Time-optimal slewing 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 proposed applications require maneuvering such vehicles between two widely spaced quiescent states or spinning up/down these vehicles in minimum time. In this dissertation, two slewing problems have been addressed: the time-optimal, rest-to-rest slewing problem (RTRSP) and the time-optimal spinup problem (SUP). The spacecraft has been modeled as a finite-dimensional, linear, undamped, nongyroscopic system. One of the major contributions of this dissertation is the recognition and rigorous proof of symmetry of the optimal open-loop control histories about the mid-maneuver time. Necessary and sufficient conditions for optimality are transformed, exploiting the symmetry property, into a set of nonlinear algebraic equations in one half of the control switching times, the maneuver time, and the costates at the mid-maneuver time. These equations are solved using a homotopy approach. The effect of residual modes on the open-loop system performance is quantified via the residual energy, the maximum post-maneuver attitude error (for the RTRSP), and the maximum post-maneuver attitude rate error (for the SUP). Upper bounds on these performance measures are given. For the special case of a single actuator located on the rigid central body, closed form expressions for these upper bounds are obtained for an infinite dimensional evaluation model. When only one control input is used to effect the slewings, it is found that the optimal control history is independent of the control input locations.; The main assumption of this work is the absence of nonlinear rotational stiffening effects. This assumption might fail to hold during slewings when 'large' rotational rates are attained. We have proposed a simple condition which, when satisfied, justifies the omission of this nonlinearity from the equations of motion. This condition is validated by numerical simulations. The results of this dissertation, therefore, can be applied to many physical situations. Moreover, the results are applicable to all linear, elastic, nongyroscopic systems possessing one rigid body mode and a finite number of undamped elastic modes.