This work is focused on the design of a robust control for the excitation field voltage input to stabilize the rotor speed and angle in an electric power system with synchronous machine connected to an infinite bus. The complete 8th order plant model including the rotor and stator dynamics, is derived. Considering that the mechanical part model parameters are unknown, an observed-based adaptive control schemes is designed based on the plant complete model, Sliding Mode (SM) control and Adaptive Backstepping techniques. The effectiveness of the proposed adaptive control scheme is confirmed by simulation.