SLAC, Menlo Park, California, USA
Stanford University, Stanford, California, USA
The high luminosity upgrade plan for the LHC (HiLumi-LHC) increases the bunch intensity and the ultimate intensities require mitigation of possible intra-bunch instabilities in the SPS. Feedback systems can stabilize intra-bunch dynamics. Model based control has promise to stabilize intra-bunch dynamics but it requires a reduced order model which captures the most significant intra-bunch dynamics. We present methods for the estimation of a multi-input multi-output (MIMO) reduced order model of intra-bunch dynamics based on data generated by nonlinear macro particle simulations (CMAD, HeadTail). These linear models are used to design optimal model-based controllers. We evaluate the effectiveness of the MIMO model-based controllers for future high intensity beam conditions within the nonlinear macro particle simulations. We highlight the use of these techniques to stabilize intra-bunch motion and as an important beam dynamics measurement technique.
