This dissertation is concerned with the dynamics and control of spacecraft consisting of a rigid platform and a given number of retargeting flexible antennas. The mission consists of maneuvering the antennas so as to coincide with preselected lines of sight while stabilizing the platform in an inertial space and suppressing the elastic vibration of the antennas. The dissertation contains the derivation of the equations of motion by a Lagrangian approach using quasi-coordinates, as well as a procedure for designing the feedback controls. Assuming that antennas are flexible, distributed parameter members, the state equations of motion are hybrid. Moreover, they are nonlinear. Following spatial discretization and truncation, these equations yield a system of nonlinear discretized state equations, which are more practical for numerical calculations and controller design. Linearization is carried out based on the assumption that the inertia of the rigid body is large relative to that of flexible body. The equations of motion for a two-dimensional model are also given. The feedback controls are designed in several ways. Disturbance-minimization control plus regulation is considered by using constant gains obtained on the basis of the premaneuver configuration of the otherwise time-varying system. ln the case of unknown constant disturbance, proportional-plus integral (PI) control has proven very effective. Pl control is used to control the perturbed motions of the platform with multi-targeted flexible appendages. A new control law is obtained for the system with small time-varying configuration during a specified time period by applying a perturbation method to the Riccati equation obtained for Pl control. According to the the proposed perturbation method, the control gains consist of zero-order time-invariant gains obtained from the solution of the matrix algebraic Riccati equation (MARE) for the post-maneuver state and first order time-varying gains obtained from the solution of the matrix differential Lyapunov equation (MDLE). The solution of the MDLE has an integral form, which can be approximated by a matrix difference equation. The adiabatic approximation, which freezes the matrix differential Riccati equation or Lyapunov equation is also discussed. Comparisons are made based on system stability by Lyapunov’s second method. A spacecraft consisting of a rigid platform and a single flexible antenna is used to illustrate disturbance-minimization control, and a spacecraft consisting of a rigid platform and two flexible antennas reorienting into different directions is used to demonstrate the effectiveness of the disturbance-accommodating control. A time-varying spring-mass-damper and a two-dimensional model, representing a reduced version of the original spacecraft model, are considered to demonstrate the perturbation and adiabatic approximation methods. To illustrate the effect of nonlinearity on the dynamic response during reorientation, a numerical example of the spacecraft having a membrane-type antenna ls presented. / Ph. D.
| Identifer | oai:union.ndltd.org:VTETD/oai:vtechworks.lib.vt.edu:10919/54227 |
| Date | January 1989 |
| Creators | Kwak, Moon Kyu |
| Contributors | Engineering Mechanics, Meirovitch, Leonard, Smith, Charles W., VanLandingham, Hugh F., Hendricks, Scott L., Telionis, Demetrios P. |
| Publisher | Virginia Polytechnic Institute and State University |
| Source Sets | Virginia Tech Theses and Dissertation |
| Language | en_US |
| Detected Language | English |
| Type | Dissertation, Text |
| Format | viii, 120 leaves, application/pdf, application/pdf |
| Rights | In Copyright, http://rightsstatements.org/vocab/InC/1.0/ |
| Relation | OCLC# 20103329 |
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