The problem of system identification for dynamic effects on spacecraft has become increasingly relevant with the surge of agile spacecraft, which must perform large amplitude maneuvers at high rates. Precise knowledge of the state of the spacecraft, as well as of the parameters characterizing its motion, is vital for the design of control algorithms enabling stabilization and pointing accuracy. Traditional rigid body models and estimation methods are no longer sufficient to provide this knowledge. This thesis focuses on estimation of flexibility effects and spacecraft parameters through methods based on the unscented Kalman filter, an estimator for nonlinear dynamic systems. A spacecraft model consisting of a rigid central body and a flexible appendage described as an Euler-Bernoulli beam in pure bending is built, and equations for its translational and rotational motion, as well as the deflection of the beam, are derived in the Newton-Euler framework considering the first bending mode of the flexible deformation. Observability tests are successfully conducted to ensure that estimation of the relevant states and parameters can be performed exclusively from linear and angular velocity measurements. A total of eight filters, estimating the spacecraft’s state along with different combinations of parameters, are developed, implemented, and tested on simulated data. Grouped under the common denomination “UFFE” (Unscented Filter for Flexibility Effects), they are made available as Simulink library blocks. State estimation is performed for the linear and angular velocities of the spacecraft and the modal coordinate and velocity of the appendage, with estimates following closely the truth model of the state variables and estimation errors at least an order of magnitude lower than true state values. Simultaneous state and parameter estimation is implemented from two approaches, joint estimation and dual estimation, whose performance and applications are compared. Estimated parameters include the moments of inertia of the system and natural frequency, damping ratio, and modal participation factors of the flexible appendage. Convergence to true parameter values is reached in the first 100s of the estimation for inertia terms and natural frequency, while the estimation for modal participation factors is conditioned to precise tuning of the filter. Estimates of the damping ratio are biased, most likely due to the control input not being optimal for observation of this parameter. The dual approach to parameter estimation is found to be advantageous when proper filter tuning is possible, as it enables the continuous operation of a state filter combined with short runs of the parameter filter activated at will; this configuration could be employed to track the variation of spacecraft parameters along space missions.  The causes of estimation error are identified and methods for automatic tuning of the process noise and process noise covariance are researched. Five such tuning techniques are implemented and tested, with promising results found for online sampling of the process noise covariance through Monte Carlo methods. A discussion on the limitations of the chosen dynamic model and estimator, along with recommendations for extensions and future applications, concludes this work.

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.

The design of an attitude control system for a flexible spacecraft using magnetic actuation is considered. The nonlinear, linear, and modal equations of motion are developed for a general flexible body. Magnetic control is shown to be instantaneously underactuated, and is only controllable in the time-varying sense. A PD-like control scheme is proposed to address the attitude control problem for the linear system. Control gain limitations are shown to exist for the purely magnetic control. A hybrid control scheme is also proposed that relaxes these restrictions by adding a minimum control effort from an alternate three-axis actuation system. Floquet and passivity theory are used to obtain gain selection criteria that ensure a stable closed-loop system, which would aid in the design of a hybrid controller for a flexible spacecraft. The ability of the linearized system to predict the stability of the corresponding nonlinear system is also investigated.

The design of an attitude control system for a flexible spacecraft using magnetic actuation is considered. The nonlinear, linear, and modal equations of motion are developed for a general flexible body. Magnetic control is shown to be instantaneously underactuated, and is only controllable in the time-varying sense. A PD-like control scheme is proposed to address the attitude control problem for the linear system. Control gain limitations are shown to exist for the purely magnetic control. A hybrid control scheme is also proposed that relaxes these restrictions by adding a minimum control effort from an alternate three-axis actuation system. Floquet and passivity theory are used to obtain gain selection criteria that ensure a stable closed-loop system, which would aid in the design of a hybrid controller for a flexible spacecraft. The ability of the linearized system to predict the stability of the corresponding nonlinear system is also investigated.

La thèse porte sur le développement des techniques non linéaires robustes de stabilisation et commande des systèmes avec perturbations de model. D’abord, on introduit les concepts de base de stabilité et stabilisabilité robuste dans le contexte des systèmes non linéaires. Ensuite, on présente une méthodologie de stabilisation par retour d’état en présence d’incertitudes qui ne sont pas dans l’image de la commande («unmatched»). L’approche récursive du «backstepping» permet de compenser les perturbations «unmatched» et de construire une fonction de Lyapunov contrôlée robuste, utilisable pour le calcul ultérieur d’un compensateur des incertitudes dans l’image de la commande («matched»). Le contrôleur obtenu est appelé «recursive Lyapunov redesign». Ensuite, on introduit la technique de stabilisation par «Immersion & Invariance» comme outil pour rendre un donné contrôleur non linéaire, robuste par rapport à dynamiques non modelées. La première technique de contrôle non linéaire robuste proposée est appliquée au projet d’un autopilote pour un missile air-air et au développement d’une loi de commande d’attitude pour un satellite avec appendices flexibles. L’efficacité du «recursive Lyapunov redesign» est mis en évidence dans le deux cas d’étude considérés. En parallèle, on propose une méthode systématique de calcul des termes incertains basée sur un modèle déterministe d’incertitude. La partie finale du travail de thèse est relative à la stabilisation des systèmes sous échantillonnage. En particulier, on reformule, dans le contexte digital, la technique d’Immersion et Invariance. En premier lieu, on propose des solutions constructives en temps continu dans le cas d’une classe spéciale des systèmes en forme triangulaire «feedback form», au moyen de «backstepping» et d’arguments de domination non linéaire. L’implantation numérique est basée sur une loi multi-échelles, dont l’existence est garantie pour la classe des systèmes considérée. Le contrôleur digital assure la propriété d’attractivité et des trajectoires bornées. La loi de commande, calculée par approximation finie d’un développement asymptotique, est validée en simulation de deux exemples académiques et deux systèmes physiques, le pendule inversé sur un chariot et le satellite rigide. / The dissertation deals with the problems of stabilization and control of nonlinear systems with deterministic model uncertainties. First, in the context of uncertain systems analysis, we introduce and explain the basic concepts of robust stability and stabilizability. Then, we propose a method of stabilization via state-feedback in presence of unmatched uncertainties in the dynamics. The recursive backstepping approach allows to compensate the uncertain terms acting outside the control span and to construct a robust control Lyapunov function, which is exploited in the subsequent design of a compensator for the matched uncertainties. The obtained controller is called recursive Lyapunov redesign. Next, we introduce the stabilization technique through Immersion \& Invariance (I\&I) as a tool to improve the robustness of a given nonlinear controller with respect to unmodeled dynamics. The recursive Lyapunov redesign is then applied to the attitude stabilization of a spacecraft with flexible appendages and to the autopilot design of an asymmetric air-to-air missile. Contextually, we develop a systematic method to rapidly evaluate the aerodynamic perturbation terms exploiting the deterministic model of the uncertainty. The effectiveness of the proposed controller is highlighted through several simulations in the second case-study considered. In the final part of the work, the technique of I\& I is reformulated in the digital setting in the case of a special class of systems in feedback form, for which constructive continuous-time solutions exist, by means of backstepping and nonlinear domination arguments. The sampled-data implementation is based on a multi-rate control solution, whose existence is guaranteed for the class of systems considered. The digital controller guarantees, under sampling, the properties of manifold attractivity and trajectory boundedness. The control law, computed by finite approximation of a series expansion, is finally validated through numerical simulations in two academic examples and in two case-studies, namely the cart-pendulum system and the rigid spacecraft.