This Automatic Generation Control (AGC) is vital for maintaining the balance between power generation and load demand. However, the performance of traditional AGC controllers often degrades due to parametric uncertainties in the power system model, such as variations in the damping constant and inertia. This paper evaluates these uncertainties in a single-area power system from a robust control perspective. We propose a robust tuning method for a Proportional-Integral (PI) controller using small-signal analysis to ensure stability across a wide range of operating conditions. Simulation results demonstrate that the robustly tuned controller maintains frequency stability even when system parameters deviate by $\pm 25\%$ from their nominal values.