 RATIONAL INTERPOLATION OF TRANSFER FUNCTIONS OF LINEAR DYNAMIC SYSTEMS WITH DISTRIBUTED PARAMETERS : научное издание | Научно-инновационный портал СФУ ## RATIONAL INTERPOLATION OF TRANSFER FUNCTIONS OF LINEAR DYNAMIC SYSTEMS WITH DISTRIBUTED PARAMETERS : научное издание

Тип публикации: статья из журнала

Год издания: 2020

Идентификатор DOI: 10.17223/19988605/53/1

Ключевые слова: rational interpolation, linear dynamic system, transfer function, system with distributed parameters, discrete fourier transform

Аннотация: The paper proposes a method of rational interpolation of the transfer function of linear dynamic systems with distributed parameters, the values of which can be found by numerical methods or by calculating the transcendental functions of the Laplace integral transform variable. The method allows you to determine the transfer function in explicit form Phi(s) = Delta Y-o/Delta Y-i = b(0) + b(1)s + b(2)s(2) + ... + b(m)s(m)/1+a(1)s + a(2)s(2) + ...++a(n)s(n), where (Delta Y-i) over bar (Delta Y-o) over bar .Yoare the Laplace transformants of dynamic functions deviations of the input action and the target output function from the stationary equilibrium position of the system, n > 0, m > 0, n > m, s is the Laplace transform variable. Application of the discrete Fourier transform to the function made it possible to reduce the problem of finding the unknown coefficients of the function to a system of linear equations Db = d for an asymmetric Toeplitz matrix Dnxn = -[l(m-1) l(m-2) ... l(2m+1) l(2in) l(m) l(m-1) ... l(2m+2) l(2m+1) l(k-3) l(k-4) ... l(m-1) l(m-2) l(k-2) l(k-3) ... l(m) l(m-1],) li = 1/k Sigma j=1k Gamma(S) over bar (i,j), Gamma(s) = -Phi-1(s), k = n+m, s1 = 1, sj =esj-1.ek-1, d1 = 1, sj =esj-1.zk-1/k Sigma j=1(k)Gamma(j.) Unlike well-known methods having cubic computational complexity (n + m)3, this linear system can be solved by special fast methods of Trench, Berlekamp-Massey or Euclid, having quadratic computational complexity m(n + m). An example of the practical use of an iterative algorithm for rational interpolation of a linear dynamic system with distributed parameters and calculation with a given accuracy of the root quality criteria for the dynamics of a bearing with gas lubrication are considered. The paper proposes a method of rational interpolation of the transfer function of linear dynamic systems with distributed parameters, the values of which can be found by numerical methods or by calculating the transcendental functions of the Laplace integral transform variable. The method allows you to determine the transfer function in explicit form (equation present)where ∆Y i, ∆Y o are the Laplace transformants of dynamic functions deviations of the input action and the target output function from the stationary equilibrium position of the system, n > 0, m > 0, n > m, s is the Laplace transform variable. Application of the discrete Fourier transform to the function (s) made it possible to reduce the problem of finding the unknown coefficients of the function to a system of linear equations Db = d for an asymmetric Toeplitz matrix (equation present) Unlike well-known methods having cubic computational complexity (n + m)3, this linear system can be solved by special fast methods of Trench, Berlekamp-Massey or Euclid, having quadratic computational complexity m(n + m). An example of the practical use of an iterative algorithm for rational interpolation of a linear dynamic system with distributed parameters and calculation with a given accuracy of the root quality criteria for the dynamics of a bearing with gas lubrication are considered. © 2020 Tomsk State University. All rights reserved.

#### Издание

Журнал: VESTNIK TOMSKOGO GOSUDARSTVENNOGO UNIVERSITETA-UPRAVLENIE VYCHISLITELNAJA TEHNIKA I INFORMATIKA-TOMSK STATE UNIVERSITY JOURNAL OF CONTROL AND COMPUTER SCIENCE

Выпуск журнала: Is. 53

Номера страниц: 4-12

ISSN журнала: 19988605

Место издания: TOMSK

Издатель: TOMSK STATE UNIV

#### Авторы

• Kodnyanko V.A. (Siberian Fed Univ, Tech Sci, Polytech Inst, Krasnoyarsk, Russia)

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