Algorithms for the implementation of a low level RF control system for a klystron amplifier

Klystrons are key components of particle accelerators since they generate the radio-frequency (RF) signals required to produce high energy particle beams. They are amplifiers characterised by nonlinear input/output dynamics and are affected by external disturbances. In order to regulate the output of the klystron to the desired level, a Low Level RF (LLRF) control system is usually employed. This paper proposes three different control methods for the design a LLRF system of a klystron: classical Proportional-Integral control, Iterative Learning Control and Model Predictive Control. Theoretical aspects of the presented control algorithms are reviewed and commented. The resulting LLRF system has been implemented on a FPGA board mounted in a PXIe chassis. Experimental results are shown to compare the algorithms and to provide an evidence of their capability to fulfil the control specifications