Analysis and Qualitative Observability of Two Vapor Compression Cycle Models

In this paper, a physically-oriented vapor compression cycle model is analyzed regarding different measures of the degree of observability. The high-dimensional nonlinear model employs pressures and enthalpies as state variables and involves two control inputs. A set of equilibrium points is determined over a grid of both input variables, and corresponding Taylor linearizations are performed. After an analysis of the eigenvalue locations, the observability properties are investigated using two alternative approaches: the first is based on the observability Gramians, the second on a stationary Kalman Filter. The analysis of the Gramians provides a deeper insight into the interconnections of states and individual measured outputs, whereas the Kalman Filter indicates the achievable estimation quality which is related to the variances. Moreover, a direct way to include equality constraints related to the overall mass conservation and its impact on the observability is discussed in detail.