Modelling, Control and Stability Analysis of an RF Cavity in CERN LINAC4

This thesis set out to explore ways to optimize cavity control loops for CERN LINAC4 linear particle accelerator. It was found that most RF cavities in linear particle accelerators in the world modelled the cavity as a first order low pass filter, and used either PI or LQ Regulators to correct for beam loading. This thesis modelled the RF accelerating cavity as a 2nd order system, which were able to describe the dynamics of the voltage in the cavity better than the first order model generally used. The thesis also designed a Kalman observer for delay handling, an LQR controller for beam loading correction and conducted a stability analysis of the designed closed loop system. It was found, that including delayed states in the Kalman predictor, can make the Kalman observer predict current states given delayed output measurements. It was also found that including an estimate of the effect to the voltage during beam loading in the input to the Kalman filter vastly improved the response to beam loading in terms of reaction time, undershoot and settling time. Lastly it was found during the stability analysis that, depending on the controller tune, the model parameters can vary at least up to 25\% of the real cavity before the system becomes unstable.