The increasing replacement of conventional generation with that supported by renewable energy, which is typically non-programmable and has very little or even no rotating inertia, causes an increase in the amplitude and speed of grid frequency fluctuations in the event of a power disturbance . Therefore, some new control actions have been introduced by network managers, in the form of fast ancillary services for frequency regulation. Here, we propose an iterative procedure—based on the Gauss-Newton approach—to calculate the necessary quantities of two fast innovative controllers, i.e. the controller implementing fast primary regulation and synthetic inertia support. In particular, the identification of an ‘output-error’ model also enabled us to consider non-linear characteristics in the calculation, such as dead bands on the frequency measurements that power the controllers, downward modulation of renewable generation and, for conventional generators, limits on available control power and limitations on the maximum gradient (derivative over time) of power. The approach was tested through simulations for the 2030 forecast scenario for the Sardinian electricity system.