This paper introduces a control strategy centered on peak current mode (PCM) control within continuous conduction mode (CCM) for regulating the terminal voltage of a constant-power load supplied by a double-inductance buck converter referred to as the "Superbuck". The analysis looks at the converter's dynamic behavior using the State Space Averaging (SSA) technique created by Middlebrook. This dynamic characterization serves the purpose of assessing and ensuring the stability and performance of the system. The suggested control strategy is validated by the experimental and simulation results that are shown, which show a favorable dynamic response and steady-state performance under significant load variations. Practical measurements have demonstrated that the mathematical models accurately predict our converter's dynamic behavior. In addition to its instantaneous response to any voltage change, we also notice that the response in the current mode is faster. In order to examine control stability, the study also includes a temporal analysis of the converter under resistive and resonant load conditions, taking into account different initial voltage conditions. We notice that the time response is a bit slow due to the delays caused by the regulation loop and the output impedance of the converter is high. The Superbuck converter is load-insensitive since it responds without oscillations, just like the output voltage. As a result, PCM has the ability to reduce or even completely eradicate the resonance phenomenon that usually affects these converters' harmonic responses. A compensation ramp is necessary to prevent the double cycle phenomenon, which is the main disadvantage of PCM. The system becomes unstable when duty cycle D surpasses 50%.