Three-axis attitude control design for a spacecraft based on Lyapunov stability criteria

A three-axis attitude control design, based on Lyapunov stability criteria, to stabilize spacecraft and orient it to its desired altitude, is presented in this paper. This attitude control system is assumed to have four reaction wheels with optimal arrangement. The reaction wheels are located in a square pyramidal conguration. Control system inputs are the attitude parameter in the quaternion form and the angular velocity of the spacecraft and reaction wheels. The controller output is the torque required to eliminate error. In this study, actuators (reaction wheels) are modeled and the required torque for the attitude maneuver is converted to the voltage of actuators. Armature voltage and current are limited to 12 volts and 3 amps, respectively. Also, each wheel has an angular velocity limit of 370 rad/sec. Numerical simulations indicate that the spacecraft reaches the desired attitude after 34 seconds, which shows the reliability of the mentioned conguration, with respect to actuator failure. The results show that in cases of failure of one reaction wheel, the spacecraft can reach the desired attitude, but needs more time. Moreover, results demonstrated controller robustness against parameter variation and disturbances. It is robust against up to a 350% change in the spacecraft moment of inertia, and robust against a disturbance of up to 0.0094 N.m, which is equal to 38% in comparison with the allowable reaction wheel capacity.