In this paper, the robustness of the dynamic instability mitigation mechanism is first examined, and then the instability mitigation phenomenon is demonstrated in a deuterium–tritium (DT) fuel target implosion by wobbling heavy-ion beams (HIBs). The results presented here show that the mechanism of the dynamic instability mitigation is rather robust against changes in the phase, the amplitude and the wavelength of the wobbling perturbation applied. In general instability would emerge from the perturbation of the physical quantity. Normally the perturbation phase is unknown, so that the instability growth rate is discussed. However, if the perturbation phase is known, the instability growth can be controlled by a superposition of perturbations imposed actively: if the perturbation is induced by, for example, a driving beam axis oscillation or wobbling, the perturbation phase could be controlled and the instability growth is mitigated by the superposition of the growing perturbations. In this paper, we realize the superposition of the perturbation by the wobbling HIBs’ illumination onto a DT fuel target in heavy-ion inertial fusion (HIF). Our numerical fluid implosion simulations present that the implosion non-uniformity is mitigated successfully by the wobbling HIBs illumination in HIF.