State space modeling for optical fiber drawing process

A method for obtaining linear state space models of the drawing process is developed. Traditionally, computational fluid dynamics methods have been used to model the drawing process. Although these models have the potential to provide very accurate details of the flow field, they incorporate thousands of dynamic states which make them unsuitable for both real-time simulations and control design. Experimental data have also been used to construct frequency response models which are suitable for control design. However, they heavily rely on the particular operating conditions for which they were obtained. Furthermore, they are constructed using large lumping techniques based on the information at the boundary and cannot predict large perturbations in the flow field. The objective of this paper is to bridge the gap between the system theoretic modeling techniques of the control engineer and the more physically motivated modeling methods of computational fluid dynamics. The method presented here consists of using the basic conservation laws (mass, momentum, and energy) to describe the mean flow of glass along the axial direction. Then, a linear state space model is obtained by spatially discretizing and linearizing the nonlinear partial differential equations. The resulting state space model incorporates all the relevant inputs and outputs of the system in a multiple-input/multiple-output framework. Furthermore, it lends itself to the application of modern control design techniques. The method is simple to implement since all that is needed is the steady state operating points, which can be computed from computational fluid dynamics simulations.