Model Predictive Control for Electron Beam Stabilization in a Synchrotron

Electron beam stabilization in a synchrotron is a large-scale 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 implementing model predictive control (MPC) for the heavily ill-conditioned plant of the electron beam stabilization problem at Diamond Light Source. If the terminal cost matrix of the MPC problem is obtained from the discrete-time algebraic Riccati equation (DARE), the ill-conditioned plant results in an ill-conditioned Hessian. Here, we propose obtaining a stabilizing terminal cost matrix from a modified version of the DARE that includes a constraint on the condition number of the Hessian. We implement our control algorithm on the hardware designated for the imminent Diamond Light Source upgrade, and show that the modified terminal cost matrix allows MPC to be executed at the rate required for synchrotron control. MPC overcomes various problems of standard electron beam stabilization techniques, and we show that the successful implementation can increase the stability of photon beams in synchrotron light sources.