Q-Law Control With Sun-Angle Constraint for Solar Electric Propulsion

Solar electric propulsion (SEP) is a desirable option for many future space missions, but trajectory design for an SEP-equipped spacecraft remains a challenging problem. In this article, a Q-Law-based feedback control algorithm is proposed that incorporates a sun-angle constraint to ensure proper alignment of the solar panels of a spacecraft with the Sun for the design of low-thrust SEP transfers. Analytical expressions for the sun-angle-constrained Q-Law-based control are made available through the application of a second-order cone constraint in the derivation of the control that minimizes the time rate of change of a candidate Lyapunov function. The resultant control law is applied to compute transfers from a geostationary transfer orbit to 1) a geostationary orbit and 2) a retrograde Molniya-type orbit. It is demonstrated that the proposed feedback control is capable of successfully computing transfers in both scenarios with parameters selected to approximately minimize the time of flight (TOF) or a performance index that considers both the TOF and the mass consumed.