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A closed-loop control system for damping undesired longitudinal oscillations of particle bunches in heavy-ion synchrotrons is presented. The system is based on technologies like digital signal processors (DSPs), modern field programmable gate arrays (FPGAs), and direct digital synthesis (DDS). After describing the technological challenges, the design of the system is presented, and some theoretical background is given. Finally, measurement results are presented which are in good agreement with simulations and theoretical predictions.