Diamond Light Source produces synchrotron radiation by accelerating electrons
to relativistic speeds. In order to maximise the intensity of the radiation,
vibrations of the electron beam are attenuated by a multi-input multi-output
(MIMO) control system actuating hundreds of magnets at kilohertz rates. For
future accelerator configurations, in which two separate arrays of magnets with
different bandwidths are used in combination, standard accelerator control
design methods based on the singular value decomposition (SVD) of the system
gain matrix are not suitable. We therefore propose to use the generalised
singular value decomposition (GSVD) to decouple a two-array cross-directional
(CD) system into sets of two-input single-output (TISO) and single-input
single-output (SISO) systems. We demonstrate that the two-array decomposition
is linked to a single-array system, which is used to accommodate
ill-conditioned systems and compensate for the non-orthogonality of the GSVD.
The GSVD-based design is implemented and validated through real-world
experiments at Diamond. Our approach provides a natural extension of
single-array methods and has potential application in other CD systems,
including paper making, steel rolling or battery manufacturing processes