Institute for Measurement, Control and Microtechnology
University of Ulm
Many technical systems exhibit temporal as well as spatial dynamics. This in particular concerns multiphysics systems where several physical effects are involved. Typical examples are chemical fixed-bed reactors, inductive heating or biomedical hyperthermia treatment. These so-called distributed-parameter systems are typically described by partial differential equations (PDE), which renders the dynamic optimization of these processes, for instance, to perform energy efficient setpoint changes, a difficult numerical task. This issue is further sharpened in the case of complex geometries or the presence of state/control constraints. The talk presents a “first-optimize-then-discretize” approach towards this problem by deriving the optimality conditions of the original PDE problem formulation. This allows for an elegant numerical solution using a tailored projected gradient method that outsources the numerical solution of the optimality conditions to dedicated FEM software. An advantage of this approach is the straightforward handling of complex geometries. The approach is presented in simulation studies for the inductive heating and surface hardening of a gear wheel. In addition, the talk presents first extensions of this approach to account for state constraints by using a tailored state transformation that inherently satisfies the constraints.
Knut Graichen received the diploma in Engineering Cybernetics as well as the Ph.D. degree from the University of Stuttgart in 2002 and 2006. During 2007 he was working as a postdoc at the Centre Automatique et Systèmes at Ecole des Mines in Paris (France) and from 2008 until 2010 as a senior researcher at the Automation and Control Institute of the Vienna University of Technology (Austria). Since 2010 he holds a professorship at the University of Ulm in the Faculty of Engineering and Computer Science. His main research interests are in nonlinear and optimal control s well as model predictive control with applications in mechatronics and chemical engineering.
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