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As it is planned to switch the heavy-ion synchrotron SIS18 from single- to dual-harmonic cavity operation after construction of the new Facility for Antiproton and Ion Research (FAIR), its closed-loop control system for the damping of coherent longitudinal oscillations needs an appropriate adjustment. To damp dipole oscillations, the phase shift, applied by the control system to the first cavity voltage (running with harmonic number h 1 ) has to be doubled for the second cavity (running with double frequency and harmonic number h 2 = 2 · h 1 ). Furthermore, the dipole oscillation frequency can no longer be estimated by linearization of the applied voltage like it is done in a single-harmonic cavity setting. In a dual-harmonic cavity setting as it is presented here, the dipole oscillation frequency depends nonlinearly on the bunch length. The control loop is closed by a digital signal processor, an optical splitter, and direct digital synthesizers. This paper describes the control loop and its theoretical background, and presents measurement results. In addition, simulation results and theoretical predictions are given, which are all in good agreement. Furthermore, optimal filter parameter settings are derived.