A perturbation approach to control of rotational/translational maneuvers of flexible space vehicles

An open loop control law is applied to a flexible spacecraft that admits translational, as well as rotational and flexural motion. The translational degrees of freedom are coupled to the rotation and deformation through the active controls applied to the structure. The objective of any maneuver is to control the attitude of the craft as well as to dissipate any vibrations of the structure.

Depending on the type of maneuver specified, the equations of motion may be divided into two distinct optimal control problems. Single-axis rotational maneuvers (with small flexural deformations) constitute a strictly linear problem. The solution of the resulting two Q point boundary value problem is accomplished through the use of matrix exponential functions. Maneuvers which involve the translational degrees of freedom, are described by nonlinear equations. The solution method presented is a algorithm that generates successive approximations similar to quasi-linearization. A perturbed linear optimal control problem is solved for each approximation. Examples are presented which illustrate the effectiveness of the solution methods for both types of maneuvers.