Recovery of the parameters of linear systems described by differential equations with variable coefficients

Krivulin, N. P.

doi:10.1007/s11018-013-0210-5

Meas Tech

2013

DOI: 10.1007/s11018-013-0210-5

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Recovery of the parameters of linear systems described by differential equations with variable coefficients

N. P. Krivulin

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Cited by 3 publications

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“…Because equations with fractional order derivatives and differences are actively being developed and used for forecast and modeling problems, methods for identifying systems described by fractional-order equations and differences are actively being developed as well. Noise-free identification methods have been treated for ordinary differential equations with fractional order derivatives [8] and for partial differential equations with fractional order derivatives [9].…”

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confidence: 99%

Identification of linear dynamic systems of fractional order with errors in variables based on an augmented system of equations

Иванов

2021

Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki

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Уравнения с производными и разностями дробного порядка находят широкое применение для описания различных процессов и явлений. В настоящее время активно развиваются методы идентификации систем, описываемых уравнениями с разностями дробного порядка. Статья посвящена идентификации дискретных динамических систем, описываемых уравнениями с разностями дробного порядка с ошибками в переменных. Задачи идентификации систем с ошибками в переменных часто бывают плохо обусловленными. В статье предложен алгоритм, использующий представление нормальной смещенной системы в виде расширенной эквивалентной системы. Данное представление позволяет уменьшить число обусловленности решаемой задачи. Тестовые примеры показали, что предложенный алгоритм обладает более высокой точностью по сравнению с алгоритмами на основе разложения Холецкого и минимизации обобщенного отношения Релея.

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mentioning

confidence: 99%

Identification of linear dynamic systems of fractional order with errors in variables based on an augmented system of equations

Иванов

2021

Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki

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Integrated GNSS antenna with an embedded inertial measurement unit

Vasilyuk

2020

Izmer. Tekhn.

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When constructing inertial/GNSS navigation systems, it is necessary to determine coordinates of a GNSS antenna relative to an inertial measurement unit. It is proposed to solve this problem by integrating of the inertial unit and GNSS antenna’s element into a common structure called an integrated antenna. This approach allows to determine the required coordinates in factory conditions, during a manufacturing of the integrated antenna. Operation principles of design modules of the integrated antenna and ways to use this antenna in the inertial/GNSS navigation systems have been described. Design features of a half-duplex digital data exchange between the antenna and a data processor have been indicated. Approaches to use this exchange to solve some service tasks of the navigation system have been proposed. It is noted that the integrated antenna has its own measuring basis. Methods of accounting of the attitude of this basis in practical applications of the integrated antennas in the single- and multi-antenna inertial/GNSS navigation systems have been described.

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Non-stationary dynamic system characteristics recovery from three test signals

Krivulin

2020

Izmer. Tekhn.

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Algorithms of exact restoration in an analytical form of dynamic characteristics of non-stationary dynamic systems are constructed. Non-stationary continuous dynamical systems modeled by Volterra integral equations of the first kind and non-stationary discrete dynamical systems modeled by discrete analogues of Volterra integral equations of the first kind are considered.The article consists of an introduction and three sections: 1) The exact restoration of the dynamic characteristics of continuous systems, 2) The restoration of the transition characteristics of discrete systems, 3) Conclusions. The introduction provides a statement of the problem and provides an overview of dynamical systems for which algorithms for exact reconstruction in ananalytical form of the impulse response (in the case of continuous systems) and the transition characteristic (in the case of discrete systems) are constructed. In the first section, the algorithm is constructed for the exact reconstruction of the impulse response of an non-stationary continuous dynamic system from three interconnected input signals. The first signal may be arbitrary, the second and third signals are associated with the first signal by integral operator. The exact formula for the Laplace transform of the impulse response, represented by an algebraic expression from the Laplace transform of the system output signals, is given. A model example illustrating the effectiveness of the algorithm is given. The practical application of the presented algorithm isdiscussed. In the second section, an algorithm is constructed for the exact reconstruction of the transition response of a non-stationary discrete dynamical system from three input signals that are interconnected. The first signal may be arbitrary, the second and third signals are associated with the first summing operator. The exact formula of the Z-transform of the transition characteristic is presented, which is represented by an algebraic expression from the Z-transform of the system output signals. A model example is given. The “Conclusions” section provides a summary of the results presented in the article and describes the dynamic systems to which the proposed algorithms can be extended.

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Recovery of the parameters of linear systems described by differential equations with variable coefficients

Cited by 3 publications

References 0 publications

Identification of linear dynamic systems of fractional order with errors in variables based on an augmented system of equations

Identification of linear dynamic systems of fractional order with errors in variables based on an augmented system of equations

Integrated GNSS antenna with an embedded inertial measurement unit

Non-stationary dynamic system characteristics recovery from three test signals

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