Low Level RF Control Algorithms for the CERN Proton LINAC4

The CERN Linac4 Low Level RF (LLRF) uses a Linear Quadratic Gaussian regulator and an Adaptive Feed Forward to stabilize the accelerating field in the cavities in the presence of strong beam loading. A Klystron Polar Loop is also implemented to compensate the RF perturbations caused by the ripples and droop in the klystron High Voltage supply. The paper presents the important parts of the regulation, shows results as the system has evolved from first prototype (2013) to operational beams (2020), and mentions some important issues encountered during the commissioning and the first years of operation, with their mitigations.