The aim of this work is to analyse the cryogenic process for cooling superconducting radio-frequency accelerator prototype cavities in the Large Electron-Positron collider (LEP) at CERN. A liquefaction cryoplant is analysed, including the production of liquid helium at 4.5 K, the systems for distribution and control of liquid helium, and the radio-frequency system used for accelerating particles. The cryogenic control problems of the cavities based on operation experiences of the prototype modules in 1991 and different solutions and modifications for the future cavity installations are presented in detail. In addition, different techniques for specifying the control programs for new cavities are evaluated. Various diagramming techniques, standards and methodologies, and ComputerAided Software Engineering (CASE) tools, are compared regarding their practical usefulness for the cryogenic process control.