Anti-windup compensation for electron beam stabilisation control systems on synchrotrons with rate constrained actuators

In modern synchrotron machines, electrons travelling at relativistic speeds in a closed circular path are bent by strong electromagnetic fields, which cause the electrons to lose energy in the form of synchrotron radiation. In order to achieve optimum performance, electron beam stability is a crucial parameter for modern synchrotrons. In particular, sub-micron stability is now a common requirement for the vertical position of the beam and to achieve the required performance, beam stabilisation feedback systems are used. A common nonlinearity encountered with the actuators in synchrotron feedback systems are the slew rate limits that are included in the circuits that apply power to the magnets in order to limit voltage changes. The large dimensions of synchrotron feedback systems and fast sample rates mean that robust Model Predictive Control (MPC) is not feasible. Therefore, for this application, anti-windup techniques for rate constrained nonlinearities are appropriate. The approach in this paper is anti-windup synthesis based on Internal Model Control (IMC) where it is demonstrated how IMC anti-windup synthesis for static constraints can be extended to rate constraints to improve constrained performance and guarantee stability. An Integral Quadratic Constraint (IQC) framework is used to analyse the robust stability of the system in the presence of both rate constraints and an infinity norm bounded uncertainty. Robust stability tests results and simulation of the anti-windup performance using machine data of the implementation of the control design on the Storage Ring of the UK's national synchrotron facility, Diamond Light Source are presented.