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This paper addresses the control optimization of a 4.5 K refrigerator used in the cryogenic system of the Large Hadron Collider (LHC) at CERN. First, the compressor station with the cold-box have been modeled and simulated under PROCOS (Process and Control Simulator), a simulation environment developed at CERN. Next, an appropriate parameter identification has been performed on the simulator to obtain a simplified model of the system in order to design an Internal Model Control (IMC) enhancing the regulation of the high pressure. Finally, a floating high pressure control is proposed using a cascade control to reduce operational costs. [ABSTRACT FROM AUTHOR]