A passivity based approach to building temperature control

Abstract

Modeling and control of building HVAC systems is recently gaining a lot of importance, due to the need for energy conservation. Building HVAC systems consume a large portion of the energy consumption in buildings. Modeling the building thermal system itself is quite challenging because it is very cumbersome to accurately the model the nonlinear time varying system, especially for large buildings. Simplified lumped heat transfer models based on thermal resistance and capacitance are most commonly used to analyze the system dynamics and design control strategies. This enables the resulting thermal network, including the zones, walls, and ambient environment to 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 that 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. The performance of the proposed control strategy is verified with the help of a simulation example and the modeling methodology has been tested on data from a real testbed.