Low-level feedback control for the phase regulation of CLIC Drive Beam Klystrons

The requirement of luminosity loss below 1% raises tight tolerances for the phase and power stability of the CLIC drive beam (DB) klystrons and consequently for the high voltage pulse ripple of the modulators. A low-level RF (LLRF) feedback system needs to be developed and combined with the modulator in order to guarantee the phase and amplitude tolerances. To this aim, three feedback control strategies were investigated, i) Proportional Integral (PI) controller, ii) Linear Quadratic Integral Regulator (LQI) and iii) Model Predictive Controller (MPC). The klystron, as well as the incident phase noise were modelled and used for the design and evaluation of the controllers. First simulation results are presented along with future steps and directions.