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

Andreas Rauh; Luise Senkel; Harald Aschemann; Vasily V. Saurin; Georgy V. Kostin

International Journal of Applied Mathematics and Computer Science (2016)

  • Volume: 26, Issue: 1, page 15-30
  • ISSN: 1641-876X

Abstract

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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 finitedimensional 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.

How to cite

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Andreas Rauh, et al. "An integrodifferential approach to modeling, control, state estimation and optimization for heat transfer systems." International Journal of Applied Mathematics and Computer Science 26.1 (2016): 15-30. <http://eudml.org/doc/276662>.

@article{AndreasRauh2016,
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 finitedimensional 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.},
author = {Andreas Rauh, Luise Senkel, Harald Aschemann, Vasily V. Saurin, Georgy V. Kostin},
journal = {International Journal of Applied Mathematics and Computer Science},
keywords = {heat transfer; predictive control; optimal control; state and disturbance estimation; distributed parameter systems; sensitivity analysis},
language = {eng},
number = {1},
pages = {15-30},
title = {An integrodifferential approach to modeling, control, state estimation and optimization for heat transfer systems},
url = {http://eudml.org/doc/276662},
volume = {26},
year = {2016},
}

TY - JOUR
AU - Andreas Rauh
AU - Luise Senkel
AU - Harald Aschemann
AU - Vasily V. Saurin
AU - Georgy V. Kostin
TI - An integrodifferential approach to modeling, control, state estimation and optimization for heat transfer systems
JO - International Journal of Applied Mathematics and Computer Science
PY - 2016
VL - 26
IS - 1
SP - 15
EP - 30
AB - 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 finitedimensional 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.
LA - eng
KW - heat transfer; predictive control; optimal control; state and disturbance estimation; distributed parameter systems; sensitivity analysis
UR - http://eudml.org/doc/276662
ER -

References

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