[en] This paper deals with multivariable constrained model predictive control for Warm Compression Stations (WCS). WCSs are subject to numerous constraints (limits on pressures, actuators) that need to be satisfied using appropriate algorithms. The strategy is to replace all the PID loops controlling the WCS with an optimally designed model-based multivariable loop. This new strategy leads to high stability and fast disturbance rejection such as those induced by a turbine or a compressor stop, a key-aspect in the case of large scale cryogenic refrigeration. The proposed control scheme can be used to achieve precise control of pressures in normal operation or to avoid reaching stopping criteria (such as excessive pressures) under high disturbances (such as a pulsed heat load expected to take place in future fusion reactors, expected in the cryogenic cooling systems of the International Thermonuclear Experimental Reactor ITER or the Japan Torus-60 Super Advanced fusion experiment JT-60SA). The paper details the simulator used to validate this new control scheme and the associated simulation results on the SBTs WCS. This work is partially supported through the French National Research Agency (ANR), task agreement ANR-13-SEED-0005. (paper)