1. Multi-Array Electron Beam Stabilization using Block-Circulant Transformation and Generalized Singular Value Decomposition
- Author
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Guenther Rehm, Stephen R. Duncan, Idris Kempf, and Paul J. Goulart
- Subjects
Accelerator Physics (physics.acc-ph) ,0209 industrial biotechnology ,Magnetic domain ,Computer science ,020209 energy ,FOS: Physical sciences ,02 engineering and technology ,Systems and Control (eess.SY) ,Topology ,Electrical Engineering and Systems Science - Systems and Control ,Matrix decomposition ,Singular value ,Matrix (mathematics) ,020901 industrial engineering & automation ,Transformation (function) ,Control theory ,Singular value decomposition ,0202 electrical engineering, electronic engineering, information engineering ,FOS: Electrical engineering, electronic engineering, information engineering ,Physics - Accelerator Physics ,Actuator ,Generalized singular value decomposition ,Circulant matrix - Abstract
We introduce a novel structured controller design for the electron beam stabilization problem of the UK’s national synchrotron light source. Because changes to the synchrotron will not allow the application of existing control approaches, we develop a novel method to diagonalize the multi-input multi-output (MIMO) system. A generalized singular value decomposition (GSVD) is used to simultaneously diagonalize the actuator response matrices, which is applicable to an arbitrary number of actuator dynamics in a cross-directional setting. The resulting decoupled systems are regulated using mid-ranged control and the controller gains derived as a function of the generalized singular values. In addition, we exploit the inherent block-circulant symmetry of the system. The performance of our controller is demonstrated using simulations that involve machine data.
- Published
- 2020
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