Fabrication of Silica Optical Fibers: Optimal Control Problem Solution

Vladimir Pervadchuk,Dmitrij Dektyarev,Alex G. Kuchumov,Daria Vladimirova,Irina Gordeeva

doi:10.3390/fib9120077

Vladimir Pervadchuk, Dmitrij Dektyarev + Show 3 more

Open Access

https://doi.org/10.3390/fib9120077

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Abstract

In this work, a new approach to solving problems of optimal control of manufacture procedures for the production of silica optical fiber are proposed. The procedure of silica tubes alloying by the Modified Chemical Vapor Deposition (MCVD) method and optical fiber drawing from a preform are considered. The problems of optimal control are presented as problems of controlling distributed systems with objective functionals and controls of different types. Two problems are formulated and solved. The first of them is the problem of the temperature field optimizing in the silica tubes alloying process in controlling the consumption of the oxygen–hydrogen gas mixture (in the one- and two-dimensional statements), the second problem is the geometric optimization of fiber shape in controlling the drawing velocity of the finished fiber. In both problems, while using an analog to the method of Lagrange, the optimality systems in the form of differential problems in partial derivatives are obtained, as well as formulas for finding the optimal control functions in an explicit form. To acquire optimality systems, the qualities of lower semicontinuity, convexity, and objective functional coercivity are applied. The numerical realization of the obtained systems is conducted by using Comsol Multiphysics.

Highlights

Nowadays, fiber optics have solidly taken leading positions among various branches of science and technology [1]
Two mathematical models are considered: a simplified model and a model that takes into account the forces of surface tension and gravity
Both fiber drawing problems are solved in a one-dimensional formulation, where the control function is the winding speed of the resulted fiber

Summary

Introduction

Fiber optics have solidly taken leading positions among various branches of science and technology [1]. Plenty of information in this area of science is either insufficiently or fragmentarily studied, mostly out of reach, not reliable enough, or not even reproducible. Such a situation leads us to the fact that to improve the characteristics of the fiber, we have to put out a lot of effort and resources. First of all, this applies to optical fibers, for which there is a need for significant improvement. Thereby, research of the technology features and fiber production is a well-timed and relevant objective

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Conclusion