Modeling and Control of Mixed and Flexible Structures
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The design of control systems for flexible spacecraft continues to be an important problem in current and future space missions. Crucial to successful controller design is accurate modeling of the underlying distributed parameter system. Current techniques frequently fail to capture the nonlinear feature of the dynamic behavior of flexible spacecraft. From a practical point of view a closely related issue is the fidelity of approximations in preserving the essential characteristics of the underlying distributed parameter system. This dissertation is concerned with distributed parameter models and rigorous approximations of the same as the basis for control system analysis and design. Specifically, we examine the generic case of a rigid spacecraft to which a flexible appendage is attached. The flexible appendage is modeled using geometrically exact rod theory. Equilibria for stationary and rotating configurations are computed and used as the basis of a subsequent linearization which preserves the Hamiltonian structure of the underlying system. These linearized models are the basis of the construction of the corresponding transfer functions. The associated transfer functions relate tip position and acceleration of the appendage to rigid body torques. In addition, stability of these equilibria is investigated using the Energy-Casimir method. Using the transfer functions of the linearized model, modern frequency domain methods can be employed to do compensator design. In addition, we show that a rigid n- body chain is a natural approximation to a limiting case of the geometrically exact beam. Such an approximation provides the basis for finite dimensional compensator design for our infinite dimensional system. The design, implementation, and actual performance of such a compensator for an existing laboratory test fixture is discussed.