Due to climate change caused by greenhouse gases, with CO2 making up the biggest share, regulatory bodies are imposing gradually stricter demands for reduction of emissions on car manufacturers. Starting from 2021., the average emissions target for a manufacturer’s fleet is set to 95 g CO2/km, which corresponds to the reduction of 27% compared to the former target of 130 g CO2/km. These demands have motivated car manufactures to develop novel technologies in order to electrify their fleets and a favorable technology from the standpoint of cost and simplicity of integration is the 48 V electrical architecture utilizing an induction motor actuator. The induction motor, which operates both as a starter and a generator, is coupled via the timing belt with the crankshaft of an internal combustion engine (ICE) and is referenced in the literature as BSG (Belt Starter Generator). The goal of this thesis was to design a vibration damping system for the belt which couples the BSG pulley with the ICE crankshaft pulley and to test the aforementioned system on the micro level (FEAD system, i.e. Front End Accessory Drive), as well as on the system level (vehicle). To this end, a mathematical model of an induction motor was made in MATLAB/SIMULINK simulation environment, within which the control system based on the damping optimum criterion has been implemented and FEAD defined as two masses coupled via spring and a damper. In order to obtain a more accurate system response, a FEAD model utilizing the elastic belt comprised of a larger number of specialized discrete elements compared to the two mass MATLAB simplification has been designed in the AVL EXCITE TM Timing Drive. The performance of the control system on this model was tested by means of EXCITE TM and MATLAB cosimulation. Furthermore, the induction motor model and the corresponding control systems from MATLAB have been compiled as an FMU (Functional Mock-up Unit) and integrated into the existing P0 hybrid vehicle model in AVL CRUISE TM M in order to perform a system level simulation. The control system has been set up to enable “on demand” start-up and boosting of the ICE, with the BSG torque being transferred to the ICE crankshaft by means of rigid coupling. Finally, in order to capture the dynamics of the elastic belt in CRUISE TM M system simulation, the equivalent torsional stiffness and damping of the FEAD system from EXCITE TM Timing Drive have been calculated and used to parametrize the coupling between the BSG rotor and ICE crankshaft in CRUISE TM M model.