This paper describes a methodology to obtain a neuro-fuzzy model of a hydro-generator unit (HGU) and its PID controller from the identification of its linear time-invariant (LTI) model. The study performs a cause-effect record, which allows a continuous time identification of the LTI type, then obtaining a classic PID controller capable of complying with a performance specification given by a pole of a second order system, which enables the training of the proposed neuro-fuzzy model. Applying the cost function of the root mean square error and the root of the percentage relative mean square error, the system parameters were adjusted using the decreasing gradient method. By means of linear models, the initialization of the singletons of the neuro-fuzzy models was done in two stages using the decreasing gradient and a cost function. The first stage was carried out without dynamics and the second stage with the dynamics of the simulated system. A case study of the Hydro-Agoyán HGU was selected and the results showed that the development of the LTI model allowed the development of the neuro-fuzzy model able to represent the behavior of the power plant and its response under variations of the power setpoint of 5, 10, 15 and 20%.