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During acceleration in SIS18/SIS100 at GSI/FAIR longitudinal beam-oscillations are expected to occur. To reduce emittance blow-up, dedicated LLRF beam feedback systems are planned. To date longitudinal beam oscillations have been damped in machine experiments with a finite-impulse-response (FIR) filter controller with 3 filter taps. An alternative approach implementing the FIR filter as a derivative estimator controller is simulated and tested. This approach shares the same controller topology and can therefore be easily integrated in the system. It exploits the fact that the sampling rate of the feedback hardware is considerably higher than the frequency of the beam oscillations. It is therefore capable of damping oscillations without overshoot within one oscillation period.