  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.
