Reduced Order Modeling of Transcritical AC System Dynamics Using Singular Perturbation

This paper presents a reduced order dynamic model of a transcritical air-conditioning system, specifically suited for multivariable controller design. An 11^th order nonlinear dynamic model of the system is derived using first principles. Two methods of deriving the governing equations are presented. The first method simplifies the governing partial differential equations using lumped parameter assumptions. The second method uses the unsteady state conservation equations, and is shown to be equivalent to the first method. Analysis of the resulting model indicates that the system is singularly perturbed. The model reduction procedure exposes that the first derivation approach results in a model ill-suited for model reduction. The second modeling approach is shown to be simpler conceptually, and well suited for model reduction. The model reduction procedure yields physical insight as to which physical phenomenon are relatively fast/slow, as well as providing a 5^th order dynamic model appropriate for multivariable controller design. Although all results shown are for a transcritical cycle, the methodology presented can easily be extended to the more common subcritical cycles.