Control of flexible spacecraft during a minimum-time maneuver

The problem of simultaneous maneuver and vibration control of a flexible spacecraft can be solved by means of a perturbation approach whereby the slewing of the spacecraft regarded as rigid represents the zero-order problem and the control of elastic vibration, as well as of elastic perturbations from the rigid-body maneuver, represents the first-order problem. The zero-order control is to be carried out in minimum time, which implies on-off control. On the other hand, the perturbed model is described by a high-order set of linear time-varying ordinary differential equations subjected to persistent, piecewise-constant disturbances caused by inertial forces resulting from the maneuver. This dissertation is concerned primarily with the control of the perturbed model during maneuver.

On-line computer limitations dictate a reduced-order compensator, thus only a reduced-order model (ROM) is controlled while the remaining states are regarded as residual. Hence, the problem reduces to 1) control in a short time period of a linear time-varying ROM subject to constant disturbances and 2) mitigation of control and observation spillover effects, as well as modeling errors, in a way that the full modeled system remains finite-time stable.

The control policy is based on a compensator, which consists of a Luenberger observer and a controller. The main features of the control design are: (1) the time-varying ROM is stabilized within the finite-time interval by an optimal linear quadratic regulator, (2) a weighted norm spanning the full modeled state is minimized toward the end of the time interval, and (3) the supremum"time constant" of the full modeled system is minimized, while (1) serves as a constraint, thus resulting in a finite-time stable modeled system. The above developments are illustrated by means of a numerical example.