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# International Journal of Applied Mathematics and Computer Science

### Journal of University of Zielona Gora and Lubuskie Scientific Society

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# An integrodifferential approach to modeling, control, state estimation and optimization for heat transfer systems

Andreas Rauh
• Corresponding author
• Chair of Mechatronics, University of Rostock, Justus-von-Liebig-Weg 6, D-18059 Rostock, Germany
• Email
• Other articles by this author:
/ Luise Senkel
/ Harald Aschemann
/ Vasily V. Saurin
/ Georgy V. Kostin
• Institute for Problems in Mechanics, Russian Academy of Sciences, Pr. Vernadskogo 101-1, 119526, Moscow, Russia
• Chair of Mechanics and Control Processes, Moscow Institute of Physics and Technology, Moscow, Russia
• Email
• Other articles by this author:
Published Online: 2016-03-31 | DOI: https://doi.org/10.1515/amcs-2016-0002

## Abstract

In this paper, control-oriented modeling approaches are presented for distributed parameter systems. These systems, which are in the focus of this contribution, are assumed to be described by suitable partial differential equations. They arise naturally during the modeling of dynamic heat transfer processes. The presented approaches aim at developing finite-dimensional system descriptions for the design of various open-loop, closed-loop, and optimal control strategies as well as state, disturbance, and parameter estimation techniques. Here, the modeling is based on the method of integrodifferential relations, which can be employed to determine accurate, finite-dimensional sets of state equations by using projection techniques. These lead to a finite element representation of the distributed parameter system. Where applicable, these finite element models are combined with finite volume representations to describe storage variables that are—with good accuracy—homogeneous over sufficiently large space domains. The advantage of this combination is keeping the computational complexity as low as possible. Under these prerequisites, real-time applicable control algorithms are derived and validated via simulation and experiment for a laboratory-scale heat transfer system at the Chair of Mechatronics at the University of Rostock. This benchmark system consists of a metallic rod that is equipped with a finite number of Peltier elements which are used either as distributed control inputs, allowing active cooling and heating, or as spatially distributed disturbance inputs.

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Revised: 2015-09-12

Revised: 2015-05-28

Published Online: 2016-03-31

Published in Print: 2016-03-01

Citation Information: International Journal of Applied Mathematics and Computer Science, Volume 26, Issue 1, Pages 15–30, ISSN (Online) 2083-8492,

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