Analysis of roll-yaw control law applied to the initial attitude acquisition of spacecraft with single pitch wheel

A sequence of control procedures is analyzed in this paper that can be applied to the initial attitude maneuver of pitch momentum biased three-axis stabilized spacecraft. B-dot control is activated first to detumble the spacecraft, and then is followed by pitch axis control to start up the pitch momentum wheel and eliminate pitch angle deviation. For the convenience of using previous control results, a simple but effective roll control law is formulated following 1-3-2 Euler angle sequence which uses roll angle and roll angle rate for feedback. The same approach can be done for yaw control law which is for 3-1-2 sequence that measures yaw angle and yaw angle rate to close the feedback control loop. The strategy for roll control law, taking the advantage of pitch angular momentum stiffness and pitch rotation, is to orient the roll angle and at the same time eliminates the yaw angle error or vice versa as roll and yaw angles are coupled and exchanged every one-quarter of the orbit. Also, the magnetic dipole generated by the control law is proportional to B_x for roll control and B_z for yaw control, which are the intensity components of geomagnetic field measured on the spacecraft and synchronize with roll-yaw libration cycle. Studies also indicate that, for magnetic torque application, orbit with higher inclination angle has better control ability.