Maneuvering with the highest speed and low power has always been a challenge to design a satellite and spacecraft control system. In this paper, apart from the complexity of modeling actuators, different control methods were used to control the satellite attitude in the presence of uncertainties and disturbances in satellites, in order to obtain an explicit response to minimize the EULERINT criterion. The EULERINT criterion is the integral of the Euler angles between the body axes and the target around Euler's axis over time and somehow interprets the speed of the satellite maneuver in the three control axes. First, using the proportional-derivative control, the comparison of the EULERINT criterion in the application of different kinematic representations (Euler, quaternion vectors and direction cosine matrix equations) in linear and nonlinear models of the satellite was carried out. Then the comparison of the EULERINT criterion between the different methods was presented using the quaternion kinematic, which has the least amount of EULERINT, through changing the proportional-derivative controller to linear-quadratic regulator controllers, pole placement, adaptive, fuzzy, and adaptive-fuzzy. The comparison was conducted to achieve the best control method in terms of frequency response, the lowest EULERINT and the least control effort to control the attitude of the satellite in the presence of disturbance and uncertainty.