Дослідження показників точності моделей нелінійних динамічних систем

Abstract

The development and improvement of methods for calculation and control of functioning processes and operating modes of technical systems, including electronic control and modeling tools, is a serious scientific problem that has actual applied significance. Carrying out calculations to ensure the qualitative optimization of the parameters of technical means in various categories, the organization of effective production and operational control is possible only on the basis of the creation of effective methods and algorithms for the analysis of functioning processes and the accuracy of complex structures and schematic diagrams of systems and devices that are designed and developed. When developing these methods and algorithms, a set of complex scientific problems arises, the solution of which requires a number of scientific studies. The task of assessing the impact of deviations of the parameters of nonlinear dynamic systems on their movement and quality indicators is considered. Both when analyzing the accuracy of dynamic systems and when solving synthesis problems with accuracy conditions, the ability to analytically express the additional motion of dynamic systems is of great importance. The corresponding formulas for the deviations of the trajectories of the dynamic system relative to the reference trajectory and relative to the excited motion were obtained and analyzed. A method of rational determination of interpolation nodes when calculating functionals from the initial coordinates of the dynamic system is proposed. The technique refers to the selection of Gaussian quadrature nodes when calculating the quality indicators of dynamic systems with the smallest calculation error.