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A modern strategy is applied to the control of the synchronous generator output voltage: the generalized predictive control. Then a complete discrete-time multi-variable predictive controller is used. Before implementing such a controller a particular method of synchronous generator modelling is presented. This last one is very suitable when tests are to be performed to validate or identify the model. In order to optimize the controller design and to make its implementation in real time domain easier, a reduction of the model order has been achieved. The simulation results presented at the end of the paper illustrate the efficiency and the handiness of the obtained controller in spite of the complexity due to the computation algorithm.