Manufacture of Microstructured Optical Fibers: Problem of Optimal Control of Silica Capillary Drawing Process

Abstract

The effective control of any technological process is essential in ensuring high-quality finished products. This is particularly true in manufacturing knowledge-intensive and high-tech products, including microstructured photonic crystal fibers (PCF). This paper addresses the issues of stabilizing the optimal control of the silica capillary drawing process. The silica capillaries are the main components of PCF. A modified mathematical model proposed by the authors is used as the basic model of capillary drawing. The uniqueness of this model is that it takes into account the main forces acting during drawing (gravity, inertia, viscosity, surface tension, pressure inside the drawn capillary), as well as all types of heat transfer (heat conduction, convection, radiation). In the first stage, the system of partial differential equations describing heat and mass transfer was linearized. Then, the problem of the optimal control of the drawing process was formulated, and optimization systems for the isothermal and non-isothermal cases were obtained. In the isothermal case, optimal adjustments of the drawing speed were obtained for different objective functionals. Thus, the proposed approach allows for the constant monitoring and adjustment of the observed state parameters (for example, the outer radius of the capillary). This is possible due to the optimal control of the drawing speed to obtain high-quality preforms. The ability to control and promptly eliminate geometric defects in the capillary was confirmed by the analysis of the numerical calculations, according to which even 15% deviations in the outer radius of the capillary during the drawing process can be reduced to 4–5% by controlling only the capillary drawing speed.