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Algorithm of obtaining the mathematical model of the system using its structural scheme

DOI 10.18127/j20700784-201812-07

Keywords:

А.А. Bisov – Post-graduate Student, Design Engineer 2 Cat., JSC «SPE «Radiosvyaz»
E-mail: glutamine@mail.ru
S.А. Bronov – Dr.Sc. (Eng.), Professor, Siberian Federal University (Krasnoyarsk)
E-mail: sa_bronov@mail.ru


JSC «SPE «Radiosvyaz» are being developed, including, electromechanical antenna guidance systems, in which electric drives of various types are used. These developments are related ti scientific research carried out in the SEL CAD SFU
[1–3] and in the department of Information technologies and mathematical support of information systems of KrasSAU [4].
It is required to develop a model of the entire system for given models of individual blocks, when appropriate control systems designing. The place of inclusion, the structure and parameters of the corresponding correcting devices are determined in the process of synthesis of the control system.
Usually the control system model is represented as an object with several inputs and several outputs, one of which is adopted by the main one.
It is necessary to be able to consider the model of the system relatively to a different combination of inputs and outputs of all indoor units, when designing. The algorithm of forming a mathematical model of a system, in fact, means obtaining a matrix of transfer functions.
In the case of a small number of blocks, it is possible to manually obtain all the necessary transfer functions. In the case of a complex structure, manually obtain are difficult and it is necessary to use facilities of automation design.
The system is specified using a structural diagram that can be executed graphically and then presented in a matrix form in accordance with the graph presentation methodology, since the block diagram is a directed graph, in the case of a small number of blocks. Wherein, general approach is used:
1) a system of equations for input and output variables is written;
2) a general expression is obtained by substituting the equations one into another.
In the case of using transfer functions in the system of equations given to obtain a system model on the basis of the structure, one can use matrix methods:
1) the introduction of vectors;
2) the matrix of transfer functions is extracted from the matrix equation between the inputs and outputs of the blocks;
3) the matrix of connecting blocks is extracted from the matrix equation of communication between blocks;
4) allocate a connection matrix from the equation for connecting external variables;
5) unite all matrix equations in the system;
6) perform successive transformations and obtain a formula for the overall transfer function of the entire system.
An algorithm for the formation of a mathematical model of the system, which is specified by the structural scheme and functions of the blocks, is considered.
The algorithm allows to automate the acquisition of a system model using a character processor and with a numerical representation of transfer function polynomials.

References:
  1. Bronov S.A., Bisov A.A. Sistema modelirovaniya dinamicheskih ob'ektov s peremennoj strukturoj // Uspehi sovremennoj radioelektroniki. 2016. № 11. S. 269–272.
  2. Bronov S.A., Nikulin N.A., Marareskul A.V., Avlasko P.V. i dr. Sistema modelirovaniya precizionnyh dinamicheskih ob'ektov // Materialy III Mezhdunar. nauch. konf. «Regional'nye problemy distancionnogo zondirovaniya Zemli» (Krasnoyarsk, 13–16 sentyabrya 2016 g.) / Nauch. red. E.A. Vaganov; otv. red. M.V. Noskov. Krasnoyarsk: Sib. feder. un-t. 2016. S. 66–69.
  3. Bronov S.A., Avlasko P.V., Povalyaev V.A., Ermakov R.A. i dr. Avtomatizaciya polucheniya matematicheskih modelej elektrodvigatelej s proizvol'nym sostavom elektromagnitnyh peremennyh sostoyaniya // Aviakosmicheskoe priborostroenie. 2013. № 6. S. 3–8.
  4. Mischenko D.D. Modelirovanie slozhnyh dinamicheskih ob'ektov // Vestnik KrasGAU. 2014. № 3 (90). S. 35–40.

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