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Cryogenics is now widely used in large accelerator projects using applied superconductivity. Economic considerations require an increase in the performance of superconducting devices. One way to achieve this is by lowering their operating temperature and cooling with superfluid helium. For this reason, large cryogenic systems operating at 1.8 K and capable of producing refrigeration capacity in the kW range have to be developed and implemented. These cryogenic systems require a large pumping capacity at very low pressure using integral cold compression or mixed cold-warm compression. This paper describes the different cooling methods using cold and hybrid cycles, describes the cycle operational capabilities, and reviews the low-pressure helium compression control strategy for these cycles developed at Fermi National Accelerator Laboratory.