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Non-stationary dynamic system characteristics recovery from three test signals
https://doi.org/10.32446/0368-1025it.2020-3-9-15
Abstract
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 nonstationary 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 an analytical 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 is discussed. In the second section, an algorithm is constructed for the exact reconstruction of the transition response of a nonstationary 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.
About the Authors
I. V. Boikov
Penza State University
Russian Federation
Russian Federation
Ilia V. Boikov
Penza
N. P. Krivulin
Penza State University
Russian Federation
Russian Federation
Nikolay P. Krivulin
Penza
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Review
For citations:
Boikov I.V., Krivulin N.P. Non-stationary dynamic system characteristics recovery from three test signals. Izmeritel`naya Tekhnika. 2020;(3):9-15. (In Russ.) https://doi.org/10.32446/0368-1025it.2020-3-9-15
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