PID control for a single-stage transcritical CO_2 refrigeration cycle

摘要

In the present work, we develop a closed-loop thermal control analysis of a transcritical refrigeration cycle, operating with CO_2 as working fluid. A compressor, a gas cooler, a throttling valve and an evaporator compose the elements of the cycle. We propose a lumped energy balance model to derive a set of non-linear first order differential equations for the gas cooler and the evaporator, which are the heat exchangers where the output temperature controllability for each device is tested. The other components, i.e., the compressor and the throttling valve are modeled by simplified relationships based on simple considerations. The resulting governing equations are written in dimensionless form and subject to two control's criteria. First, we reduce the governing equations to a linear system and the well-known Proportional-Integral-Derivative (PID) control technique is used to find the best scenarios of control. Second, the non-linear system is analyzed by using a commercial numerical code to improve the general characteristics of the control. Comparing both methods, we conclude that is more difficult to reach stable conditions with a linear technique because the overshoots of temperature are more pronounced. In addition and even when it is easier to control the evaporator, the stable operation of this system can be drastically modified by the thermal performance of the gas cooler.