For the High Luminosity LHC (HL-LHC) project at CERN, a dedicated cryogenic test facility—HL-LHC IT String—is being commissioned. This cryogenic system including a helium refrigerator, a 100 m-long cryogenic distribution line, and a low-pressure pumping system with a cold compressor (CC). A key challenge is the management of time-varying delays in the system's thermal and pressure responses, especially in the presence of dynamic components, which requires control due to its axial-centrifugal configuration and thermal constraints. This paper presents a study on the design of a model-based controller employing a Smith Predictor architecture to compensate for time-varying delays in the cryogenic process. The controller is specifically tailored to the cold compressor’s operating sequence, which includes conditioning, regulation, and controlled stop phases—all of which impose strict operational and safety requirements due to the thermal and mechanical sensitivity of the system. Simulation results using simulation software are presented alongside experimental data from the commissioning of the IT String. The proposed control strategy enables stable operation of Line B during transient phases, such as magnet pre-loading and cooldown, and ensures the preservation of system integrity by limiting thermal gradients and compressor acceleration. The study gives some perspective in advance control model-based delay compensation in complex cryogenic infrastructures like those at CERN.