This research explores the application and performance of the Linear Quadratic Regulator (LQR) and Model Predictive Controller (MPC) in satellite attitude control. The study involves deriving the satellite equations of motion by defining the kinematics and dynamics equations. The nonlinear state-space equations are constructed, and dimension reduction linearization is used to make the system controllable. The theory of the controllers is explained, and simulations are conducted to evaluate their effectiveness. The simulations assess the impact of control input saturation on LQR controller and show the time response of the designed MPC controller. The comparison of the two controllers focuses on their disturbance rejection performance. Results demonstrate that the disturbance performance of the MPC controller is significantly better than LQR controller and that the constrained MPC controller can dampen step disturbance, while the LQR controller has no impact on rejection. Overall, this study contributes to the growing knowledge base on satellite attitude control and provides valuable insights for improving its efficiency and effectiveness.