(486f) Energy Efficient Model Predictive Control of Buildings

Environmental concerns as well as increased prices of fuels have brought energy efficiency to the forefront of research priorities. Canada currently ranks as the world's sixth largest user of primary energy. A significant portion of that energy is spent by systems providing comfort control that regulate temperatures and humidities in buildings. Development of a systematic framework that can yield the most energy efficient comfort control, is therefore important, both economically, and environmentally.

The components to achieving energy efficient comfort control can be organized in a hierarchical fashion progressing from primary devices to air distribution and handling systems to an integrated framework with multiple primary devices. At the lowest level is the operation and control of the primary devices to provide the comfort conditions prescribed in terms of controllable variables such as temperature and humidity. At the next level is the interaction between different zones within a building. It is at this level that uncertainties that arise due to the external cooling loads (e.g., environmental effects) or the multivariable interactions between different rooms in a building must be accounted for. The topmost level includes accounting (and deciding) for discrete effects such as start up and shutdowns of primary devices, and the incorporation of energy and cost efficiency.

One commonly used primary device is a Vapor Compression Cycle (VCC). In a VCC the refrigerant enters the compressor as a superheated vapor and is compressed to a higher pressure, resulting in the superheated vapor having a higher temperature than the ambient temperature. From the compressor, the superheated refrigerant vapor enters an condenser, condensing to a sub-cooled liquid at the condenser exit as a fan blows the ambient air over the condenser. The high pressure saturated liquid then flows into an expansion valve which decreases the pressure and temperature of the refrigerant, causing a liquid-vapor mixture to form. Then, the two-phase refrigerant mixture enters an evaporator that is exposed to the environment to be cooled. The environment temperature prior to cooling is above the temperature of the refrigerant, resulting in the evaporation and subsequent heating of the refrigerant to a superheated vapor at the evaporator exit. The air, in turn is cooled and available as primary air to be distributed for cooling. The saturated vapor from the evaporator exit then flows into the compressor, completing the cycle.

The control objectives are typically defined in terms of degrees of superheat at the evaporator exit and the temperature of the environment air being cooled. A change in the temperature set point gives rise to the regulation problem while variations in the cooled environment heat loads act as disturbances. The manipulated variables are typically the compressor rpm and the expansion valve opening. Traditional VCC control strategies have included PID/PI decentralized control (i.e. multiple independent single-input-single-output (SISO) controllers) and simple on/off control see, e.g., [1, 2]. The VCC dynamics, however, are significantly nonlinear, and the control problem is subject not just to input constraints (due to valve saturation and rpm limitations) but also state constraints (requiring the superheat to be within certain bounds), motivating the use of model predictive control strategies.

In this work, implementations of adaptations of recently developed Model Predictive Control (MPC) formulations, [3, 4], on a VCC model will be demonstrated and compared with classical control techniques. The performance improvement for temperature regulation as well as disturbance handling (accounting for low and high frequency disturbances) will be demonstrated both using a linear MPC and a nonlinear MPC. Practical issues such as limited availability of measurements and robustness will be handled through robust and output feedback MPC designs and evaluated through simulations.

References

1. A. Alleyne, M. Keir, B. Hencey, L. Bin and N. Jain. Decentralized feedback structures of a vapor compression cycle system. IEEE Transactions on Control Systems Technology, 2009.

2. M. Keir, A. Alleyne. Feedback Structures for Vapor Compression Cycle Systems, New York City, July 2007. American Control Conference.

3. P. Mhaskar. Robust model predictive control design for fault-tolerant control of process systems. Ind. & Eng. Chem. Res., 45:8565-8574, 2006.

4. M. Mahmood and P. Mhaskar. Enhanced stability regions for model predictive control of nonlinear process systems. AIChE J., 54:1487-1498, 2008.