Time-optical spinup maneuvers of flexible spacecraft

Attitude controllers for spacecraft have been based on the assumption that the bodies being controlled are rigid. Future spacecraft, however, may be quite flexible. Many applications require spinning up/down these vehicles. In this work the minimum time control of these maneuvers is considered. The time-optimal control is shown to possess an important symmetry property. Taking advantage of this property, the necessary and sufficient conditions for optimality are transformed into a system of nonlinear algebraic equations in the control switching times during one half of the maneuver, the maneuver time, and the costates at the mid-maneuver time. These equations can be solved using a homotopy approach. Control spillover measures are introduced and upper bounds on these measures are obtained. For a special case these upper bounds can be expressed in closed form for an infinite dimensional evaluation model. Rotational stiffening effects are ignored in the optimal control analysis. Based on a heuristic argument a simple condition is given which justifies the omission of these nonlinear effects. This condition is validated by numerical simulation.