This study applied the Ziegler-Nichols maximum gain method to the speed regulation loop of a Pelton turbine in the Mazar hydroelectric plant in Ecuador. The research focused on approximating a sixth-order system to a third-order system, facilitating mathematical analysis. P, PI, and PID controllers were used, highlighting their effectiveness in applications like Pelton turbines. The dynamic characterization of the turbine was performed by identifying the dominant poles of the transfer function, allowing a better understanding of the system behavior. The results showed that the third-order system approach and the use of PI and PID controllers provide more accurate and stable control of the speed governor, improving the operational efficiency of the turbine. This approach optimizes the system design and ensures reliable and robust performance.