Electric vehicles (EVs) are rapidly replacing fossil-fuel-powered vehicles, creating a need for a fast-charging infrastructure that is crucial for their widespread adoption. This research addresses this challenge by improving the control of dual active bridge converters, a popular choice for high-power EV charging stations. A critical issue in EV battery charging is the smooth transition between charging stages (constant current and constant voltage) which can disrupt converter performance. This work proposes a novel feedforward control method using a combination of droop-based techniques combined with a sophisticated linear active disturbance rejection control system applied to a single-phase shift-modulated dual active bridge. This combination ensures a seamless transition between charging stages and enhances the robustness of the system against fluctuations in both input voltage and load. Numerical simulations using MATLAB/Simulink R2024a demonstrated that this approach not only enables smooth charging but also reduces the peak input converter current, allowing for the use of lower-rated components in the converter design. This translates to potentially lower costs for building these essential charging stations and faster adoption of EVs.