In closed Brayton cycle power generation systems, sudden load disturbances can induce a compressor surge in turbine–alternator–compressor systems, posing significant risks to dynamic stability and operational reliability. To address this challenge, this study proposes a PID control strategy optimized via a genetic algorithm. A high-fidelity dynamic model of the turbine–alternator–compressor system under closed Brayton cycle conditions is developed in Simulink, incorporating surge boundaries derived from performance maps. Control parameters are tuned using a weighted multi-objective fitness function that integrates overshoot, rise time, and the integral of absolute error. Simulation results demonstrate that the proposed control scheme markedly enhances system responsiveness—achieving approximately a 70% improvement in rotational speed regulation—and effectively maintains the operating point outside the surge region. The proposed framework provides a practical and robust approach for improving the dynamic stability and reliability of closed Brayton cycle power generation systems.