Model Predictive Control for Electron Beam Stabilization in a Synchrotron

Abstract

Electron beam stabilization in a synchrotron is a disturbance rejection problem, with hundreds of inputs and outputs, that is sampled at frequencies higher than $10$ kHz. In this feasibility study, we focus on the practical issues of an efficient implementation of model predictive control (MPC) for the heavily ill-conditioned plant of the electron beam stabilization problem. To obtain a tractable control problem that can be solved using only a few iterations of the fast gradient method, we investigate different methods for preconditioning the resulting optimization problem and relate our findings to standard regularization techniques from cross-directional control. We summarize the single- and multi-core implementations of our control algorithm on a digital signal processor (DSP), and show that MPC can be executed at the rate required for synchrotron control. MPC overcomes various problems of standard electron beam stabilization techniques, and the successful implementation can increase the stability of photon beams in synchrotron light sources.