Magnetic resonance (MR) scanners are important tools in medical diagnostics and in many areas of neuroscience. MR technology is moving towards ultra-high field (UHF) 7T and 9.4T scanners which provide more signal intensity. However they also suffer from inhomogeneity of the static (B0) magnetic field which can lead to artifacts and uninterpretable data. B0 shimming is a technique used to reduce inhomogeneities but most MR scanners use static shim settings for the duration of the experiment. Dynamic shim updating (DSU) updates the shim in real-time while the scan is in process and can hence reduce any fluctuations in B0 field which may arise due to patient breathing, mechanical vibrations and soforth. However DSU is currently very slow and if we intend to increase the update rate then control theory needs to be applied. This paper presents an application of basic system identification and signal processing in the context of MR systems for DSU. Although system identification of these systems has been done before, they are non-parametric frequency domain approaches. These systems can be modelled as linear multivariable systems.