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

TL;DR

This paper presents a novel structured control method for electron beam stabilization in synchrotron light sources, utilizing block-circulant transformations and generalized singular value decomposition to achieve decoupled, effective regulation.

Contribution

The paper introduces a new control design that diagonalizes multi-input multi-output systems with arbitrary actuator dynamics using GSVD, tailored for the unique constraints of synchrotron systems.

Findings

Effective stabilization demonstrated through simulations with machine data.

Decoupling of MIMO system achieved via GSVD and block-circulant symmetry.

Controller gains derived from generalized singular values.

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.