Approaches to control design and optimization in heat transfer problems

In this paper, boundary control problems are considered for a distributed heating system. The dynamical model of the heating system under consideration is given by a parabolic partial differential equation. In the first stage, the implementation of the Fourier method is discussed for the problem of heat convection and conduction. In the second stage, two alternative solutions to the design of tracking controllers are discussed. On the one hand, an optimal control problem is solved based on the method of integrodifferential relations. On the other hand, this procedure is used to verify the quality of a flatness-based control strategy. The results obtained by the integrodifferential approach are compared with finite-node Fourier approximations. After derivation of suitable, general-purpose solution procedures for the design of open-loop as well as closed-loop boundary control strategies, experimental results are presented. These results highlight the applicability of these procedures in a real-world experiment. For the experimental validation, a test setup at the University of Rostock has been used.