The electrical grid is evolving from a network consisting of mostly synchronous machines to a mixture of synchronous machines and inverter-based resources such as wind, solar, and energy storage. This transformation has led to a decrease in mechanical inertia, which necessitate a need for the new resources to provide frequency responses through their inverter interfaces... In this paper we proposed a new strategy based on model predictive control to determine the optimal active-power set-point for inverters in the event of a disturbance in the system. Our framework explicitly takes the hard constraints in power and energy into account, and we show that it is robust to measurement noise, limited communications and delay by using an observer to estimate the model mismatches in real-time. We demonstrate the proposed controller significantly outperforms an optimally tuned virtual synchronous machine on a standard 39-bus system under a number of scenarios. In turn, this implies optimized inverter-based resources can provide better frequency responses compared to conventional synchronous machines. (read more)