Discrete-time control of a spacecraft with retargetable flexible antennas

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Virginia Polytechnic Institute and State University

This dissertation considers the discrete-time control of a spacecraft consisting of a rigid-platform with retargetable flexible antennas. The mission consists of independent minimum-time maneuvers of each antenna to coincide with pre-determined lines of sight, while the platform is stabilized in an inertial space and elastic vibration of the antennas is suppressed. The system is governed by a set of linearized, time-varying equations of motion. A discrete-time approach permits consideration of the time-varying nature of the system in designing the control law.

Both global and decentralized controls are proposed for a noise-free system with full-state feedback. Initially, a time-varying linear-quadratic regulator (LQR) is implemented, followed by two types of decentralized controllers. First, a collocated control law is devised in which actuator forces are based on the position and velocity at the actuator locations. Next, a new method called Substructure-Decentralized Control is proposed, where each flexible substructure is controlled based on state measurements associated with the substructure modes of the separately modeled appendages.

In both global and decentralized cases, a linear control law is first implemented coupled with an open-loop disturbance-accommodating control based on the known inertial disturbances caused by the maneuver. Elastic motion is next controlled using nonlinear (on-off) antenna controllers for each decentralized case. For Substructure-Decentralized Control, the controls translate into quantized actual controls. Lastly, nonlinear (on-off) control laws are also used to control the rigid-body motion for each case.

Next, the problem of controlling the time-varying system in the presence of noisy actuators and sensors is examined. It is assumed that only displacements, not velocities, are sensed for both rigid-body and elastic motion, making state reconstruction also necessary. A discrete-time, full-order Kalman filter is constructed for the time·varying system. A pseudo-decentralized control is proposed whereby feedback controls are based on system state estimates. As before, both linear and nonlinear controls are implemented. For each case mentioned, a numerical example is presented involving a spacecraft with a single flexible maneuvering antenna.