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Superfluid helium is used in the cryogenic circuit that cools down and stabilizes temperature of more than 1600 high performance, main superconducting magnets of the Large Hadron Collider (LHC) - the new particle accelerator at European Organization for Nuclear Research (CERN). This paper presents a simulation study of the application of Nonlinear Model Predictive Control (NMPC) to the Superfluid Helium Cryogenic Circuit. First, the new first principles, distributed parameter model of the circuit to be used in online optimization is reviewed. Then stabilization of the superconducting magnets temperature using NMPC based on the model and Continuation/ Generalized Minimum Residual (C/GMRES) algorithm is described. Finally the small computational cost of C/GMRES solution/approximation method and resulting real-time feasibility are highlighted.