Zoned HVAC Control via PDE-Constrained Optimization

TL;DR

This paper introduces a PDE-constrained optimization algorithm for HVAC control that enhances energy efficiency and comfort by modeling air flow and temperature dynamics with PDEs, enabling precise localized control.

Contribution

The paper presents a novel PDE-based optimization framework for HVAC control, allowing for detailed modeling and control of temperature and airflow within rooms.

Findings

Significant energy savings achieved

Maintains comfort levels during optimization

Enables localized temperature and airflow control

Abstract

Efficiency, comfort, and convenience are three major aspects in the design of control systems for residential Heating, Ventilation, and Air Conditioning (HVAC) units. In this paper we propose an optimization-based algorithm for HVAC control that minimizes energy consumption while maintaining a desired temperature in a room. Our algorithm uses a Computer Fluid Dynamics model, mathematically formulated using Partial Differential Equations (PDEs), to describe the interactions between temperature, pressure, and air flow. Our model allows us to naturally formulate problems such as controlling the temperature of a small region of interest within a room, or to control the speed of the air flow at the vents, which are hard to describe using finite-dimensional Ordinary Partial Differential (ODE) models. Our results show that our algorithm produces significant energy savings without a decrease in comfort.