Modeling of Vapor Compression Cycles for Multivariable Feedback Control of HVAC Systems

This paper presents a new lumped-parameter model for describing the dynamics of vapor compression cycles. In particular, the dynamics associated with the two heat exchangers, i.e., the evaporator and the condenser, are modeled based on a moving-interface approach by which the position of the two-phase/single-phase interface inside the one-dimensional heat exchanger can be properly predicted. This interface information has never been included in previous lumped-parameter models developed for control design purpose, although it is essential in predicting the refrigerant superheat or subcool value. This model relates critical performance outputs, such as evaporating pressure, condensing pressure, and the refrigerant superheat, to actuating inputs including compressor speed, fan speed, and expansion valve opening. The dominating dynamic characteristics of the cycle around an operating point is studied based on the linearized model. From the resultant transfer function matrix, an interaction measure based on the Relative Gain Array reveals strong cross-couplings between various input-output pairs, and therefore indicates the inadequacy of independent SISO control techniques. In view of regulating multiple performance outputs in modern heat pumps and air-conditioning systems, this model is highly useful for design of multivariable feedback control.