Observer-based predictive temperature control for distributed heating systems based on the method of integrodifferential relations

Abstract

In many practical applications, the control design for thermal systems aims at either preventing local overtemperatures or at achieving temperature distributions which are homogeneous in the spatial coordinates. For the purpose of control synthesis, the nonstationary system model, which is naturally given by a parabolic partial differential equation, is commonly discretized in the spatial coordinate to derive realtime applicable control laws. However, classical finite volume discretization procedures as well as finite element techniques do not allow for a direct quantification of the resulting approximation quality of the finite-dimensional model that is used for the control synthesis. In contrast, the method of integrodifferential relations (MIDR) provides a direct possibility to quantify the approximation quality. In this paper, the MIDR is therefore employed to design an observer-based predictive control strategy for a distributed heating system. Moreover, experimental results are presented in which the advantages of the MIDR system formulation are highlighted in comparison with a cascaded state and output feedback control approach derived on the basis of a classical finite volume model.