The boundary control problem of optical fiber drawing

• Published in: Journal of physics. Conference series 2019-03, Vol.1172 (1), p.12047
• Main Authors: Pervadchuk, V P, Vladimirova, D B, Gordeeva, I V
• Format: Article
• Language: English
• Subjects: Algorithms; Boundary control; Coercivity; Convexity; Differential geometry; Initial conditions; Optical fibers; Optimal control; Partial differential equations; Shape optimization; Winding
• ISSN: 1742-6588; 1742-6596
• DOI: 10.1088/1742-6596/1172/1/012047

In the paper a new approach to solving problem of optimal control of technological process for the optical fiber production is proposed. The process of optical fiber drawing from a preform are considered. The optimal control problem of this process is formulated as problem of controlling partial differential equation system. The problem of the geometric fiber shape optimization in controlling the winding speed of the resulted fiber is formulated and solved. The optimality system in the strong form is obtained with the help of an analog of the Lagrange method. The optimal control function is determined from solving of this system. To obtain optimality system the properties of convexity, lower semi-continuity and coercivity of objective functional are used. In conclusion, an algorithm for realizing the optimal control problem is proposed and the results are analyzed. The problem is solved for several types of initial conditions for the radius deviation function from its stationary (programmed) solution. In these cases, optimality systems are solved with the help of algorithms of multi-physical modeling, control functions are found. The obtained correction values for the winding speed of the resulted fiber correspond to the possibilities of real production.