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.

Vapor compression systems form the basis for the majority of air conditioning and refrigeration systems. A primary control challenge addressed here is the coupled nonlinear multiple-input-multiple-output (MIMO) dynamics associated with the multiphase heat and mass transfer in the primary refrigerant loop. This paper develops a MIMO gain scheduled control strategy to regulate system efficiency while meeting changing demands for cooling capacity. An approach based on the Youla parameterization is shown to be a generalization of the more common local controller network method, while exposing several degrees of design freedom that can be exploited to improve stability. The challenge of guaranteeing stability of the nonlinear closed loop systems, despite endogenous and arbitrarily fast gain scheduling, is addressed. Experimental results confirm the effectiveness of the proposed approach.