This paper deals with the design of an adaptive and robust control scheme to achieve the rotor speed stability enhancement and the terminal voltage regulation through the excitation control of a single synchronous generator connected to an infinite bus through a transmission line. A comprehensive 10th-order plant model of the plant is provided, including the exciter system dynamics, under the condition that all model parameters are completely unknown. The scheme design is developed based on a combination of modified adaptive backstepping, second-order constrained SM, and fuzzy logic methods. Based on the stator currents and the rotor angle-speed sensors data and the plant model structure, an adaptive sliding mode observer is designed to estimate the unmeasured rotor flux. Using the estimated rotor flux to overcome the uncertainty in the plant model, two sliding surfaces on which the rotor speed and terminal voltage errors asymptotically tend to zero are formulated. With only one excitation control input, a discontinuous control algorithm is proposed in combination with fuzzy logic to achieve finite-time convergence of the closed-loop system state to the intersection of the two designed sliding surfaces. The effectiveness of the proposed control scheme is confirmed by simulation.