| This dissertation is concerned with the motion of large flexible space structures, characterized by high order mathematical models, during large angle slewing maneuvers. For the model reduction problem, two different model reduction methods are developed and applied to models formulated by the finite element method. The algorithms, called frequency dependent Krylov vectors (FDKV), are for both positive definite and semipositive definite damped systems. A projection subspace for the algorithms is presented by employing a spectrum shifting technique, inverse iteration formulation, and singular value decomposition in order to match the low and high frequency parameters. The projection subspace preserves the symmetry and physical meaning of the system matrices by utilizing a second-order formulation. The concept of component mode synthesis is, especially, employed for the semipositive definite damped system. It is shown that the dynamic accuracy with the FDKV is significantly improved over the solution with eigenvectors as admissible vectors to approximate the system deflection. The proposed FDKV algorithm is used to present the quasi-Krylov equations of motion for computational efficiency and vibration control implementation, based on the formulation for nonlinear, time-varying, multibody dynamic systems by the perturbation method. In the control problem, the large flexible structure is associated with a multivariable system. For the multi-input multi-output (MIMO) control problem, common to large flexible structures, a stochastic optimal sliding mode controller is developed in conjunction with a time-varying Kalman filter and global reaching technique. In order to provide the ideal tracking states to the controller, a tracking model is developed by considering the influence of angular acceleration. The ideal trajectory is generated with the input shaping technique to allow only a half period of vibration of a system. It is found that tracking of first mode elastic vibration performs more efficiently than the regulation of a rigid-body state does for the reduction of residual vibration with less control energy consumption. The designed controller using output feedback also shows robustness with respect to unknown disturbances. |
