Attitude controller for under-actuated spacecraft with two flywheels

The spacecraft with flywheels becomes under-actuated and the attitude controllability goes worse when only two flywheels can work. We deal with this problem for a rigid spacecraft with two flywheels. A new controller is designed by using the Backstepping design method, under the assumption of zero momentum for the spacecraft. The design process is in two steps: First, the desired angular velocity is designed to stabilize the attitude of the spacecraft, by considering the kinematics only. Next, the dynamics is combined to give the attitude control torque. The controller is a discontinuous one. It makes the attitude of the under-actuated spacecraft globally asymptotically converge to zero, and the system has a rapid and desirable transient process. Finally, simulation results indicate the feasibility of the controller presented above.