| Summary: | A relatively general formulation for studying dynamics of flexible multibody orbiting
systems in a tree topology is developed. It is applicable to a large class of present
and future spacecraft, and readily amenable to simulation of closed loop systems as
well as control system synthesis. Some of the distinctive features of the formulation
include:
(a) its ability to simulate an arbitrary number of rigid, plate and beam-type structural
members, each free to undergo translational and rotational maneuvers,
as well as an arbitrary number of force and moment actuators on each member;
(b) the modelling of orbital perturbations through consideration of the trajectory
radius and true anomaly as generalized coordinates;
(c) inclusion of structural damping, the foreshortening effect, and quasi-comparison
functions for the improved discretization of flexibility;
(d) development of a compact set of nonlinear, nonautonomous, coupled governing
equations by exploiting the cancellation of terms in the equations;
(e) determination of a linear model, indispensable for the controller design, through
computation of the Jacobian matrices by finite differences;
(f) ability to include a dynamic compensator model which allows for the simulation
of the closed loop system consisting of a nonlinear plant and a linear
controller.
After presenting a brief introduction to the subject and a review of the relevant
literature in the areas of multibody dynamics and control, the Lagrangian formulation
of interconnected flexible systems is introduced. Issues pertaining to the numerical
implementation of the formulation and its validation are discussed next. The latter
is accomplished through verification of energy conservation as well as comparisons
with particular cases reported by other investigators. An approximate, closed-form,
analytical treatment of the problem, developed in Chapter 4, is applicable to a general
set of n second order nonlinear differential equations. The approach proves to be
quite accurate promising considerable savings in computational time and effort. It is
particularly suitable during the preliminary design stage.
Now, the attention is directed towards application of the formulation to study
dynamics of several flexible systems of contemporary interest, exposed to a variety of
disturbances, thus illustrating versatility of the approach. It also helps explain the
foreshortening effect and the improved matching of boundary conditions through the
use of quasi-comparison functions. The results clearly establish a need for active control
of the Space Station. Finally, attitude control of the First Element Launch (FEL)
of the Station, and simultaneous attitude and vibration control for the Permanently
Manned Configuration (PMC) are studied, in the presence of realistic disturbances,
using three linear methods: the Linear Quadratic Regulator (LQR), Linear Quadratic
Gaussian/ Loop Transfer Recovery (LQG/LTR), and Hoo. The controller design is
substantiated, in each case, through its application to the complete nonlinear system.
The results suggest all the three approaches to be effective, however, the Hoo
controller shows better performance but at a cost of a larger compensator.
The thesis concludes with a summary of significant results and recommendations
for future investigations. === Applied Science, Faculty of === Mechanical Engineering, Department of === Graduate
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