NMPC for superfluid helium cryogenics

We present a proof of concept Non-linear Model Predictive Controller (NMPC) for the Superfluid Helium Cryogenic Circuit at the Large Hadron Collider (LHC). The realtime online output feedback economic NMPC is based on a complexrst principles model. Through the paper, we highlight the practical methods leading to the real-time feasibility: 1) widespread use of approximations, handling of stiness and algebraic equations in modelling and simulation, 2) hybrid Luenberger Observer - Moving Horizon Estimation, 3) parametrisation of the optimized variables trajectories, 4) approximation of a non-linear optimization problem with inequality constraints as one with box inequality constraints and 5) application of a one-step Quasi-Newton solver. We present two NMPC congurations corresponding to different control strategies and sets of manipulated variables: #1 manipulating two control valves, tested at the LHC, and #2 manipulating the two valves and 12 electric heaters, tested in simulations.