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

A three-axis attitude control design, based on lyapunov stability criteria, tostabilize spacecraft and orient it to its desired altitude, is presented in this paper. thisattitude control system is assumed to have four reaction wheels with optimal arrangement.the reaction wheels are located in a square pyramidal conguration. control system inputsare the attitude parameter in the quaternion form and the angular velocity of the spacecraftand reaction wheels. the controller output is the torque required to eliminate error. inthis study, actuators (reaction wheels) are modeled and the required torque for the attitudemaneuver is converted to the voltage of actuators. armature voltage and current arelimited to 12 volts and 3 amps, respectively. also, each wheel has an angular velocity limitof 370 rad/sec. numerical simulations indicate that the spacecraft reaches the desiredattitude after 34 seconds, which shows the reliability of the mentioned conguration, withrespect 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, resultsdemonstrated controller robustness against parameter variation and disturbances. it isrobust against up to a 350% change in the spacecraft moment of inertia, and robust againsta disturbance of up to 0.0094 n.m, which is equal to 38% in comparison with the allowablereaction wheel capacity.