Passivity-Based Thermohygrometric Control in Buildings

This paper presents a modeling and control method for the thermohygrometric condition (temperature and humidity) in a multizone building. The interconnection between the zones is captured through an undirected graph. Employing an electrical circuit analogy, rooms represent capacitances, and walls and doors/windows are resistances. This model characterizes both mass and heat transfer between the zones and their coupling within each zone, extending the temperature-only resistance-capacitance models commonly used in the building control literature. By using physics-based computational fluid dynamics (CFD) simulation, we verify that this lumped-parameter model is a reasonable approximation of the physical system. The control objective is to drive the temperature and humidity of each zone into the comfort region in the psychrometric chart, using the mass-flow rate of the supplied air into the zone as the control input. In contrast to thermal-only building control, the challenge of this problem is to use a single control variable, mass-flow rate, to regulate both temperature and humidity. Our approach is to first design a feedforward control based on the desired steady-state condition within the comfort zone. We then draw on our previous work on passivity-based building temperature control to show that the thermohygrometric model around the steady state is strictly passive, from the mass-flow rate to a synthetic output combining temperature and humidity. This allows the use of any passive feedback controller combined with the feedforward to achieve robust stabilization about the desired operating point. The feedforward may be further adaptively updated, resulting in an integral-control term in the controller. Finally, to reduce the energy usage, we only apply the controller outside of the comfort zone and turn OFF the controller within the comfort zone. To illustrate the effectiveness of the proposed control strategy, simulation results using both the lumped and CFD models are presented for an existing physical six-room testbed.