This paper presents a novel virtual synchronous machine controller for converters in power systems with a high share of renewable resources. Using an interval-based approach, the emulated inertia and damping constants are adaptively adjusted according to the frequency disturbance in the system, while simultaneously keeping the frequency within prescribed limits. Furthermore, the sufficient stability conditions for control tuning are derived. The proposed design is integrated into a state-of-the-art converter control scheme and tested through time-domain simulations. A comparative study against the existing approaches in the literature verifies the control effectiveness.