Development of a mathematical model of the lidar of the collision avoidance system of the vehicle

DOI: 10.34759/trd-2023-128-16


Vataeva E. Y.

Saint Petersburg State University of Aerospace Instrumentation, 67, Bolshaya Morskaya str., Saint Petersburg, 190000, Russia



Active technological development and improvement of technologies in various industries implies the use of non-linear discrete, discrete-continuous and impulse automatic control systems (ACS), the dynamics of which is described by high-order differential equations. In the modern theory of automatic control, the problem of synthesizing the parameters of the control laws of impulse systems containing elements and devices with nonlinear static and dynamic characteristics is a complex scientific and engineering problem. In this regard, in order to successfully solve this problem for the entire range of quality indicators and for the whole variety of systems from a unified mathematical and methodological position, it is necessary to develop new methods.The development of Automatic control systems (ACS) control laws is directly related to the method of approximating a nonlinear characteristic, since it is necessary to maintain the degree of adequacy of the mathematical model. Since there are no universal approaches to the issue of approximation, for each specific case, it is required to take into account the specific modes of operation of the system. As you know, the most widely used piecewise linear approximation, however, the accuracy of the result obtained with such a mathematical model is not always sufficient. The various methods of approximation are considered, including irrational, integral, and analytical ones. This article proposes to use a polynomial approximation. As a method for synthesizing nonlinear systems, it is proposed to use the generalized Galerkin method, which makes it possible to synthesize control laws for automatic control systems of different classes (continuous automatic control systems and systems with various types of signal modulation, the dynamics of which is described by both linear and nonlinear equations of an arbitrarily high order).


nonlinear systems, nonlinear impulse systems, polynomial approximation, generalized Galerkin method


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