IFAC PapersOnLine 50-1 (2017) 13020–13025 ScienceDirect Available online at www.sciencedirect.com 2405-8963 © 2017, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved. Peer review under responsibility of International Federation of Automatic Control. 10.1016/j.ifacol.2017.08.1999 © 2017, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved. Keywords: NMR, Field-Frequency Lock, PID, Bloch Equations, LS 1. INTRODUCTION NMR allows to gather information about properties of an unknown sample by studying its resonance frequency ω 0 when placed in a known, constant magnetic field B 0 . The resonance frequency ω 0 is in fact given by ω 0 = -γB 0 (1) where γ is the gyromagnetic ratio typical of the nuclear specie (may not be known a priori) and B 0 is the main magnetic field, typically generated by a resistive or superconducting magnet. If the value of B 0 is known and stable, it is then possible to identify the nuclear specie in the sample, as well as to study molecular structures and interactions. The FFL system is a well-known approach to avoid magnetic field oscillations, which may degrade the performance of the NMR experiment. The idea is to obtain an indirect but very fine grained measure of the magnetic field fluctuations from a parallel NMR experi- ment, that is carried out over a known sample (e.g. 2H) experi- encing the same magnetic field we wish to control (Hoult et al. (1978); Kan et al. (1978); Maly et al. (2006); Samra (2008); Yanagisawa et al. (2008); Jiang et al. (2010); Li et al. (2011)). If a field deviation ∆B(t) (which may arise from current oscillations or from external electromagnetic disturbances) is present, Equation (1) can be written as ω 0 +∆ω(t)= -γ(B 0 +∆B(t)) therefore ∆B(t) results in a frequency deviation ∆ω(t) such that ∆ω(t)= -γ∆B(t) (2) ⋆ This project has received funding from the European Union’s Horizon 2020 research and innovation programme under grant agreement No 668119 (project IDentIFY). where the value of γ is known for the lock sample. The NMR lock signal is obtained after the quadrature detector and oscillates at ∆ω(t); it is used to setup a closed loop which must reduce oscillations in the magnetic field. In FFC NMR a standard control loop takes care of the tracking of the field profile, but cannot provide the desired precision during the measurement phase. The FFL loop must then be used when the field reaches a neighbourhood of the desired measurement value. This means that the FFL must deal with the following requirements: • steady state perfect tracking of a step reference; • maximum settling time T sett smaller than a given value; • disturbance rejection. Since no FFL systems for FFC are currently available, it is necessary to update the conventional solutions to cope with the former specifications. According to the literature, different approaches are possible to implement the FFL. The classical one is to realize the loop as a Phase Locked Loop (PLL), where the NMR lock signal is compared to a reference one and an error signal proportional to ∆ω(t) is generated. This error signal can be used to feed a P or PI regulation block (see Kan et al. (1978); Hoult et al. (1978); Jiang et al. (2010)). Still, this approach suffers from low SNR and is ineffective in rejecting high frequency noise (Samra (2008)). To overcome these problems a different approach is required. The lock sample is stimulated with a series of low power, high repetition rate pulses, which bring the sample in the so called Steady State Free Precession (SSFP) regime (Carr (1958); Patz (1988); Gyngell (1989); Bagueira de Vasconce- los Azeredo et al. (2000)). However, this approach calls for a de- tailed model of the NMR lock experiment for a proper synthesis ∗ Dipartimento di Ingegneria Industriale e dell’Informazione, University of Pavia, Via Ferrata 5, Pavia, Italy ∗∗ Dipartimento di Ingegneria Civile e Architettura, University of Pavia, Via Ferrata 5, Pavia, Italy ∗∗∗ Stelar s.r.l., Via Enrico Fermi, 4 Mede (PV), Italy Abstract: Nuclear Magnetic Resonance (NMR) relaxometry is a powerful technique that allows to investigate the properties of materials. More advanced NMR relaxometry techniques such as Fast Field-Cycling (FFC) require the magnetic field to reach any desired value in a very short time (few milliseconds) and field oscillations to stay within few ppms. Such specifications call for the introduction of a suitable Field Frequency Lock (FFL) system. FFL relies on an indirect measure of the magnetic field which can be obtained by performing a parallel NMR experiment with a known sample. In this paper we propose a PID controller to guarantee field fluctuations to stay below the desired level and short settling time. The tuning of the controller is based on a mathematical description of the entire process, which is validated by performing real experiments. Numerical simulations show promising results that we expect to be confirmed by real experiments. G. Galuppini ∗∗ C. Toffanin ∗ D. M. Raimondo ∗ A. Provera ∗∗∗ Y. Xia ∗∗∗ R. Rolfi ∗∗∗ G. Ferrante ∗∗∗ L. Magni ∗∗ Towards a Model-Based Field-Frequency Lock for NMR