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Temperature Stabilization of Long Strings of Superconducting Magnets using Superfluid
(Actualized on 04-11-2012)
The subject of this thesis is conception, design, implementation and tests of new prototype control system for temperature stabilisation of long strings of superconducting magnets at the Large Hadron Collider (LHC).
More than 1600 NbTi superconducting magnets are used to guide and focus particles accelerated to record energy levels in the 27 km circumference LHC. NbTi is superconducting only at very low temperatures - below few Kelvin and helium is the only coolant available at these extremely low temperatures. Moreover, at temperatures below 2.15 K superfluid Helium II (He II) is available having a number of properties that make it very suitable for thermal stabilisation of the superconductors. Its key property is very high heat conductivity, being a strongly nonlinear function of temperature and peaking at 1.9 K. Thus, the superconducting magnets cooled with He II are operated in a very narrow temperature range close to the optimal value of 1.9 K and limited by the maximum value of 2.15 K. That is why in presence of various impulse-like perturbations that occur during normal operation, the quality of the temperature stabilisation of magnets cooled using He II is of great importance. Currently, the maximal temperature over each 107 m long standard cell of the cryogenic circuit cooling eight LHC main superconducting magnets is stabilized by one Proportional-Integral (PI) controller. Those controllers are tuned in a conservative manner as the temperature dynamics is highly nonlinear, non-self regulating, with varying dead times, inverse response, couplings between cells and constraints on the minimal and maximal magnet temperatures and coolant mass flow rates. Important constraints are imposed on the sum of all coolant mass flow rates and its rate of change in the 27 cells present in each of eight, 3.3 km long sectors of the LHC.
The prototype control system presented in this thesis is based on a novel first-principles, thermo-hydraulic, distributed parameters, dynamic model of the He II cryogenic circuit that cools the magnets in the LHC arcs. A simulation using the model is integrated into a novel non-linear programming algorithm characterized by very low computational cost. The algorithm is able to perform real-time optimization based on computationally expensive simulation of the stiff circuit dynamics. This enables application of moving horizon state estimation and non-linear predictive control to the stabilization of the superconducting magnets temperatures in multiple interconnected cells. The performance of the proposed prototype control system is superior to the actual control system due to the fact that it explicitly treats the non-linearities, dead times, couplings and constraints during calculation of optimal controller output.
The development of the model of the cryogenic circuit enhanced our understanding of the circuit dynamics and the complex interactions between its components. It has enabled the development of the prototype control system and it has the potential to be a basis for further applications in simulation, controls, fault detection, operator training, etc. The the real-time non-linear programming algorithm presented in this thesis demonstrates the applicability of non-linear predictive control and moving horizon state estimation to complex, highly non-linear, large scale, distributed parameters systems with stiff dynamics characterized by high computational cost of simulation.
Bibliography R Noga. "PhD Thesis description: Non-linear Model based Predictive Control (NMPC)of the Large Hydron Collider's (LHC) Super fluid Helium Cryogenic Circuit". University of Valladolid, CERN. 2008 (Download)
 R Noga. Modeling and control of the String2 LHC Prototype at CERN. Master's thesis, Gdansk University of Technology, University of Karlsruhe, Grenoble Institute of Technology, 2007. (Download)
R Noga, C de Prada. First principles modeling of the Large Hadron Colliders (LHC) Super Fluid Helium Cryogenic Circuit. In Proceedings of 20th European Modeling and Simulation Symposium (EMSS08), 2008. (Download)
 R Noga, T Ohtsuka, C de Prada, E Blanco, and J Casas. Nonlinear Model Predictive Control for the Superfluid Helium Cryogenic Circuit of the Large Hadron Collider. In Proceedings of the 2010 IEEE International Conference on Control Applications, 2010. (Download)
 R Noga, T Ohtsuka, C de Prada, E Blanco, and J Casas. Simulation Study on Application of Nonlinear Model Predictive Control to the Superfluid Helium Cryogenic Circuit. Accepted to IFAC WC2011, 2010. (Download)
 R Noga, T Ohtsuka. NMPC for stiff, distributed parameter system: Semi-Automatic Code Generation and optimality condition evaluation. Submitted to PC2011, 2010. (Download Paper,Download Presentation)