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This dissertation considers the discrete-time control of a spacecraft consisting of a rigid-platform with retargetable flexible antennas. The mission consists of independent minimum-time maneuvers of each antenna to coincide with pre-determined lines of sight, while the platform is stabilized in an inertial space and elastic vibration of the antennas is suppressed. The system is governed by a set of linearized, time-varying equations of motion. A discrete-time approach permits consideration of the time-varying nature of the system in designing the control law. Both global and decentralized controls are proposed for a noise-free system with full-state feedback. Initially, a time-varying linear-quadratic regulator (LQR) is implemented, followed by two types of decentralized controllers. First, a collocated control law is devised in which actuator forces are based on the position and velocity at the actuator locations. Next, a new method called Substructure-Decentralized Control is proposed, where each flexible substructure is controlled based on state measurements associated with the substructure modes of the separately modeled appendages. In both global and decentralized cases, a linear control law is first implemented coupled with an open-loop disturbance-accommodating control based on the known inertial disturbances caused by the maneuver. Elastic motion is next controlled using nonlinear (on-off) antenna controllers for each decentralized case. For Substructure-Decentralized Control, the controls translate into quantized actual controls. Lastly, nonlinear (on-off) control laws are also used to control the rigid-body motion for each case. Next, the problem of controlling the time-varying system in the presence of noisy actuators and sensors is examined. It is assumed that only displacements, not velocities, are sensed for both rigid-body and elastic motion, making state reconstruction also necessary. A discrete-time, full-order Kalman filter is constructed for the time·varying system. A pseudo-decentralized control is proposed whereby feedback controls are based on system state estimates. As before, both linear and nonlinear controls are implemented. For each case mentioned, a numerical example is presented involving a spacecraft with a single flexible maneuvering antenna. / Ph. D.

An open loop control law is applied to a flexible spacecraft that admits translational, as well as rotational and flexural motion. The translational degrees of freedom are coupled to the rotation and deformation through the active controls applied to the structure. The objective of any maneuver is to control the attitude of the craft as well as to dissipate any vibrations of the structure. Depending on the type of maneuver specified, the equations of motion may be divided into two distinct optimal control problems. Single-axis rotational maneuvers (with small flexural deformations) constitute a strictly linear problem. The solution of the resulting two Q point boundary value problem is accomplished through the use of matrix exponential functions. Maneuvers which involve the translational degrees of freedom, are described by nonlinear equations. The solution method presented is a algorithm that generates successive approximations similar to quasi-linearization. A perturbed linear optimal control problem is solved for each approximation. Examples are presented which illustrate the effectiveness of the solution methods for both types of maneuvers. / Master of Science

The equations of motion are derived for the de-spinning of a rigid body payload by the use of weights attached to the ends of unwinding cables of finite mass that are released when colinear with a radius of the payload. / Master of Science

It is well known that Fourier series of discontinuous functions converge slowly and that the derivatives of the series may not converge at all. Since modal expansion of structural response is a generalization of the Fourier series, slow convergence of modal expansion can be expected when the applied loads exhibit discontinuities in time or space. Thus, in a structure controlled by point actuators, slow convergence of derivatives of structural response with respect to system parameters can be expected. To demonstrate this, the sensitivity of the closed-loop response to structural changes is calculated for a multi-span beam with three control systems of increasing complexity that utilize point actuators. Reduced models based on the natural modes of the structure are formed and derivatives of the damping ratios of the closed-loop eigenvalues are calculated. As expected, the convergence of the derivatives of the damping ratios with increasing number of modes is slower than the convergence of the damping ratios themselves. The convergence is improved when distributed actuators replace the point actuators. When the control system is designed based on a reduced model, the damping ratios also converge slowly. In transient response problems, it is known that complementing the vibration modes with a mode representing static response to the loads can greatly improve convergence. Indeed, for the examples studied, when Ritz vectors corresponding to static responses due to unit loads at the actuators are added to the basis vectors, the convergence of the reduced-model derivatives is greatly enhanced. Also, when the control system is designed using a reduced model containing both vibration modes and Ritz vectors, its prediction of the full-model response is greatly improved. / Ph. D.

The problem of simultaneous maneuver and vibration control of a flexible spacecraft can be solved by means of a perturbation approach whereby the slewing of the spacecraft regarded as rigid represents the zero-order problem and the control of elastic vibration, as well as of elastic perturbations from the rigid-body maneuver, represents the first-order problem. The zero-order control is to be carried out in minimum time, which implies on-off control. On the other hand, the perturbed model is described by a high-order set of linear time-varying ordinary differential equations subjected to persistent, piecewise-constant disturbances caused by inertial forces resulting from the maneuver. This dissertation is concerned primarily with the control of the perturbed model during maneuver. On-line computer limitations dictate a reduced-order compensator, thus only a reduced-order model (ROM) is controlled while the remaining states are regarded as residual. Hence, the problem reduces to 1) control in a short time period of a linear time-varying ROM subject to constant disturbances and 2) mitigation of control and observation spillover effects, as well as modeling errors, in a way that the full modeled system remains finite-time stable. The control policy is based on a compensator, which consists of a Luenberger observer and a controller. The main features of the control design are: (1) the time-varying ROM is stabilized within the finite-time interval by an optimal linear quadratic regulator, (2) a weighted norm spanning the full modeled state is minimized toward the end of the time interval, and (3) the supremum"time constant" of the full modeled system is minimized, while (1) serves as a constraint, thus resulting in a finite-time stable modeled system. The above developments are illustrated by means of a numerical example. / Ph. D.

Thesis. 1976. M.S. cn--Massachusetts Institute of Technology. Dept. of Aeronautics and Astronautics. / MICROFICHE COPY AVAILABLE IN ARCHIVES AND AERO. / Includes bibliographical references. / M.S.cn

This dissertation is concerned with the problem of slewing large flexible structures in space and simultaneously suppressing any vibrations. The equations of motion for a three-dimensional spacecraft undergoing large rigid-body maneuvers are derived. The elastic motions are assumed to remain in the linear range. A method of substructure synthesis is presented which spatially discretizes the equations of motion. A perturbation approach is used to solve the equations of motion. The zero-order equations describing the rigid-body maneuver are independent of the first-order vibration problem which includes small rigid-body motions. The vibration problem is described by linear nonself-adjoint equations with time-dependent coefficients. Minimum-time, single-axis rotational maneuvers are considered. The axis of rotation is not necessarily a principal axis. The optimal maneuver force distribution is proportional to the corresponding rigid-body modes with the mass acting as the control gain. The premaneuver eigenvectors are used as admissible vectors to reduce the degrees of freedom describing the vibration of the spacecraft during the maneuver. Natural control and uniform damping control are used to suppress the vibrations during the maneuver. Actuator dynamics cause a degradation of control performance. The inclusion of the actuator dynamics in the control formulation partially offsets this effect. The performance of these control techniques is adversely affected by actuator saturation but they remain effective. Numerical results are presented for a spacecraft in orbit and in an earth-based laboratory. / Ph. D.

Most present day spacecrafts have large interconnected solar panels. The dynamic behavior of the spacecraft in orbit can be modeled as a free rigid mass with flexible elements attached to it. The natural frequencies of such spacecrafts with deployed solar panels are very low. The low values of the natural frequencies pose difficulties for maneuvering the spacecraft. The control torque required to maneuver the spacecraft is influenced by the flexibility of the solar arrays. The control torque sets up transient oscillations in the flexible solar panels which in turn induces disturbances in the rigid satellite body and the payload within. Therefore the payload operations can be carried out only after the disturbances die out. For any reduction of the above disturbances it is necessary to understand the dynamic behavior of such systems to an applied torque. The present work first studies the nature of the disturbances. The influence of structural parameters on these disturbances is then investigated. Finally, the use of passive damping treatment using viscoelastic material is investigated for the reduction of the disturbances. In order to understand the nature of vibrations induced in the flexible appendages of a satellite during maneuvers, we model the maneuver loads in terms of applied angular acceleration as well as varying torque. The transient decay of the disturbance of the rigid element is characterized by the dynamic characteristics of the flexible panels or appendages. It is shown that by changing the stiffness of the panel the response of the rigid element can be modified. A simple model consisting of an Euler-Bernoulli beam attached to a free mass is next considered. The influence of various parameters of the EulerBernoulli beam in mitigating vibration and thereby the disturbance in the rigid mass is investigated. As the response of the rigid system mounted with the large flexible panels are influenced by the dynamics of the flexible panels, reduction of these disturbances can be achieved by reducing the vibration in the flexible panels. Therefore application of viscoelastic materials for passive damping treatment is investigated. The loss factor of a structure is significantly improved by using constrained viscoelastic layer damping treatment. However providing a constrained layer damping treatment on the entire structure is very inefficient in terms of the additional mass involved. Therefore damping material is applied at suitable optimal locations. In previous studies reported in literature, modal strain energy distribution in the viscoelastic material as well as the base structure is used as a tool to arrive at the optimum location for the damping treatment. It is shown in this study that such locations selected are not the optimum. A new approach is proposed in this study by which both the above shortcomings are overcome. It is shown that use of a parameter that is the ratio of the strain in the viscoelastic material to the angle of flexure is a more reliable measure in arriving at optimal locations for the application of constrained viscoelastic layers. The method considers the deformations in the viscoelastic material and it is shown that significant values of loss factors are achieved by providing material in a small region alone. We also show that loss factor can be improved by providing damping material near the interface region. The loss factor can be further improved by incorporating spacers by using spacer material having higher extensional modulus. Also shown is the fact that loss factor is unaffected by the shear modulus of the spacer material. Experiments have been conducted to validate these results. In a related study we consider honeycomb type flexible structures since in most of the spacecraft applications honeycomb sandwich constructions are employed. But loss factors of sandwich panels with constrained layer damping treatment are seldom discussed in the literature. Use of viscoelastic layers to improve the loss factors of the honeycomb sandwich beams is explored. The results show that the loss factors are enhanced by increasing the inplane stiffness of the constraining layer. These conclusions too are validated by experimental results. Finally a typical satellite with flexible solar panels is considered, and the use of the viscoelastic material for improving the damping is demonstrated.

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.