Control of multi-array cross-directional systems using the generalised singular value decomposition

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 rates exceeding 10 kHz. For future accelerator configurations, in which two separate arrays of magnets with different bandwidths and constraints are used in combination, standard accelerator control design methods are not suitable. To address this, we develop a transformation based on the generalised singular value decomposition (GSVD) to decouple the two-array cross-directional (CD) dynamics into sets of two-input single-output (TISO) and single-input single-output (SISO) systems. This transformation allows the controller to be designed in modal space using SISO and TISO methods and to be tuned to each actuator array separately. The non-orthogonality of the GSVD and potentially ill-conditioned response matrices are compensated for by incorporating static compensator matrices. This approach results in a simple controller structure that can be implemented to meet the 100 kHz sampling frequency of the Diamond’s future configuration with 252 outputs and 396 inputs. The GSVD-based design is implemented and validated through real-world experiments at Diamond. Our approach provides a natural extension of the modal decomposition for single-array systems and has potential application in other CD systems, including paper making, steel rolling, or battery manufacturing processes.