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-her 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-infinity/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.