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The printing quality delivered by a Drop-on-Demand (DoD) piezo inkjet printhead is limited mainly due to the residual oscillations in the ink channel. The maximal jetting frequency of a DoD inkjet printhead can be increased by quickly damping the residual oscillations and thus bringing an ink channel to rest after jetting an ink drop. In this paper, we propose a robust optimization-based method to design the input actuation waveform for the piezo actuator in order to improve the damping of the residual oscillations in the presence of parametric uncertainties in the ink-channel model. The proposed method obtains a robust actuation pulse by minimizing the tracking error under the parametric uncertainty. Experimental results with a small-droplet DoD inkjet printhead are presented to show the efficacy of the proposed method and the significant improvement in the ink drop consistency.