In recent years the problem of designing a feedback control law to stabilize a linear, time-varying uncertain system has received considerable attention. However, the problem is usually limited to the case of systems which satisfy the "matching" assumptions. Moreover, the question of the existence of a linear stabilizing control, if a nonlinear stabilizing control exists, is still unanswered. In the present work an attempt is made to design a stabilizing, linear, feedback control law for a specific second order, linear system which contains time-varying uncertainties into both the state and input matrices and does not satisfy the matching conditions. For specific values of the uncertainty bounds this system is quadratically stabilizable but not quadratically stabilizable via linear control. / Master of Science

An approximate method of calculating the minimum total weight of the two-insulation--two-coolant thermal protection system is developed. The equations derived in the development of the approximate method enable insight into the parameters that control the system weight. Two cases are considered: the case where the outer coolant location is unrestricted within the insulating wall and the case where the outer coolant location is restricted within the insulating wall. The effects on system weight of material properties and the outer coolant location within the insulating wall are discussed. A comparison of weights predicted by the approximate method and numerical solutions is shown. / Master of Science

A recently developed viscous shock-layer method (VSL81) has been applied to predict laminar viscous flows over the windward surface of a shuttle-like vehicle with a perfect gas and an equilibrium air model at high angles-of-attack to simulate reentry conditions. The predictions of wall pressure and heat-transfer data compare well with the limited experimental data available requiring relatively short computing times compared to parabolized Navier-Stokes (PNS) methods. Velocity, pressure and enthalpy profiles are compared at some stations on the body. This method can be used to predict viscous flows over general lifting bodies during reentry. / Master of Science

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.

For direct reentry from a lunar or deep space mission, considerable variation in reentry plane, reentry point, and reentry angle must be anticipated. The returning vehicle must therefore, possess the ability to control its range after reentry in order to touch down in the desired recovery area. Recent studies have indicated that considerable ranging capability is available with even low lift-drag ratio vehicles operating wholly within the atmosphere if aerodynamic maneuvering is initiated while the vehicle still possesses greater than satellite velocity. In these studies, maneuvering was initiated shortly after the initial pull-up. Range control is also available during the initial pull-up, but such control results in little gain in longitudinal ranging capability in most cases. It is the purpose of the present thesis to investigate the feasibility of increasing lateral ranging capability by banking during the initial pull-up. Low lift-drag ratio vehicles reentering the atmosphere in a banked attitude are considered and the effects of such reentries on allowable corridor width, and lateral range capability are studied. Equations are developed for the motion of a vehicle reentering the atmosphere of a spherical, non-rotating earth, and some permissible approximations applicable for the present problems are discussed. Numerical results obtained for the developed system of equations through use of an IBM 7090 high-speed computer are used throughout the investigation to furnish accurate evaluations of the effects being studied and to check the validity of some of the approximations used. Particular emphasis is placed on reentry at escape velocity, but the effects determined apply in character to reentry at other supercircular velocities. / Master of Science

A general approach is presented for the estimation of spacecraft attitude from rate gyroscope measurements of angular velocity and indirect inertial orientation measurements obtained from a pair of star sensors. The estimation algorithm is developed in such a way that the measured minus estimated angular velocity residuals are consistent with the apriori knowledge of the instrument error variance. The angular velocity history is modeled as a Fourier Series. whereas the attitude is modeled as the solution of the appropriate kinematic differential equations. The study presented addresses computer implementation issues and provides numerical results from several simulated attitude and velocity histories. The software is presented in FORTRAN code in an appendix. / Master of Science

The time optimal slewing problem for flexible spacecraft is considered. We study single-axis rotational maneuvers for a simple flexible system, consisting of a rigid hub with an elastic appendage. The equations of motions are derived by Hamilton’s Principle, and a discrete nonlinear model is obtained by the assumed modes method. The problem is first solved in a discrete linearized space by parameter optimization. Optimality is verified by Pontryagin’s Maximum Principle. The linear solutions are then used to obtain time optimal solutions for the non-linear problem by a multiple-shooting algorithm. Although this approach is applicable to arbitrary boundary conditions, this work is confined, almost exclusively, to rest-to-rest maneuvers. These maneuvers are shown to possess some interesting symmetric and asymptotic properties. The problem is further analyzed in infinite-dimensional space, and the convergence of the finite-dimensional approximations is studied. Finally, a soft version of the time optimal slewing problem is considered, where the control is bounded only by a penalty term in the cost functional. A perturbation technique is applied to further simplify this problem. / Ph. D.

Solving the optimal open-loop control problems for spacecraft large-angle attitude maneuvers generally requires the use of numerical techniques whose reliability is strongly case dependent. The primary goal of this dissertation is to increase the solution reliability of the associated nonlinear two-point boundary-value problems as derived from Pontryagin’s Principle. Major emphasis is placed upon the formulation of the best possible starting or nominal solution. Constraint relationships among the state and costate variables are utilized. A hybrid approach which begins with the direct gradient method and ends with the indirect method of particular solutions is proposed. Test case results which indicate improved reliability are presented. The nonlinear optimal control law derived from iterative procedures cannot adjust itself in accordance with state deviations measured during the control period. A real-time near-optimal guidance scheme which takes the perturbed states to the desired manifold by tracking a given optimal trajectory is also proposed. Numerical simulations are presented which show that highly accurate tracking results can be achieved. / Ph. D.

Polynomial feedback controls are developed for large angle, nonlinear spacecraft attitude maneuvers. Scalar and two-state systems are presented as simple examples to demonstrate the method, and several systems of state variables to parameterize spacecraft motion are considered. Both external and internal control torques are treated; in the latter, attention is restricted to momentum transfer maneuvers that permit several order reductions. Several stability theorems with their application to polynomial feedback systems are discussed. / Ph. D.

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.