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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 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.

Control problems for distributed heating systems described by parabolic partial differential equations are considered in this paper. The goal of the paper is to develop an adaptive strategy including online parameter identification for efficient control of heat transfer systems. The developed strategy is based on the method of integrodifferential relations, a variational approach, and a suitable finite element technique. An adaptive control algorithm with predictive estimates of the desired output trajectories is proposed and its specific features are discussed. A validation of the presented control laws is performed taking into account the explicit local and integral error estimates resulting directly from the method of integrodifferential relations. [ABSTRACT FROM AUTHOR]

In this paper, we consider boundary control problems for a distributed heating system. The dynamical model of the heating system under consideration is given by a parabolic partial differential equation. This type of mathematical model is also a common description for other distributed parameter systems involving heat and mass transfer. After derivation of a suitable, general-purpose solution procedure for the design of flatness-based open-loop as well as closed-loop boundary control strategies, we present experimental results, which highlight the applicability in a real-world experiment. An alternative solution to the control problem is derived based on the method of integrodifferential relations. The quality of the flatness-based approximation is verified by comparison of the results of both design procedures. For the experimental validation, a test setup at the University of Rostock is used. It consists of a metallic rod equipped with a finite number of Peltier elements which are used as distributed control inputs allowing for active cooling and heating. To compensate unmodeled disturbances, closed-loop output feedback control strategies are extended by state and disturbance observers. [ABSTRACT FROM AUTHOR]