<![CDATA[This study presents a dynamic and stability analysis of an Automatic Voltage Regulator (AVR) system for a synchronous generator using time-domain and frequency-domain approaches. The system is modelled as a series of first-order linear subsystems consisting of an amplifier, exciter, generator, and feedback sensor, resulting in a fourth-order closed-loop system. Numerical simulations are conducted to compare the performance of the AVR without a controller and with a PID controller. Time-domain analysis indicates that the uncontrolled system exhibits a rise time of 0.339 s, an overshoot of 57.937%, and a damping ratio of approximately 0.17, indicating a heavily underdamped response. After implementing the PID controller, the rise time decreases to 0.295 s and the overshoot is significantly reduced to 14.368%, with the damping ratio increasing to approximately 0.53. Frequency-domain analysis using Bode diagrams shows an improvement in phase margin from less than 20° to more than 40°, and gain margin from below 6 dB to above 10 dB. The dominant pole shifts from approximately Re(s) ≈ −0.2 to Re(s) ≈ −1.0 in the complex plane, confirming enhanced relative stability and faster transient decay. Overall, the results demonstrate that the PID controller significantly improves stability, response speed, and damping performance, making it suitable for voltage regulation in power system applications]]>
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