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For the new Facility for Antiproton and Ion Research (FAIR) at GSI Helmholtzzentrum für Schwerionenforschung GmbH (http://www.gsi.de), the heavy ion synchrotron SIS18 will be operated with a double harmonic cavity system. The second cavity, running at twice the fundamental frequency, is used to create a lengthened bucket which introduces nonlinearities to the control system. To damp longitudinal rigid dipole oscillations a digital feedback system consisting of a filter and an integrator is used. For the existing single-harmonic setup an FIR-filter is implemented which realizes a multiple bandpass filter with the first passband centre frequency close to the synchrotron frequency. Both, the feedback gain and the passband frequency of the filter depend on the actual value of the synchrotron frequency. It was shown by simulations and in an experiment that this setup can be transferred to a double-harmonic cavity system obtaining similar results for the region of stabilizing feedback parameters, if the oscillation frequency of the bunch barycenter is considered instead of the synchrotron frequency of a linearized bucket.