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

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Verfasserangaben:Azhar Iqbal Kashif Butt
URN (Permalink):urn:nbn:de:hbz:386-kluedo-23844
Betreuer:Rene Pinnau
Sprache der Veröffentlichung:Englisch
Jahr der Fertigstellung:2009
Jahr der Veröffentlichung:2009
Veröffentlichende Institution:Technische Universität Kaiserslautern
Titel verleihende Institution:Technische Universität Kaiserslautern
Datum der Annahme der Abschlussarbeit:28.09.2009
Datum der Publikation (Server):12.10.2009
Freies Schlagwort / Tag:First Order Optimality System; Optimal Control; Optimization Algorithms; Second Order Conditions; Tube Drawing
Fachbereiche / Organisatorische Einheiten:Fachbereich Mathematik
DDC-Sachgruppen:5 Naturwissenschaften und Mathematik / 510 Mathematik
Lizenz (Deutsch):Standard gemäß KLUEDO-Leitlinien vor dem 27.05.2011