Control and stabilization of flexible space structures

Research in the control and stabilization of large, flexible space structures has progressed rapidly in the last decade. It is the purpose of this thesis to investigate several control system issues arising from the use of distributed parameter formulations in the modelling of these flexible spaced structures.; The organization of this thesis is as follows. After a brief introduction in chapter one, chapter two focuses on flexible beam dynamics and control. Standard distributed parameter beam models are introduced. This is followed by the main result of the chapter, which gives sufficient conditions for a single collocated sensor/actuator pair to uniformly exponentially stabilize an undamped, Euler-Bernoulli beam.; In chapter three, a simple spacecraft consisting of a flexible beam attached to a rigid body is introduced. The kinematics and dynamics for this structure are derived. This is followed by several control laws which uniformly exponentially stabilize the proposed spacecraft. The obtained results extend well-known results for modally truncated spacecraft models to the infinite dimensional models used here.; In chapter four, the attitude control problem is considered for the spacecraft configurations of chapter three. Attitude control laws are derived using Lyapunov techniques under various assumptions on the nonlinear, infinite dimensional spacecraft models. The control laws bear striking resemblance to well-known results obtained from finite dimensional, linearized spacecraft models.; In chapter five, the attitude control problem is again considered. Attitude control laws are again obtained for several spacecraft models derived in chapter three, but the control methodology differs from chapter four in that the methods of exact linearization are employed. The approach is novel because the methods of exact linearization are normally reserved for finite dimensional nonlinear systems, whereas the systems under consideration here are infinite dimensional, nonlinear systems. Implementation issues for the control laws are also discussed.