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

I. Kempf, S. Duncan, P. J. Goulart and G. Rehm

@inproceedings{KDGR:2020,
  author = {I. Kempf and S. Duncan and P. J. Goulart and G. Rehm},
  title = {Multi-Array Electron Beam Stabilization using Block Circulant Transformation and Generalized Singular Value Decomposition},
  booktitle = {2020 IEEE Conference on Decision and Control (CDC)},
  year = {2020}
}

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.