Design and verification of controllers for longitudinal oscillations using optimal control theory and numerical simulation: predictions for PEP-II

We present a technique for the design and verification of efficient bunch-by-bunch controllers for damping longitudinal multibunch instabilities. The controllers attempt to optimize the use of available feedback amplifier power-one of the most expensive components of a feedback system-and define the limits of closed loop system performance. Our design technique alternates between analytic computation of single bunch optimal controllers and verification on a multibunch numerical simulator. The simulator identifies unstable coupled bunch modes and predicts their growth and damping rates. The results from the simulator are shown to be in reasonable agreement with analytical calculations based on the single bunch model. The technique is then used to evaluate the performance of a variety of controllers proposed for PEP-II