This paper presents a methodology for developing a low 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. Analysis indicates that the system exhibits multiple time scale behavior, and that model reduction is appropriate. Model reduction using singular perturbation techniques yields physical insight as to which physical phenomena are relatively fast/slow, and 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 subcritical cycles.
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