Building Temperature Control: A Passivity-Based Approach

This paper focuses on the temperature control in a multi-zone building. The lumped heat transfer model based on thermal resistance and capacitance is used to analyze the system dynamics and control strategy. The resulting thermal network, including the zones, walls, and ambient environment, may be represented as an undirected graph. The thermal capacitances are the nodes in the graph, connected by thermal resistances as links. We assume the temperature measurements and temperature control elements (heating and cooling) are collocated. We show that the resulting input/output system is strictly passive, and any passive output feedback controller may be used to improve the transient and steady state performance without affecting the closed loop stability. The storage functions associated with passive systems may be used to construct a Lyapunov function, to demonstrate closed loop stability and motivates the construction of an adaptive feedforward control. A four-room example is included to illustrate the performance of the proposed passivity based control strategy.