О УСТОЙЧИВОСТИ ЧЕТЫРЁХПОЛЮСНИКА ПУАНКАРЕ-СТЕКЛОВА ДЛЯ РЕШЕНИЯ ЗАДАЧ ПО ПОЛУНАТУРНОМУ МОДЕЛИРОВАНИЮ СИСТЕМ

Abstract

The article considers the stability of the Poincare–Steklov filter both from the point of viewof the theory of four-poles and from the point of view of iterative numerical methods for solving asystem of linear algebraic equations. HIL simulation involves splitting the initial system into parts, with one part being modeled numerically on a computer, and the second part is represented by a realphysical object. The parts of the system exchange data with each other through a hardware-softwareinterface, which can be implemented in different ways and should ensure stability, as well as convergenceof the results of HIL simulation to the results of modeling the original system. The variants ofconstructing software and hardware interfaces ITM, TLM, TFA, PCD, DIM, GCS and the Poincare-Steklov filter are described in the relevant literature sources. At the first stage, the article formulatedin a generalized form the problem of analyzing the stability of a system divided into parts using thePoincaré-Steklov filter. The parameters of this system are found. At the second stage, the analysis ofthe stability of the system divided into parts was carried out both from the point of view of the theoryof quadripoles and numerical methods for solving a system of linear algebraic equations. At the nextstage, the article presents the results of numerical modeling of the initial and partitioned system inMATLAB. When modeling in parts, the parts of the system exchanged data with each other at eachstep of the simulation only once with a delay of h. This method of numerical modeling of a systemdivided into parts is as close as possible to the processes occurring during HIL modeling of systems.A comparison of the obtained simulation results of the initial and fragmented system allowed us toconclude that the Poincare-Steklov filter, with the correct choice of values of stabilizing parameters,allows for stability and convergence of the results of HIL modeling of systems, and can also easilyensure the stability of the results of PHIL modeling.