Low-thrust spacecraft trajectory optimization is often a difficult and time-consuming process. One alternative is to instead use a closed-loop, feedback-driven control law, which calculates the control using knowledge of only the current state and target state, and does not require the solution of a nonlinear optimization problem or system of nonlinear equations. Though generally suboptimal, such control laws are attractive because of the ease and speed with which they may be implemented and used to calculate feasible low-thrust maneuvers. This thesis presents the theoretical foundations for seven modern low-thrust control laws based on control law "blending" and Lyapunov control theory for a particle spacecraft operating in an inverse-square gravitational field. The control laws are evaluated critically to determine those that present the best combinations of thoroughness of method and minimization of user input required. The three control laws judged to exhibit the most favorable characteristics are then compared quantitatively through three numerical simulations. The simulations demonstrate the effectiveness of feedback-driven control laws, but also reveal several situations in which the control laws may perform poorly or break down altogether due to either theoretical shortcomings or numerical difficulties. The causes and effects of these issues are explained, and methods of handling them are proposed, implemented, and evaluated. Various opportunities for further work in the area are also described. / text

The design of controllers subject to the nonlinear H-infinity criterion is explored. The plants to be controlled are the attitude motion of spacecraft, subject to some disturbance torque. Two cases are considered: the regulation about an inertially-fixed direction, and an Earth-pointing spacecraft in a circular orbit, subject to the gravity-gradient torque. The spacecraft attitude is described using the modified Rodrigues parameters. A series of controllers are designed using the nonlinear H-infinity control criterion, and are subsequently generated using a Taylor series expansion to approximate solutions of the relevant Hamilton-Jacobi equations. The controllers are compared, using both input-output and initial condition simulations. A proof is used to demonstrate that the linearized controller solves the H-infinity control problem for the inertial pointing problem when describing the plant using the modified Rodrigues parameters.

The design of controllers subject to the nonlinear H-infinity criterion is explored. The plants to be controlled are the attitude motion of spacecraft, subject to some disturbance torque. Two cases are considered: the regulation about an inertially-fixed direction, and an Earth-pointing spacecraft in a circular orbit, subject to the gravity-gradient torque. The spacecraft attitude is described using the modified Rodrigues parameters. A series of controllers are designed using the nonlinear H-infinity control criterion, and are subsequently generated using a Taylor series expansion to approximate solutions of the relevant Hamilton-Jacobi equations. The controllers are compared, using both input-output and initial condition simulations. A proof is used to demonstrate that the linearized controller solves the H-infinity control problem for the inertial pointing problem when describing the plant using the modified Rodrigues parameters.

The time-dependent modulation of galactic cosmic rays in the heliosphere is studied by computing intensities using a two-dimensional, time-dependent modulation model. The compound approach of Ferreira and Potgieter (2004), which describes changes in the cosmic ray transport coefficients over a solar cycle, is improved by introducing recent theoretical advances in the model. Computed intensities are compared with Voyager 1 and 2, IMP 8 and Ulysses proton observations in search of compatibility. It is shown that this approach gives realistic cosmic ray proton intensities on a global scale at Earth and along both Voyager spacecraft trajectories. The results show that cosmic ray modulation, in particular during the present polarity cycle, is not just determined by changes in the drift coefficient but is also dependent on changes in the diffusion coefficients. Furthermore, a comparison of computations to observations along the Voyager 1 and Voyager 2 trajectories illustrates that the heliosphere is asymmetrical. Assuming the latter, E > 70 MeV and 133-242 MeV cosmic ray proton intensities along Voyager 1 and 2 trajectories are predicted from 2012 onwards. It is shown that the computed intensities along Voyager 1 can increase with an almost constant rate since the spacecraft is close to the heliopause. However, the model shows that Voyager 2 is still under the influence of temporal solar activity changes because of the relatively large distance to the heliopause when compared to Voyager 1. Along the Voyager 2 trajectory the intensities should remain generally constant for the next few years and then should start to steadily increase. It is also found that without knowing the exact location of heliopause and transport parameters one cannot conclude anything about local interstellar spectra. The effect of a dynamic inner heliosheath width on cosmic ray modulation is also studied by implementing a time-dependent termination shock position in the model. This does not lead to improved compatibility with spacecraft observations so that a time-dependent termination shock along with a time-dependent heliopause position is required. The variation of the heliopause position over a solar cycle is found to be smaller compared to that of the termination shock. The model predicts the heliopause and termination shock positions along Voyager 1 in 2012 at 119 AU and 88 AU respectively and along Voyager 2 at 100 AU and 84 AU respectively. / Thesis (PhD (Space Physics))--North-West University, Potchefstroom Campus, 2013

The time-dependent modulation of galactic cosmic rays in the heliosphere is studied by computing intensities using a two-dimensional, time-dependent modulation model. The compound approach of Ferreira and Potgieter (2004), which describes changes in the cosmic ray transport coefficients over a solar cycle, is improved by introducing recent theoretical advances in the model. Computed intensities are compared with Voyager 1 and 2, IMP 8 and Ulysses proton observations in search of compatibility. It is shown that this approach gives realistic cosmic ray proton intensities on a global scale at Earth and along both Voyager spacecraft trajectories. The results show that cosmic ray modulation, in particular during the present polarity cycle, is not just determined by changes in the drift coefficient but is also dependent on changes in the diffusion coefficients. Furthermore, a comparison of computations to observations along the Voyager 1 and Voyager 2 trajectories illustrates that the heliosphere is asymmetrical. Assuming the latter, E > 70 MeV and 133-242 MeV cosmic ray proton intensities along Voyager 1 and 2 trajectories are predicted from 2012 onwards. It is shown that the computed intensities along Voyager 1 can increase with an almost constant rate since the spacecraft is close to the heliopause. However, the model shows that Voyager 2 is still under the influence of temporal solar activity changes because of the relatively large distance to the heliopause when compared to Voyager 1. Along the Voyager 2 trajectory the intensities should remain generally constant for the next few years and then should start to steadily increase. It is also found that without knowing the exact location of heliopause and transport parameters one cannot conclude anything about local interstellar spectra. The effect of a dynamic inner heliosheath width on cosmic ray modulation is also studied by implementing a time-dependent termination shock position in the model. This does not lead to improved compatibility with spacecraft observations so that a time-dependent termination shock along with a time-dependent heliopause position is required. The variation of the heliopause position over a solar cycle is found to be smaller compared to that of the termination shock. The model predicts the heliopause and termination shock positions along Voyager 1 in 2012 at 119 AU and 88 AU respectively and along Voyager 2 at 100 AU and 84 AU respectively. / Thesis (PhD (Space Physics))--North-West University, Potchefstroom Campus, 2013

The James Web Space telescope will replace the aging Hubble in 2012. One instrument onboard will be the Near Infrared Spectroscope which will require a reconfigurable slit mask to control light incident upon it. One design for this device is called the Mechanically Actuated Reconfigurable Slit mask (MARS). The MARS uses several electromagnetic clamps to move shutters though the focal plane. The goal of this thesis is to develop a system to characterise these clamps at cryogenic temperatures. FEA simulations predicted clamp performance and aided in the development of a test apparatus. An apparatus which utilises the Lorentz force to force the clamp jaws open was developed, built and tested. The device was built inside a cryostat which operated at 30 K. It was found that the test apparatus performed as intended. The clamps themselves proved to be problematic. Small perturbations or misalignments caused significant inconsistencies in experimental results.

This dissertation is concerned with identification of nonlinear instabilities in rotating multibody systems and subsequent control to eliminate the vibrations. Three nonlinear mechanical systems of this type are investigated and instabilities arising from their inherent nonlinearities are shown to exist for a range of system parameters and conditions. Subsequently, various nonlinear methods of vibration control have been employed to eliminate or suppress the instabilities. Analytical and numerical models have been designed to demonstrate various unstable dynamical behaviour with consistent results. The motion is studied by means of time history, phase space, frequency spectrum, Poincare map, Lyapunov characteristic exponents and Correlation Dimension. Numerical simulations have also shown the effectiveness and robustness of the control techniques over a range of instability conditions for each model. The dynamics of a rotating body with internal energy dissipation is first investigated. Such a model may be considered to be representative of a simplified spinning spacecraft. A comprehensive stability analysis is performed and regions of highly nonlinear behaviour are identified for more rigorous investigation. Numerical simulations using typical satellite parameter values are performed and the system is found to exhibit chaotic motion when a sinusoidally varying torque is applied to the spacecraft for a range of forcing amplitude and frequency. Analysis of this model using Melnikov’s method is performed and a sufficient criterion for chaotic instabilities is obtained in terms of system parameters. Evidence is also presented, indicating that the onset of chaotic motion is characterised by period doubling as well as intermittency. Subsequently, Control of chaotic vibrations in this model is achieved using three techniques. The control methods are implemented on the model under instability conditions. The first two control techniques, recursive proportional feedback (RPF) and continuous delayed feedback are recently developed model independent methods for control of chaotic motion in dynamical systems. As such these methods are employed on all three rotating multibody systems in this dissertation. Control of chaotic instability in this model is also achieved using an algorithm derived using Lyapunov’s second method. Each technique is outlined and the effectiveness of the three strategies in controlling chaotic motion exhibited by the present system is compared and contrasted. The dynamics of a dual-spin spacecraft with internal energy dissipation in the form of an axial nutational damper is also investigated for non-linear phenomena. The problem involves the study of a body with internal moving parts that is characterised by a coupling of the motions of the damper mass and the angular rotations of the platform and rotor of the spacecraft. Two realistic spacecraft parameter configurations are investigated and each is found to exhibit chaotic motion when a sinusoidally varying torque is applied to the spacecraft rotor for a range of forcing amplitude and frequency. Onset of chaotic motion was shown to be characterised by period doubling and Hopf bifurcations. An investigation of the effects of damping upon the configuration is also performed. Predicted instabilities indicate the range of rotor speeds, perturbation amplitudes and damping coefficients to be avoided in the design of dual-spin spacecraft. Control of chaotic vibrations in this model is also achieved using recursive proportional feedback (RPF) and continuous delayed feedback. Subsequently a more effective model dependent method based on energy considerations is derived and implemented. The effectiveness and robustness of each technique is shown using numerical simulations. Another rotating multibody system that is physically distinct from the previously described models is also investigated for nonlinear instabilities and control. The model is in the form of a driveline which incorporates a commonly used coupling called a Hooke’s joint. In particular, torsional instabilities due to fluctuating angular velocity ratio across the joint are examined. Linearised equations are used for the prediction of critical speed ranges where parametric instabilities characterised by exponential build up of torsional response amplitudes occur. Predicted instabilities indicate the range of driveshaft speeds to be avoided during the design of a driveline which employs a Hooke's joint. Numerical simulations further demonstrate the existence of parametric, quasi-periodic and chaotic instabilities. Subsequently, suppression of these vibrations is achieved using the previously described model independent techniques. Chaotic vibrations have also been observed in a range of simple mechanical systems such as a periodically kicked rotor, forced pendulum, synchronous rotor, aeroelastic panel flutter and impact print hammer to name but a few. It is thus becoming of increasing importance to engineers to be aware of chaotic phenomena and be able to recognise, quantify and eliminate these undesirable vibrations. The analytical and numerical methods described in this dissertation may be usefully employed by engineers for detecting as well as controlling chaotic vibrations in an extensive range of physical systems.

Thesis (M.A.)--University of North Texas, Dec., 2007. / Title from title page display. Includes bibliographical references.

Thesis (Ph. D.)--Virginia Polytechnic Institute and State University, 2000. / Computer printout. "April 2000." "March 7, 2000"--Cover. Includes bibliographical references (p. 360-377).

Space missions increasingly require sophisticated guidance, navigation and control algorithms, the development of which is reliant on verification and validation (V&V) techniques to ensure mission safety and success. A crucial element of V&V is the assessment of control system robust performance in the presence of uncertainty. In addition to estimating average performance under uncertainty, it is critical to determine the worst case performance. Industrial V&V approaches typically employ mu-analysis in the early control design stages, and Monte Carlo simulations on high-fidelity full engineering simulators at advanced stages of the design cycle. While highly capable, such techniques present a critical gap between pessimistic worst case estimates found using analytical methods, and the optimistic outlook often presented by Monte Carlo runs. Conservative worst case estimates are problematic because they can demand a controller redesign procedure, which is not justified if the poor performance is unlikely to occur. Gaining insight into the probability associated with the worst case performance is valuable in bridging this gap. It should be noted that due to the complexity of industrial-scale systems, V&V techniques are required to be capable of efficiently analysing non-linear models in the presence of significant uncertainty. As well, they must be computationally tractable. It is desirable that such techniques demand little engineering effort before each analysis, to be applied widely in industrial systems. Motivated by these factors, this thesis proposes and develops an efficient algorithm, based on the cross entropy simulation method. The proposed algorithm efficiently estimates the probabilities associated with various performance levels, from nominal performance up to degraded performance values, resulting in a curve of probabilities associated with various performance values. Such a curve is termed the probability profile of performance (PPoP), and is introduced as a tool that offers insight into a control system's performance, principally the probability associated with the worst case performance. The cross entropy-based robust performance analysis is implemented here on various industrial systems in European Space Agency-funded research projects. The implementation on autonomous rendezvous and docking models for the Mars Sample Return mission constitutes the core of the thesis. The proposed technique is implemented on high-fidelity models of the Vega launcher, as well as on a generic long coasting launcher upper stage. In summary, this thesis (a) develops an algorithm based on the cross entropy simulation method to estimate the probability associated with the worst case, (b) proposes the cross entropy-based PPoP tool to gain insight into system performance, (c) presents results of the robust performance analysis of three space industry systems using the proposed technique in conjunction with existing methods, and (d) proposes an integrated template for conducting robust performance analysis of linearised aerospace systems.