Optimal Control of Building HVAC Systems in the Presence of Imperfect Predictions, ASME Dynamic System Control Conference

OPTIMAL CONTROL OF BUILDING HVAC SYSTEMS IN THE PRESENCE OF IMPERFECT PREDICTIONS Mehdi Maasoumy ∗ Alberto Sangiovanni-Vincentelli Department of Mechanical Engineering University of California Berkeley, California 94720 Email: mehdi@me.berkeley. edu Department of Electrical Engineering University of California Berkeley, California 94720 Email: alberto@eecs.berkeley. edu ABSTRACT This paper deals with the problem of robust model predic- tive control of an uncertain linearized model of a building en- velope and HVAC system. Uncertainty of the model is due to the imperfect predictions of internal and external heat gains of the building. The Open-Loop prediction formulation of the Ro- bust Model Predictive Control (OL-RMPC) is known to be un- necessarily over-conservative in practice. Therefore, we adopt a Closed-Loop prediction formulation of Robust Model Predictive Control (CL-RMPC) which exploits an uncertainty feedback pa- rameterization of the control sequence and results in a tractable formulation of the problem. To improve on the efficiency of CL- RMPC we propose a new uncertainty feedback parameterization of the control input, which leads to a number of decision vari- ables linear in time horizon as opposed to quadratic as in previ- ous approaches. To assess our approach we compare three differ- ent robust optimal control strategies: nominal MPC which does not have a priori information of the uncertainty, OL-RMPC and CL-RMPC. We show results from a quantitative analysis of per- formance of these controllers at different prediction error values of the disturbance. Simulations show that CL-RMPC provides a higher level of comfort with respect to OL-RMPC while con- suming 36% less energy. Moreover, CL-RMPC maintains per- fect comfort level for up to 75% error in the disturbance predic- tion. Finally, the newly proposed parameterization maintains the performance of CL-RMPC while reducing the simulation time by an average of 30%. ∗ Address all correspondence to this author. 1 Introduction Advanced control algorithms are considered critical en- ablers to achieve low energy consumption in commercial build- ings. Entire sections of the ASHRAE 90.1 standard [1] are ded- icated to the specification of control requirements. Although the optimal control of an HVAC system is a complex multi-variable problem, it is standard practice to rely on simple control strate- gies that include PID and bang-bang controllers with hystere- sis. In most cases, standard sequences of operations for typi- cal installations are used by control contractors. Each sequence controls the HVAC equipment during an operation phase such as optimal start, safety shutdown and normal operation. After installation and tuning, the building is inspected by a commis- sioning agent that verifies that the building satisfies the owner’s expectations. The commissioning agent does not only verify the expected performance right after installation, but also after the building has started its operations. This short summary of design and validation practices in the building industry shows the importance of a model-based design flow for building controls. To attain energy efficiency, control algorithms need to be tailored to the physical properties of the building at hand rather than being an adaptation of a standard sequence designed for a “typical” building. To design an opti- mal controller that balances comfort and energy usage, a ther- mal model of the building is needed. To achieve building-level energy-optimality, the model should be able to capture the in- teraction between physically connected spaces in the building, occupancy schedules, and state and input constraints. Optimal control of HVAC components using model-based control techniques has shown promising results for achieving en- ergy efficiency in buildings [2–6]. However, these control tech-