<![CDATA[The stability and reliability of modern power systems are critically dependent on maintaining a nominal frequency. The increasing integration of non-synchronous renewable energy sources (RES) has led to a significant reduction in system inertia, making the grid more susceptible to rapid frequency excursions and a high Rate of Change of Frequency (RoCoF) following disturbances. This research investigates frequency stabilization of a synchronous generator connected to an infinite bus, modeled through the swing equation and linearized at the unstable operating point. A state-space representation of the system is derived, and its controllability and observability are verified to enable modern control design. Two approaches are implemented: full-state feedback (FSF) and observer-based output feedback using a Luenberger observer. Controller gains are designed via pole placement to achieve desired closed-loop dynamics, while observer poles are chosen to be faster to ensure rapid state estimation. Simulation results demonstrate that both controllers stabilize the otherwise unstable generator, with the observer-based feedback offering faster frequency recovery when only partial state measurements are available. A comparative analysis of rotor angle and frequency trajectories shows that FSF ensures robustness when full measurements are accessible. At the same time, the observer-based design provides a practical solution under realistic measurement limitations. The results confirm that advanced control strategies can effectively stabilize low-inertia power systems.]]>
