Revisit to B-dot Rate Damping Algorithm

For satellites running in their orbits, rate damping is the first and fundamental attitude control mode, which is applied to de-tumble the satellites. B-dot algorithm is the well-known and widely adopted rate damping control algorithm, which has been applied successfully to de-tumble hundreds of satellite. However, in several actual scenarios, B-dot algorithm failed to de-tumble the corresponding satellites and under the control efforts, the angular velocities corresponding to each satellite had been improved to the larger ones. The author had analyzed the drawbacks of the classical B-dot algorithm and two critical angular velocities corresponding to this algorithm had been determined according to the magnetic based attitude control effect. The first critical angular velocity is the watershed value and when the initial angular velocity is lower than it, the damping control effort would de-tumble the satellite successfully. While if the initial angular velocity is larger than the first critical angular velocity, under the damping control effort, the angular velocity would gradually increase and finally reach the second angular velocity, which is the saddle point and it is very hard for the satellite to escape from this state. However, the previous analysis process is rough and the employed phase plane has not been explained. Base on this, this paper would analyze the effectiveness and shortcomings of B-dot algorithm and propose a certain method to improve the previous conclusions. Simulations have been presented to verify the proposed Updated B-dot algorithm and the corresponding conclusions.