Nonlinear observer design using contraction theory with application to heat exchangers having varying phase transition

Abstract

Thermo-fluid systems such as air conditioning and refrigeration systems are widely used in residential, commercial, and industrial applications. By the end of the 20th century, nearly 70 percent of U.S. households had air conditioning, and 99.5 percent had at least one refrigerator. Advanced control and monitoring of the thermo-fluid systems has become an inevitable but challenging issue in this century as the energy efficiency has become increasingly important. Air conditioning and refrigeration systems transport heat by means of refrigerant, repeating phase transition, which is a highly nonlinear process. Mixture of vapor and liquid refrigerant distributed in heat exchangers makes the process dynamics highly complex, including many state variables that are important for stringent control but are not directly measurable. In this thesis, nonlinear observers for estimating those inaccessible state variables are designed and are applied to the control and monitoring of an air conditioning system. First heat exchanger dynamics including complex phase transition phenomena are analyzed. It is shown that the order of the system varies dynamically depending on the distribution of vapor and liquid, which makes the system a varying-order switched system.

(cont.) Second, a switched observer for the varying order switched system is designed by augmentation using real system dynamics. The convergence conditions of the switched observer are derived using contraction theory. This observer design is applied to heat exchangers of an air conditioning system. The nonlinear observer design of the heat exchanger with invariant phase transition is validated by extensive experimental tests using a residential air conditioner. For the switched observer of the heat exchanger with varying phase transition, simulation validation is conducted by using the parameters from the real air conditioning system. Finally, this heat exchanger observer is applied to lubrication oil monitoring and nonlinear control for the air conditioning systems. A lubrication oil circulation observer for estimating oil concentration and oil amount in refrigerant compressors is developed based on state observers of heat exchangers. It is validated by experimental tests and can be applied directly to residential and commercial air conditioning and refrigeration systems to improve reliability of the systems.