Systems requiring online discrete operating decisions, also known as actuators in the control context, are ubiquitous. In the historical development of feedback control theory relevant to process control, however, the discrete decisions were always removed from the online control problem and considered at a different level in the automation system, often using heuristic rules, such as cycling through some bank of furnaces or chillers in a pre-specified order. As a result, optimization of these discrete decisions has seen essentially no implementation in process control applications, while optimization of the continuous decisions (valve positions, applied voltages, torques, etc.) has reached a high level, as demonstrated by the widespread use of model predictive control (MPC) in the process industries. The goal of this research project is to enable optimization and feedback control of processes that have discrete as well as continuous decision variables. The PI proposes to develop both new theory and computational software to address this class of problems. The research will be conducted in close collaboration with an industrial partner, Johnson Controls, and the research results will be tested in applications involving control of heating, ventilation, and air conditioning (HVAC) systems in commercial buildings. Energy use in buildings is responsible for a significant fraction of energy consumption and carbon emissions in the US.
The proposed new theory encompasses both nominal closed-loop stability and inherent robustness to model errors and disturbances, and requires extension of standard MPC with continuous decisions (valve positions, applied voltages, torques, etc.) to MPC with both continuous and discrete variables (on/off switches for chillers, heaters, pumps; which equipment to use when during a periodic, cyclic operation, etc.). The proposed project aims to develop: (i) new theory for MPC with discrete/continuous actuators, (ii) new free-source software to solve the MPC control problem with discrete actuators, and (iii) an approach for decomposing the large-scale, complex building HVAC control problem into tractable sub-problems. The enabling computational software will be made available to all researchers in the free-source language CasADi, which has become the leading language for solving large, complex, and structured optimal control problems. Adding discrete decision variables to CasADi will provide practitioners with a tool to implement the results of this research in a broad range of industrial applications. The PI plans to train a graduate student and develop new educational materials on control system design.
