Fabrication of Silica Optical Fibers: Optimal Control Problem Solution

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.