Ph.D. Proposal Presentation by Zhiyong Wei
Friday, October 25, 2002
(Dr. Kok-Meng Lee, advisor)
"Modeling and Nonlinear Control of the Distributed System of Fiber Drawing Process"
Optic fiber drawing is a complex diffusion-convection process which can be described by non-linear parabolic partial differential equations (PDE). In this process, a glass rod called preform of about two meters long and several centimeters in diameter is fed into a cylindrical furnace and heated above the softening point, and then pulled downward at the bottom to form a fiber of usually 125µm in diameter.
Uniformity of the fiber diameter is one of the most important quality factors of optic fibers. During the drawing process, the fiber diameter may undergo significant fluctuations due to different sources of disturbances. The prior control designs were based on linearized models, most of which utilized draw speed as the control input and simply applied gain adjustment scheme. The draw speed may undergo large variations which adversely affect subsequent operations such as the coating process.
The objectives of this research are to develop the two-dimensional thermo-fluid dynamic model of the fiber drawing process, which serves as a basis for the development of an accurate reduced-order control model, and finally design a robust nonlinear output feedback controller to achieve better control of fiber diameter without large variations in the draw speed. Finite volume method (FVM) is used to solve the radiative transfer inside the glass instead of the Rosseland’s approximation used in the prior works. The glass interface is assumed to be optically smooth. Finite difference method is used to solve the 2-D PDEs for both glass and air flows. The prediction of the free surface profile by the 2-D full model is validated by the comparison with the experimental measurements. Empirical eigenfunctions are obtained through Karhunen-Loeve expansion with the numerical simulations of the fluid dynamic model. The reduced-order ODE model is then developed by nonlinear Galerkin’s method with the construction of approximate inertial manifold (AIM). The robust controller with a state observer is synthesized on the nonlinear ODE model via Lyapunov’s direct method. In the end, the control system is compared with the prior design through the simulations of the full dynamic model.