Design of LQG/LTR controller for attitude control of geostationary satellite using reduced quaternion model

In this paper، a LQG/LTR controller is proposed for attitude control a geostationary satellite at nominal phase. Basically، proposed methodology includes three parts: LQR regulator، EKF، and loop transfer recovery. Controller design is based on the linearized equations of the spacecraft dynamics using reduced quaternion model. Reduced quaternion model solve uncontrollable problem in some subspaces in the linearized state space quaternion model using all four components of quaternion. Spacecraft actuators are reaction wheels and attitude determination sensors are sun and earth sensors. LQR controller is ideal and it doesn’t account for the model uncertainty and sensor noise and it uses the feedback of the full states. To consider the model uncertainty and sensor noise، we have designed EKF which is used by LQG and LQG/LTR controllers. Controller gain coefficients are obtained using a reduced quaternion model، and based on linearization around the equilibrium point and the natural frequency of the closed loop system. To increase the robustness of the design with respect to solar radiation disturbance، singular values of LQG are approximated to Kalman filter، in LTR section. The results demonstrate that LQG/LTR performance is better than LQG’s and LQG/LTR has a good robust stability margin with respect to disturbances.