Modelling and Simulation of a Two-Stage Refrigeration Cycle
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A two-stage refrigeration cycle was modelled and optimized in MATLAB. The optimum was found to be very flat, resulting in small losses from disturbances and implementation errors. The two unconstrained degrees of freedom were used to implement self-optimizing controllers. A subset of five measurements was used for the self-optimizing controller since this gave reasonably small losses. The controllers assured optimal steady-state operation of the refrigeration cycle even when disturbed. Studies of the dynamic responses of the closed-loop system showed relatively large initial deviations from the optimum caused by large time constants for the measurements. An alternative process model with constant temperature differences between the evaporator and the process stream was also investigated. The model was used to show the feasibility of including cost data in the measurements of the self-optimizing controller. It was found that the resulting controllers were able to keep the operation of the refrigeration cycle optimal despite fluctuations in the prices. In both the original and the alternative case it was found that the open-loop responses with constant inputs were almost as good as the closed-loop responses of the self-optimizing controllers. Control is thus not strictly necessary, and a constant input policy may give acceptable losses.