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Number 1 - March 2016
Volume 26 - 2016
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
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.
Keywords
heat transfer, predictive control, optimal control, state and disturbance estimation, distributed parameter systems, sensitivity analysis