Reduced Order Modeling of Transcritical AC System Dynamics Using Singular Perturbation

Bryan Rasmussen, Andrew Alleyne, Rajat Shah

Research output: Contribution to journalConference articlepeer-review


This paper presents a reduced order dynamic model of a transcritical air-conditioning system, specifically suited for multivariable controller design. An 11th 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 5th 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.

Original languageEnglish (US)
Pages (from-to)2264-2269
Number of pages6
JournalProceedings of the American Control Conference
StatePublished - 2003
Event2003 American Control Conference - Denver, CO, United States
Duration: Jun 4 2003Jun 6 2003

ASJC Scopus subject areas

  • Electrical and Electronic Engineering


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