# Article

 Article title APPROXIMATING MODELS OF TRANSFER FUNCTIONS OF DISTRIBUTED OBJECTS Authors I.М. Pershin, G.Е. Veselov, M.I. Pershin Section SECTION III. MODELING AND DESIGN Month, Year 07, 2015 @en Index UDC 681.5 DOI Abstract Deals with the important problem of constructing approximate models for objects with distributed parameters. This problem is important because many processes to be automated are described by partial differential equations, mathematical models which do not have analytical solutions. If an analytical solution is obtained (determined by the object"s reaction to the eigenvector-functions of the operator of the object (spatial modes)), then the transfer function for each spatial mode can be represented as a ratio of analytic entire functions. If you do not have analytical solutions, the dynamic characteristics of such objects are defined using approximation models of transfer functions of distributed object on the selected spatial modes. Consider approximation models are based on the numerical simulation of the distributed object, or using experimental results. Because distributed objects have some specific properties, such as transfer functions of distributed objects and systems at each spatial fashion inputs are described by a relation of infinite polynomials, approximation and model of such facilities should take into account the specific properties. Classical methods of approximation, in the form of aperiodic link and link with a pure time delay, give large errors in the calculation of the dynamic characteristics of distributed objects. The article aims to develop a new approximations model the transfer function of the object for each spatial fashion inputs, taking into account the specific properties of distributed objects. The scientific challenge is to develop methods for determining the parameters of the approximating segment. The technique focuses on the use of numerical simulation results of the distributed object or experimental studies on the physical object and to be constructive. The article also presents the results of the comparison of dynamic characteristics of distributed object obtained using the analytical solution, approximations models and numerical simulations. Download PDF Keywords Distributed objects; the approximation of the transfer function. References 1. Venot A., Pronrato L., Walter E. And Lebrucnec J.F. A Distribution–free criterion for "Robust Identification, with Applications in systems Modelling and Image Processing, Automatica, 1986, Vol. 22, No. 1, pp. 105-109. 2. Pasca La., Levis A.H. and Jin V.Y.-Y. On the design of Distributed Organisational structures, Automatica, 1988, Vol. 24, No. 1, pp. 81-86. 3. Valeev K.G, Zhautykov O.A. Beskonechnye sistemy differentsial'nykh uravneniy [Infinite system of differential equations]. Alma-Ata: Nauka Kazakhskoy SSR, 1974, 415 p. 4. 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