

mentioning

confidence: 99%

Parameter Estimation Using An Orthogonal Series Expansion

Rico

Heydt²

2000

Electric Machines & Power Systems

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This paper presents an innovative alternative to estimate parameters of a system for which a dynamic model is known. The focus of this paper is the estimation of the armature circuit parameters of large utility generators using real time operating data. Other applications are possible. The alternatives considered are the use of orthogonal series expansions, in general, and the Hartley series, in particular. The main idea considers the use of orthogonal series expansions for tting operating data (e.g., voltage and currents measurements). This allows writing a set of linear algebraic equations that can be " solved" in the least squares sense for the unknown parameters. The method shown utilizes the pseudoinverse in the solution. The essence of the approach is linear state estimation. Several alternative types of orthogonal expansions are brie y discussed. Although solutions are the same in all domains, one wishes to employ the expansion that gives the most e cient computation. The approach may be used for static as well as dynamic problems. The approach is tested for noise corruption likely to be found in measurements. The method is found to be suitable for the processing of digital fault recorder data to identify synchronous machine parameters.

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Parameter identification of a class of time-varying systems via orthogonal shifted legendre polynomials

Cited by 22 publications

References 23 publications

Uncertain Models and Robust Control

Uncertain Models and Robust Control

Parameter identification of a class of time-varying linear systems via polynomial series

Parameter Estimation Using An Orthogonal Series Expansion

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