SNS LLRF control system model design

This paper addresses part of the design of the LLRF control system for the Spallation Neutron Source. Based on the Matlab/Simulink model of the Klystron and Cavity, considered as a two input two output (TITO) system, we design a PID controller which achieves the tracking of the set point reference. The PID controller design method modifies a relay-feedback-based PID auto-tuner for a single input single output (SISO) system. The original modeling was developed for the Low Energy Demonstration Accelerator and has been modified for the SNS. The advantage of this method is that the only system information required for tuning the PID controller gains is the oscillation gain (critical gain) and the oscillation frequency (critical frequency) from the relay-feedback control of the open loop system. From the oscillation gain (critical gain), we obtain the proportional gain, and from the oscillation frequency (critical frequency), we obtain the integration time and the derivative time by applying some algebraic rules