Controllability of a square solar sail with movable membrane tips

Abstract

This paper presents a controllability study for a square solar sail that uses the wing tip displacement method for its attitude control. The goal is to determine whether this method of attitude control guarantees full control authority over normal attitude maneuvers that would be expected during a typical solar sail mission. The controllability of a given state is determined by first linearizing the full nonlinear equations of motion of the craft about the chosen state, and then applying the classical controllability test to the resulting linear model. This process is then repeated enough times to adequately span the allowable states of the vehicle. Because of the nature of the expressions for the control torques, direct analytical linearizations are not practical; and a full numerical approach is inefficient because of the sheer volume of computations involved. A hybrid linearization method that judiciously combines analytical and numerical approaches was therefore adopted. Results obtained show that the sailcraft is controllable throughout the tested region. A study of the influence of various actuator failure scenarios on controllability revealed that the wing tip displacement method of attitude control exhibits a very high degree of redundancy. The system’s controllability only becomes seriously impaired if more than half of its actuators fail.