Non-linear moving horizon state estimation and control for the superfluid helium cryogenic circuit at the large Hadron Collider

We consider the problem of temperature stabilization of the Large Hadron Collider's (LHC) superconducting magnets, cooled with superfluid helium 4 (He II). The temperature dynamics is highly non-linear, exhibiting inverse response, variable dead-times, strong couplings between process variables and strong saturation effects. Multiple operational constraints must be respected. We present a prototype application of a hybrid Non-linear Moving Horizon State Estimation - Luenberger observer (MHSE-LO) and Non-linear Model Predictive Control (NMPC). It is based on: 1) a detailed, low computing cost, first principles model of the temperature dynamics and 2) a simple optimization approach tailored for systems with stiff dynamics. The prototype control system has been tested at the LHC, demonstrating excellent, robust performance.