To improve the equivalent inertia of DC microgrids (DCMGs), a unified control is proposed for the first time for a bi-directional DC-DC converter based super-capacitor (SC) system, whereby power smoothing and SC terminal voltage regulation can be achieved in a DCMG simultaneously. The proposed control displays good plug-and-play features using only local measurements. For quantitative analysis and effective design of the critical parameter of unified control, two indices, equivalent power supporting time and inertia contributed by the unified controlled SC system, are introduced firstly. Then, with a simple but effective reduced-order model of a DCMG, analytical solutions are obtained for the two indices. In addition, a systematic design method is presented for the proposed unified control. Finally, to verify the proposed unified control, a switching model is developed for a typical DCMG in PSCAD/EMTDC, and theoretical analyses are conducted for different operating conditions.