Compressors are the main driving components of heating, ventilation and air conditioning (HVAC) systems in modern buildings. The performance and efficiency characteristics of these compressors are given by their characteristic curves, which map the steady-state compressor pressure rise as a function of the gas flow-rate. The peak of the characteristic curve not only determines the maximum operating capacity/efficiency of a compressor, but it also marks the inception point for a system instability known as compressor surge. Control methods for surge have been studied extensively in the literature. These controllers would allow HVAC systems to operate safely at their peak efficiency. However, a common limitation of these surge control methods is that they require exact knowledge of the compressor steady-state characteristics, and their effectiveness degrades rapidly when errors are introduced to the characteristic curve. The objective of this research project is to develop the necessary theoretical tools for this and similar situations, and to use the developed theory to design surge controllers for unknown or uncertain compressor characteristic curves. Analytical tools will be developed to maximize the safe operating region of an HVAC system under the developed controllers, and to quantify the maximum level of uncertainty in the characteristic curve that the system can tolerate. Finally, these results will lead to the development of a surge control method that allows HVAC systems to operate safely and continuously at their peak energy efficiency condition, and is robust to variations in external conditions that may affect the steady state characteristics of the system.
The main research objective of this project is to develop new control-theoretic methods for the robust stabilization of nonlinear systems with unknown or uncertain equilibrium states. Most methods for the analysis and control of nonlinear systems assume precise knowledge of the equilibrium states. It is however not always possible to obtain this information accurately when complex nonlinear dynamics are involved, due to model uncertainties and/or system chaotic dynamics. The challenges introduced by uncertain equilibrium states are amplified when nonlinear systems are subjected to strict control constraints. For example, uncertainties may introduce a static offset in the control effort, limiting the control available to compensate for unwanted external disturbances. Furthermore, uncertain equilibrium states can reduce the accuracy of modeling assumptions on the controlled plant, adding further uncertainty to the open loop dynamics. These factors can significantly reduce the domain of attraction of the steady states, even if stability is achieved. This research will provide theoretical arguments to demonstrate the validity of methods considered in the literature for the control of chaotic systems with unknown steady states. Furthermore, these control methods will be extended to incorporate new capabilities using robust and optimal control techniques. The proposed research will offer novel control methods for constrained systems with uncertain steady states, and optimization methods to maximize the corresponding domains of attraction. The motivating application of this research is active control of compressor surge to achieve increased energy efficiency of HVAC systems. Application of the developed control methods to the active control of surge with uncertain characteristic curves will demonstrate the industrial relevance of the methods developed in the project.
