# FAST RATIONAL INTERPOLATION OF TRANSFER FUNCTIONS OF LINEAR DYNAMIC SYSTEMS WITH DISTRIBUTED PARAMETERS

## Authors

• V. A. Kodnyanko Polytechnic Institute, Siberian Federal University, Krasnoyarsk, Russian Federation

## Keywords:

Rational interpolation, linear dynamic system, transmission function, distributed parameter system, discrete Fourier transform.

## Abstract

Contex. Fast method of rational interpolation of the transfer function of linear dynamical systems with distributed parameters is described, the values of which can be found by numerical methods or by calculating the transcendental functions of the Laplace integral transform variable. The method makes it possible to determine explicitly the transfer function and, in particular, the characteristic equation of such a degree, which is sufficient to meet the accuracy requirements when calculating the root quality criteria for the dynamics of automatic control systems.

Objective. According to the proposed method, rational interpolation is reduced to solving a system of linear equations, the order of which is much lower (more than twice) the order of similar systems used for rational interpolation of functions by known methods. The properties of this system are such that its solution can be obtained by special fast methods of the quadratic order of complexity.

Method. An iterative algorithm for calculating the transfer function coefficients of a linear dynamic system with distributed parameters is carried out using the methods of complex variable functions theory using the discrete Laplace transform. The proposed approach made it possible to significantly speed up the calculations by decomposing the system of linear equations with respect to the coefficients of the transfer function to a system of approximately half the order, which allows a quick solution by the methods of Trench, Berlekamp-Massey, or Euclid.

Results. An example of the practical use of an iterative algorithm for rational interpolation and calculation with a given accuracy of the root quality criteria for the dynamics of a support with gas lubrication is considered.

Conclusions. The method allows to define explicitly the characteristic equation of such a degree, which is sufficient to meet the accuracy requirements when calculating the root quality criteria for the dynamics of automatic control systems. Rational interpolation is reduced to solving a system of linear equations, the order of which is much lower (more than twice) the order of similar systems used for rational interpolation of functions by known methods. The properties of the system are such that its solution can be obtained by special fast methods of the quadratic order of complexity.

## Author Biography

### V. A. Kodnyanko, Polytechnic Institute, Siberian Federal University, Krasnoyarsk

Dr. Sc., Professor

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