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Multi-Array Electron Beam Stabilization using Block-Circulant Transformation and Generalized Singular Value Decomposition

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Document pages: 6 pages

Abstract: We introduce a novel structured controller design for the electron beamstabilization problem of the UK s national synchrotron light source. Becausechanges to the synchrotron will not allow the application of existing controlapproaches, we develop a novel method to diagonalize the multi-inputmulti-output (MIMO) system. A generalized singular value decomposition (GSVD)is used to simultaneously diagonalize the actuator response matrices, which isapplicable to an arbitrary number of actuator dynamics in a cross-directionalsetting. The resulting decoupled systems are regulated using mid-ranged controland the controller gains derived as a function of the generalized singularvalues. In addition, we exploit the inherent block-circulant symmetry of thesystem. The performance of our controller is demonstrated using simulationsthat involve machine data.

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