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Abstract

The paper presents a method for reducing the order of the thermal dynamics model of a building or room, obtained by application of a lumped parameter method. The reduced model has the same dynamic characteristics as the primary model, while additionally it is an observable one. The described model order reduction method involves the identification and aggregation of non-distinguishable state variables. The paper presents a sample calculation confirming the validity of the deliberations. The proposed reduction method of state variables can be used with other dynamic systems provided that the assumptions concerning the structures of the system matrices are fulfilled.

Practical application : The use of simplified but accurate mathematical models of the dynamics of heat in buildings enables the efficient design of high-performance control systems, e.g. the stabilisation of air temperature in the building. Simplified mathematical models also require less computing power and can be implemented in embedded control systems. This gives the ability to design, for example, distributed systems of predictive control, which requires mathematical models of controlled processes.

Keywords

Thermal modelling observability lumped parameter modelling model reduction

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Aggregation of state variables in an RC model

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