APPLICATION OF STOCHASTIC DIFFERENTIAL EQUATIONS FOR INVESTIGATION OF A FREQUENCY-PULSED SYSTEM OF AUTOMATIC CONTROL OF THE TEMPERATURE CONTROL OF THE PROCESS OF DRAWING OF OPTICAL FIBER

. In modern conditions it is necessary to ensure reliable and high-quality functioning of a complex of interconnected information, computer and telecommunication technologies. The main medium for data transmission, at medium and long distances of telecommunications, is optical fiber. To solve the problem of the stability of the diameter of the original rods, the preservation of which ensures the specified transmission mode, constant monitoring and control of the technological process of manufacturing light guides are necessary. Another important task is to increase the dynamic accuracy of regulation. Low dynamic accuracy of regulation is due to the inertia of the regulation object and the presence of a delay. The latter is determined by the time it takes for the drawn glass product to pass from the forming zone to the sensor that determines the cross-sectional dimensions. The construction of an automatic fiber drawing control system, in turn, requires the construction of adequate models of the controlled object. The temperature mode of optical fiber drawing, which forms the specified tension and diameter of the drawn fiber, is considered as the control object. The paper presents a mathematical model of the automatic temperature control system for the optical fiber drawing process. The mathematical model is obtained in the form of stochastic differential equations in the Langevin form with its subsequent transformation into a mathematical model in the Ito form. The modified Euler method is used for the numerical solution of the stochastic differential equation. Digital statistical modeling is performed to check the adequacy of the system. The experimental study procedures are disclosed, and estimates of the mathematical expectation and variance are derived. The procedure and results of the experimental study to check the adequacy of the obtained model to the original system are presented. The paper presents estimates of the mathematical expectation and dispersion of a typical system with a sigma frequency-pulse modulator and its developed mathematical model. As can be seen, estimates of the statistical characteristics of the output signal of a typical system and its model in the form of Ito stochastic differential equations are quite close, which allows us to assert that the model is adequate to the original system. Moreover, estimates of the characteristics of random variables and processes of the stochastic model majorize similar parameters of a typical system with a sigma frequency-pulse modulator, which confirms the theoretical justification of the model obtained in this paper and makes it possible to analyze and synthesize this class of systems.