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.
Control-Oriented Modeling of Transcritical Vapor Compression Systems
Contributed by the Dynamic Systems, Measurement, and Control Division of THE AMERICAN SOCIETY OF MECHANICAL ENGINEERS for publication in the ASME JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received by the ASME Dynamic Systems and Control Division April 16, 2003; final revision August 19, 2003. Associate Editor: N. Manring.
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Rasmussen, B. P., and Alleyne, A. G. (April 12, 2004). "Control-Oriented Modeling of Transcritical Vapor Compression Systems ." ASME. J. Dyn. Sys., Meas., Control. March 2004; 126(1): 54–64. https://doi.org/10.1115/1.1648312
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