Том 7, № 4 (2020)

The previously developed adaptation models of the program regime used the so-called “local” adaptation model, i.e. when the correction of the control currents was carried out at each moment of time regardless of their change at other times. The main element was that the adaptation algorithms used were linear, i.e. are based on the linearization of the Kirchhoff system of equations describing the evolution of the control currents during the discharge. In this paper, an algorithm for “global” adaptation of control currents is proposed. It is based on a mathematical model for controlling the discharge in an iron-core tokamak, taking into account the nonlinear behavior of a ferromagnetic. In this model, the evolution of currents is described by the Kirchhoff equations with nonlinear mutual induction coefficients, and the restrictions on the control currents, voltages, and the equilibrium and stability conditions for the plasma are included in the corresponding discrepancy functional. To find the discharge scenario, the optimal control problem is formulated and solved. The algorithm of “global” adaptation consists in the fact that information about the previous discharges is included in the minimized functional, and then the problem of optimal control is solved and a new program scenario of the discharge and the corresponding control currents and voltages are found. As a result, the model of adaptation of the program regime, first, is nonlinear, i.e. nonlinearized Kirchhoff equations are used to describe the evolution of the control currents, and, secondly, the “global” one, since the correction of all currents is carried out interdependently and consistently during the entire discharge scenario. This approach allows us to redistribute the currents in advance in the critical situation (for example, additional heating) and provide the required program regime. This is especially important in an iron-core tokamak, when the connections between the control currents become highly nonlinear. In this work, using the example of the problem of additional heating for the T-15 tokamak, the work of the “global” adaptation algorithm is demonstrated.

This article discusses forced vibrations of a rectangular two-layer piecewise homogeneous plate of constant thickness, when the material of the upper layer of the plate is elastic and the other satisfies Maxwell’s model, that is, viscoelastic. The transverse displacement of points of the contact plane of a two-layer plate is determined, which satisfies the approximate equation obtained in [1], replacing only the viscoelastic operators of the upper layer of the plate with the elastic Lames coefficients, respectively. Fluctuation rectangular is free a piecewise-homogeneous plate at nonzero initial conditions, frequencies of own fluctuations are calculated, and the analytical decision of this problem is under construction. The received theoretical results for the decision of dynamic problems of cross-section fluctuation of piecewise homogeneous two-layer plates of a constant thickness taking into account viscous properties of their material allow to count more precisely cross-section displacement of points of a plane of contact of plates at non-stationary external loadings.

The purpose of research. The article discusses the procedure for finding alternatives to a management solution based on weighted boundary conditions of firefighting, taking into account deviations in firefighting tactics. The purpose of the research is the substantiate the possibility of making reference decisions on fire extinguishing based on the analysis of alternatives of the choice of the reference decisions in the tactics of fire extinguishing. This is necessary to determine the main directions of development of the control system of fire and rescue units in the context of the development of ongoing changes in the modern mechanism of regulation in the field of fire safety within the competence of the participants in extinguishing the fire, who makes these reference decisions. Results. The result of the research shows the authors came to the conclusion that the system of making reference decisions in firefighting reflects the classical principle of minimizing empirical risk for a finite set of alternatives by the operational management in decision-making. In the task of making reference decisions depending on the boundary conditions, the fire extinguishing manager needs to find an unknown set of alternatives in achieving the main task. The authors conclude that the empirical risk function that occurs for each alternative from the set of fire-fighting boundary conditions is determined for the assessment, and the desired values should minimize this function. Deviations in the boundary conditions of fire extinguishing were considered here. In this case, the amount of distortion of the empirical risk function depends on the values of distortions in the empirical distribution of losses of the reference solution of fire extinguishing. If there are a lot of distortions, and they are large, minimizing such an empirical risk function will lead to a distortion of the desired conditions for choosing a management decision. To do this, you should resort to the class of M-means, which include almost all well-known functions for calculating the average value of the alternative to choosing a management decision when managing the actions of fire and rescue units.

Introduction. The article is devoted to the study of the synthesized concept of frictional contact of solids in crank presses. As a result of the analysis, the possibility of obtaining the maximum load characteristic of the friction contact within the interval of variation of the friction coefficient has been established. The possibility of equality of the values of the friction force of the friction contact at the boundaries of the indicated interval in the presence of a maximum and the achievement of their greatest stability under these conditions is also revealed. Materials and methods. When the angle value changes, the position of the maximum point changes. Since only the angle ratio establishes the equality of the friction forces at the boundaries of the interval of variation of the friction coefficient, changing the position of the maximum point of the function leads to a violation of this equality. In this case, the accuracy coefficient should be determined by the ratio of the maximum of the function to the smallest boundary value. To do this, it is necessary to establish trends in the change of the boundary values of the function associated with the variation of the angle. To solve this problem, a new value of the pressure tangent was presented as a product of the coefficient of variation and the base value of the tangent angle. The results of the study. The results show a high stability of the friction force during sliding of the friction contact bodies, although at large values of the pressure angle of the sensitive elements of the transducer sensor, the maximum friction force may briefly be proportional to the current value of the friction coefficient. Discussion and conclusions. As we see, the upgraded concept of frictional contact allows theoretically to obtain a very high stability of the friction force, however, due to the relatively large value of the angle and force parameter, it is used inefficiently. A necessary condition for the absence of vanishing of the output parameter of the main friction group of the friction contact in the interval of variation of the friction coefficient and the presence of the maximum function of the load capacity of the friction contact is the transfer of its full load by the sensitive elements of the additional friction group. An additional condition for the existence of a maximum is the need for the sensitive elements of the main friction group to transfer part of its full load with an equal number of friction pairs of both friction groups, and the sensitive elements to transfer the full load of the main friction group with less than the additional friction group number of friction pairs.

The article considers mathematical modeling of the technological process of drift of coordinate-sensitive detectors based on silicon with nuclear radiation, the sensor size of which is 50 × 50 × 1.5 mm and 8 bands, and compares them.