Investigation, modelling and control of the 1.9 K cooling loop for superconducting magnets for the Large Hadron Collider

The temperature of the superconducting magnets for the 27 km LHC particle accelerator under construction at CERN is a control parameter with strict operating constraints imposed by (a) the maximum temperature at which the magnets can operate, (b) the cooling capacity of the cryogenic system, (c) the variability of applied heat loads and (d) the accuracy of the instrumentation. A pilot plant for studying aspects beyond single magnet testing has been constructed. This magnet test string is a 35-m full-scale model if the LHC and consists of four superconducting cryogmagnets operating in a static bath of He II at 1.9 K. An experimental investigation of the properties dynamic characteristics of the 1.9 K cooling loop of the magnet test string has been carried out. A first principle model of the system has been created. A series of experiments designed for system identification purposes have been carried out, and black box models of the system have been created on the basis on the recorded data. A Model Predictive Controller has been implemented for controlling the temperature of the 1.9 K level, using models obtained in the system identification. A temperature control with a narrower control band can in principle be achieved with an MPC-type controller than when using a PID controller. Experiments show that the controller has promising properties for tackling the dynamic challenges posed by the design of the 1.9 K cooling loop. Through the experimental investigation it has been found that: - the amount of pressurised He II in the cold mass is 180 kg - the thermal conductance of the heat exchanger tube is 74 W/Km - the velocity of the advancing liquid in the heat exchanger is in the order of 10 cm/s. The interaction between the gas and liquid phase is weak - longitudinal and transverse heat transfer capability is very high The system is found to be: - strongly non-linear primarily through He II and the density of the helium gas - non-minimum phase and exhibiting inverse response - open loop unstable, also denoted non self-regulating - containing variable transport delay The first principle model is capable of reproducing steady state and transient characteristics of the system. Of particular importance the pressure drop calculation in the heat exchanger is verified to be in good agreement with observed behaviour. Linear black box models are verified to satisfactory represent the system around the working point. Using linear models the performance of the MPC controller was found to be as good as or better than the classical PID control structure used up to date. Results indicate that improved performance will offset the increased initial cost and technical complexity of the control system and add to a robust and fault tolerant operation of the system.