Attitude Control of a Spacecraft with Two Reaction Wheels

Abstract

This paper deals with the attitude control of a rigid spacecraft with two reaction wheels. First, we derive a discontinuous state feedback law based on Lyapunov control. The control input is obtained by multiplying the gradient vector of the Lyapunov function by a matrix that is composed of a symmetric matrix and an asymmetric one. Under this method, when the angular momentum of the system is zero, the desired point is the only stable equilibrium point of the controlled system. Next, we investigate the behavior of the controlled system when the angular momentum of the system is not zero but small. In this case, the system converges to either a limit cycle or an equilibrium point which is not the desired point however, in both cases, the error in attitude remains small.