The process and the apparatus serve for the low-temperature fractionation of air in a distillation column system, which has at least one separating column. Feed air is compressed in a main air compressor. Compressed feed air is cooled in a main heat exchanger. Cooled feed air is introduced into the distillation column system. At least one product stream is drawn off from the distillation column system, heated in the main heat exchanger and drawn off as a gaseous end product. At least one process parameter is set by a basic controller. The control of the process parameter is set by a combination of an ALC control and an MPC controller. This involves the ALC control outputting a first target value to the MPC controller. The MPC controller calculates from the first target value a setpoint value or a change to a setpoint value for a primary setpoint value output by the ALC control. The setpoint value determined by the MPC controller or a secondary setpoint value, which is calculated from the primary setpoint value output by the ALC control and the change to the setpoint value, is transmitted to the basic controller.

An air separation device comprises: a main heat exchanger; a nitrogen rectification column; a nitrogen condensers disposed in a top portion of the nitrogen rectification column; a high-purity oxygen rectification column; and an oxygen evaporator disposed in a bottom portion of the high-purity oxygen rectification column. An oxygen-containing fluid discharged from an intermediate stage of the nitrogen rectification column is rectified in the high-purity oxygen rectification column and is concentrated in the bottom portion of the high-purity oxygen rectification column.