## Optimal Control of Tube Drawing Processes

• This study deals with the optimal control problems of the glass tube drawing processes where the aim is to control the cross-sectional area (circular) of the tube by using the adjoint variable approach. The process of tube drawing is modeled by four coupled nonlinear partial differential equations. These equations are derived by the axisymmetric Stokes equations and the energy equation by using the approach based on asymptotic expansions with inverse aspect ratio as small parameter. Existence and uniqueness of the solutions of stationary isothermal model is also proved. By defining the cost functional, we formulated the optimal control problem. Then Lagrange functional associated with minimization problem is introduced and the first and the second order optimality conditions are derived. We also proved the existence and uniqueness of the solutions of the stationary isothermal model. We implemented the optimization algorithms based on the steepest descent, nonlinear conjugate gradient, BFGS, and Newton approaches. In the Newton method, CG iterations are introduced to solve the Newton equation. Numerical results are obtained for two different cases. In the first case, the cross-sectional area for the entire time domain is controlled and in the second case, the area at the final time is controlled. We also compared the performance of the optimization algorithms in terms of the solution iterations, functional evaluations and the computation time.
• Optimale Steuerung bei der Herstellung von Glasröhren

• Dokument_1.pdf • Dokument_1.djvu Author: Azhar Iqbal Kashif Butt urn:nbn:de:hbz:386-kluedo-23844 Rene Pinnau Doctoral Thesis English 2009 2009 Technische Universität Kaiserslautern Technische Universität Kaiserslautern 2009/09/28 2009/10/12 First Order Optimality System; Optimal Control; Optimization Algorithms; Second Order Conditions; Tube Drawing Kaiserslautern - Fachbereich Mathematik 5 Naturwissenschaften und Mathematik / 510 Mathematik Standard gemäß KLUEDO-Leitlinien vor dem 27.05.2011