Virtual synchronous generators (VSG) are designed to mimic the inertia and damping characteristics of synchronous generators (SG), which can improve the frequency response of a microgrid. Unlike synchronous generators whose inertia and damping are restricted by the physical characteristics of the SG, VSG parameters can be more flexibly controlled to adapt to different disturbances. This paper therefore proposes a fuzzy logic controller designed to adaptively set the parameters of the VSG during a frequency event to ensure an improved frequency nadir and rate of change of frequency (ROCOF) response. The proposed control method is implemented and tested on the power inverter for the battery energy storage system of the Banshee Microgrid Feeder 2 test case system using MATLAB/SIMULINK. The effectiveness of the adaptive control scheme is validated by comparing its performance with a constant parameter VSG, a virtual inertia only fuzzy controller, and an inertial-less inverter control.