In this paper, a model predictive controller based on a generator model for prediction purposes is proposed to replace a standard generator controller with a stabilizer of a power system. Such a local controller utilizes an input-output model of the system taking into consideration not only a generator voltage Ug but also an additional, auxiliary signal (e.g., α, Pg, or ωg). This additional piece of information allows for taking oscillations into account that occur in the system and minimizing their impact on the overall system performance. Parameters of models used by the controller are obtained on the basis of the introduced black-box models both for a turbine and a synchronous generator, parameters of which are estimated in an on line fashion using a RLS method. The aim of this paper is to compare the behavior of the classical generator control system with a power system stabilizer and a model predictive control with an additional feedback signal. The novelty of the paper is related to the use of the predictive controller instead of the classical controller/stabilizer system and its possibility of stabilizing the power system. Contrary to the solutions found in the literature, which are commonly-based on a fuzzy logic approach, the authors propose the use of an adaptive model predictive controller, which takes advantage of the knowledge concerning the plant in the form of a model and adapts itself to the operating point of the system using the model parameters estimation mechanism. Moreover, the adaptive predictive controller, unlike other solutions, automatically adjusts signal levels to changes in the plant. The proposed solution is able to calculate the best control signal regardless of whether these changes of the plant are caused by a change in the operating point, or resulting from operation, e.g., wear of mechanical parts.