Boundary control of distributed systems in the problems of quartz optical fiber drawing
DOI:
https://doi.org/10.7242/1999-6691/2018.11.4.29Keywords:
optimal stabilizing control, distributed systems, optical fiber, drawing, optimality systemAbstract
The problem of optimal control of distributed systems describing the process of optical fiber production is considered. Production of quartz optical fibers is a complex technological process, which consists of several stages. At the final stage of fiber production (fiber drawing), the fiber diameter is continuously measured and there is a good correlation between the constancy of the resulted fiber diameter and the constancy of its other characteristics along the fiber length. Therefore, all control and management systems of this process are developed on this basis. The introduction of the paper is a short excursus into the history of the theory of optimal control: main approaches to the formulation and justification of optimization problems are considered. Further, the formulation of the optimal control problem for the optical fiber drawing is proposed. A definition of the generalized solution for the problem is given. This problem is a one-dimensional problem with boundary observation and boundary control. The third part of the paper presents a detailed derivation of the optimality system. In our case, the control function is the winding speed of the resulted fiber. In conclusion, an algorithm for realizing the optimal control problem is proposed and the results are analyzed. The problem is solved for two types of initial conditions for the function of radius deviation from its stationary (programmed) solution. In both cases, optimality systems are solved using the algorithms of multi-physical modeling, and control functions are found. The obtained correction values for the winding speed of the resulted fiber correspond to real production possibilities.
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