An optimal multivariable controller for transcritical CO₂ refrigeration cycle with an adjustable ejector

The fixed ejector has to work under a restricted operating condition to keep its positive effectiveness on the transcritical CO₂ refrigeration cycle, and a controllable ejector will be helpful. In this paper, an optimal multivariable controller based on the dynamic model is proposed to improve transcritical CO₂ refrigeration cycle with an adjustable ejector (TCRAE). A nonlinear dynamic model is first developed to model the dynamic characteristic of TCRAE. The corresponding model linearization is carried out and the simulation results reproduce transient behavior of the nonlinear model very well. Based on the developed model, an optimal multivariable controller with a tracker based linear quadratic state feedback algorithm and a predictor using steepest descent method is designed. The controller is finally applied on the experimental apparatus and the performance is verified. Using the tracker only, the gas cooler pressure and chilled water outlet temperature (cooling capacity) are well tracked rejecting the disturbances from each other. Furthermore, by the predictor, the optimal gas cooler pressure for a constant cooling capacity is actually approached on the experimental apparatus with a settling time about 700 s.