<abstract xmlns="http://www.w3.org/1999/xhtml"><p>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.</p></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.

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

Chair of Mechatronics, University of Rostock, Justus-von-Liebig-Weg 6, D-18059 Rostock, Germany

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

International Journal of Applied Mathematics and Computer Science

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

In this paper, control-oriented modeling approaches are presented for distributed parameter systems. These systems, which are in the focus of this...

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

Published Online: Mar 31, 2016

Page range: 15 - 30

Received: Sep 19, 2014

DOI: https://doi.org/10.1515/amcs-2016-0002

Keywords
heat transfer, predictive control, optimal control, state and disturbance estimation, distributed parameter systems, sensitivity analysis

© 2016 Andreas Rauh et al., published by De Gruyter Open

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

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

Published Online: Mar 31, 2016

Page range: 15 - 30

Received: Sep 19, 2014

DOI: https://doi.org/10.1515/amcs-2016-0002

Keywordsheat transfer, predictive control, optimal control, state and disturbance estimation, distributed parameter systems, sensitivity analysis

© 2016 Andreas Rauh et al., published by De Gruyter Open

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
heat transfer, predictive control, optimal control, state and disturbance estimation, distributed parameter systems, sensitivity analysis