Low-inertia power systems can experience high rates of change of frequency and large frequency deviations during power imbalances. Inertia emulation using high power density storage system such as a Flywheel Energy Storage System (FESS), can help limit the rate of change of frequency, following sudden changes in the generation or demand. In this presentation, a new adaptive inertia emulation controller for a high-speed FESS is proposed. In order to validate the behavior of the FESS with the proposed control design, the controller is implemented on a real 60 kW high-speed FESS, using the concept of rapid control prototyping. The performance of the FESS, equipped with the adaptive inertia emulation controller, is evaluated by means of Power Hardware-in-the-Loop (PHIL) simulations using the real-time simulation model of a low voltage microgrid. In order to reduce the overall loop delay, the established PHIL setup uses fiber optic connections to the power amplifier and several I/O expansion units. The State-space Nodal (SSN) solver is also applied for reducing the simulation time step of the microgrid model. The results of PHIL simulations show that the FESS with the newly proposed adaptive inertia emulation controller outperforms the previously suggested adaptive control designs, in terms of reducing the maximum rate of change of frequency and limiting the maximum frequency deviation, while not demanding significantly more energy from the FESS.