The space elevator has been proposed as an alternate method for launching cargo into space. However, the construction of such a structure requires a material much stronger than any currently in existence. Instead, a partial elevator is considered for satellite placement. In the first part of the thesis, the fundamentals of very long tethered systems are studied. From static analysis on a simple two-body system, it is demonstrated that an assumption made in the conventional analysis does not apply to very long tethered systems. For a uniform tether, the axial stress distribution is obtained. Following the Lagrangian approach, the equations of motion governing the planar librations of a multi-body tethered system are derived. From a linearization of these equations, the libration frequencies are found. Then, by solving the nonlinear equations numerically, the responses to various changes in the system parameters are determined. In the second part of the thesis, the use of a partial elevator in satellite placement is studied. In the case of single climber transit, residual librations occur, which alter the shape and size of the orbit of a satellite launched from the climber. An approach using two climbers is investigated in order to decrease the residual libration and thereby reduce orbit placement errors. Also, some energy calculations are done to determine whether the partial elevator offers significant advantages.

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This dissertation is concerned with the dynamics and control of spacecraft consisting of a rigid platform and a given number of retargeting flexible antennas. The mission consists of maneuvering the antennas so as to coincide with preselected lines of sight while stabilizing the platform in an inertial space and suppressing the elastic vibration of the antennas. The dissertation contains the derivation of the equations of motion by a Lagrangian approach using quasi-coordinates, as well as a procedure for designing the feedback controls. Assuming that antennas are flexible, distributed parameter members, the state equations of motion are hybrid. Moreover, they are nonlinear. Following spatial discretization and truncation, these equations yield a system of nonlinear discretized state equations, which are more practical for numerical calculations and controller design. Linearization is carried out based on the assumption that the inertia of the rigid body is large relative to that of flexible body. The equations of motion for a two-dimensional model are also given. The feedback controls are designed in several ways. Disturbance-minimization control plus regulation is considered by using constant gains obtained on the basis of the premaneuver configuration of the otherwise time-varying system. ln the case of unknown constant disturbance, proportional-plus integral (PI) control has proven very effective. Pl control is used to control the perturbed motions of the platform with multi-targeted flexible appendages. A new control law is obtained for the system with small time-varying configuration during a specified time period by applying a perturbation method to the Riccati equation obtained for Pl control. According to the the proposed perturbation method, the control gains consist of zero-order time-invariant gains obtained from the solution of the matrix algebraic Riccati equation (MARE) for the post-maneuver state and first order time-varying gains obtained from the solution of the matrix differential Lyapunov equation (MDLE). The solution of the MDLE has an integral form, which can be approximated by a matrix difference equation. The adiabatic approximation, which freezes the matrix differential Riccati equation or Lyapunov equation is also discussed. Comparisons are made based on system stability by Lyapunov’s second method. A spacecraft consisting of a rigid platform and a single flexible antenna is used to illustrate disturbance-minimization control, and a spacecraft consisting of a rigid platform and two flexible antennas reorienting into different directions is used to demonstrate the effectiveness of the disturbance-accommodating control. A time-varying spring-mass-damper and a two-dimensional model, representing a reduced version of the original spacecraft model, are considered to demonstrate the perturbation and adiabatic approximation methods. To illustrate the effect of nonlinearity on the dynamic response during reorientation, a numerical example of the spacecraft having a membrane-type antenna ls presented. / Ph. D.

A Variable Speed Control Moment Gyro (VSCMG) is a recently introduced actuator for spacecraft attitude control. As its name implies, a VSCMG is essentially a single-gimbal control moment gyro (CMG) with a flywheel allowed to have variable spin speed. Thanks to its extra degrees of freedom, a VSCMGs cluster can be used to achieve additional objectives, such as power tracking and/or singularity avoidance, as well as attitude control. In this thesis, control laws for an integrated power/attitude control system (IPACS) for a satellite using VSCMGs are introduced. The power tracking objective is achieved by storing or releasing the kinetic energy in the wheels. The proposed control algorithms perform both the attitude and power tracking goals simultaneously. This thesis also provides a singularity analysis and avoidance method using CMGs/VSCMGs. This issue is studied for both the cases of attitude tracking with and without a power tracking requirement. A null motion method to avoid singularities is presented, and a criterion is developed to determine the momentum region over which this method will successfully avoid singularities. The spacecraft angular velocity and attitude control problem using a single VSCMG is also addressed. A body-fixed axis is chosen to be perpendicular to the gimbal axis, and it is controlled to aim at an arbitrarily given inertial direction, while the spacecraft angular velocity is stabilized. Finally, an adaptive control algorithm for the spacecraft attitude tracking in case when the actuator parameters, for instance the spin axis directions, are uncertain is developed. The equations of motion in this case are fully nonlinear and represent a Multi-Input-Multi-Output (MIMO) system. The smooth projection algorithm is applied to keep the parameter estimates inside a singularity-free region. The design procedure can also be easily applied to general MIMO dynamical systems.