Supercapacitors are well suited for braking energy recovery in electrical drive application, and they can also supply electrical power to compensate voltage sags or provide energy for a short term to safely stop a device. For voltage sensitive devices a small voltage drop is only acceptable and therefore the voltage controller of backup power system should be fast. This paper analyses the design of such controller for DC bus voltage stabilization considering GaN transistor-based converter with high switching frequency. Based on Matlab calculations and Simulink simulation model, Bode plot analysis of the cascaded current and voltage control design process and simulation results have been shown. System characteristics change due to the discharge of supercapacitor stack has been considered. 2p1z controller has been developed for current loop achieving 10 kHz bandwidth. 2p1z voltage cascaded controller with variable coefficients with around 2 kHz bandwidth has been developed. The results show that developed controller is faster than controller with fixed parameters and can limit voltage drop to 44 volts and recover voltage faster than 2 ms.