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.