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UBC Theses and Dissertations

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UBC Theses and Dissertations

A study of flexible space structures : dynamics and control Grewal, Anant Kiran Singh

Abstract

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.

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