Modeling by numerical reduction of modes for multivariable control of an optical-fiber draw process
Motivated by a need for a method to derive practical and physical-based dynamic models that capture the essential characteristics of an optical-fiber draw process for precision control of diameter uniformity, we extend the Karhunen-Loeve decomposition technique with a Galerkin procedure to derive a reduced-order model (ROM) for a multivariable distributed-parameter system. We validated the ROM derived from a high-fidelity physics-based model by simulating a modern optical-fiber draw process, the numerical solutions for which have been experimentally verified in our earlier studies. Perturbation studies demonstrated that the 24th-order ROM agrees remarkably well with the original nonlinear semi-two-dimensional and quasi-one-dimensional distributed models. We further examine the efficiency of the ROM in the context of a model-based H/sub /spl infin///LQG fiber drawing control system for the regulation of the fiber diameter and tension. The results show that variations in fiber diameter can be reduced significantly by appropriately distributing the number of retained eigenmodes among the physical state variables in the ROM. We also demonstrate that controlling the surrounding air temperature in addition to the draw speed is very effective in regulating both the fiber diameter and tension while simultaneously keeping the draw speed and temperature fluctuations to a minimum. Note to Practitioners-Because of the stringent production requirements (on draw speed, tension, and temperature), diameter uniformity is a challenging distributed control problem in modern fiber production where progressively larger diameter preforms are drawn at higher speeds. The reduced-order model offers an effective way to observe physical variables in a multivariable distributed-parameter system, which may not be physically measured. While developed in the context of fiber diameter control, the modeling techniques presented in this paper are applicable to other material processing systems, such as deposition thickness control in semiconductor wafer manufacturing.