Building Temperature Control with Adaptive Feedforward

A common approach to the modeling of temperature evolution in a multi-zone building is to use thermal resistance and capacitance to model zone and wall dynamics. The resulting thermal network may be represented as an undirected graph. The thermal capacitances are the nodes in the graph, connected by thermal resistances as links. The temperature measurements and temperature control elements (heating and cooling) in this lumped model are collocated. As a result, the 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 motivate the construction of an adaptive feedforward control to compensate for the variation of the ambient temperature and zone heat loads (due to changing occupancy). The approach lends itself naturally to an inner-outer loop control architecture where the inner loop is designed for stability, while the outer loop balances between temperature specification and power consumption. Energy efficiency consideration may be added by adjusting the target zone temperature based on user preference and energy usage. The initial analysis uses zone heating/cooling as input, but the approach may be extended to more general model where the zonal mass flow rate is the control variable. A four-room example with realistic ambient temperature variation is included to illustrate the performance of the proposed passivity based control strategy.