In this thesis, attitude control of small satellites with dissimilar actuator is studied and the effects of control allocation methods on maneuvering are examined in detail. Magnetorquers and reaction wheels are considered as the actuators of a modeled remote sensing -nadir pointing- small satellite. Matlab&reg / Simulink simulation models are developed to model the satellite dynamics and the actuators on the satellite. The simulations are based on conceptual RASAT satellite, and, for verification, orbit data is taken from BILSAT satellite that is operated by TUBITAK Space Research Institute. Basic satellite control modes are developed and tested to obtain nominal control. Actuator failures are analyzed for different possible cases. A control allocation method called Blended Inverse that was originally proposed for steering CMGs is applied to select the actuators to avoid actuator saturation and singularity transition. The performance of traditional pseudo inverse method is compared with the blended inverse method and simulation results are given and discussed. The superiority of blended inverse over pseudo inverse is demonstrated.

Neural networks play an important role in the execution of goal-oriented paradigms. They offer flexibility, adaptability and versatility, so that a variety of approaches may be used to meet a specific goal, depending upon the circumstances and the requirements of the design specifications. Development of higher-order neural units with higher-order synaptic operations will open a new window for some complex problems such as control of aerospace vehicles, pattern recognition, and image processing. The neural models described in this thesis consider the behavior of a single neuron as the basic computing unit in neural information processing operations. Each computing unit in the network is based on the concept of an idealized neuron in the central nervous system (CNS). Most recent mathematical models and their architectures for neuro-control systems have generated many theoretical and industrial interests. Recent advances in static and dynamic neural networks have created a profound impact in the field of neuro-control. Neural networks consisting of several layers of neurons, with linear synaptic operation, have been extensively used in different applications such as pattern recognition, system identification and control of complex systems such as flexible structures, and intelligent robotic systems. The conventional linear neural models are highly simplified models of the biological neuron. Using this model, many neural morphologies, usually referred to as multilayer feedforward neural networks (MFNNs), have been reported in the literature. The performance of the neurons is greatly affected when a layer of neurons are implemented for system identification, pattern recognition and control problems. Through simulation studies of the XOR logic it was concluded that the neurons with linear synaptic operation are limited to only linearly separable forms of pattern distribution. However, they perform a variety of complex mathematical operations when they are implemented in the form of a network structure. These networks suffer from various limitations such as computational efficiency and learning capabilities and moreover, these models ignore many salient features of the biological neurons such as time delays, cross and self correlations, and feedback paths which are otherwise very important in the neural activity. In this thesis an effort is made to develop new mathematical models of neurons that belong to the class of higher-order neural units (HONUs) with higher-order synaptic operations such as quadratic and cubic synaptic operations. The advantage of using this type of neural unit is associated with performance of the neurons but the performance comes at the cost of exponential increase in parameters that hinders the speed of the training process. In this context, a novel method of representation of weight parameters without sacrificing the neural performance has been introduced. A generalised representation of the higher-order synaptic operation for these neural structures was proposed. It was shown that many existing neural structures can be derived from this generalized representation of the higher-order synaptic operation. In the late 1960s, McCulloch and Pitts modeled the stimulation-response of the primitive neuron using the threshold logic. Since then, it has become a practice to implement the logic circuits using neural structures. In this research, realization of the logic circuits such as OR, AND, and XOR were implemented using the proposed neural structures. These neural structures were also implemented as neuro-controllers for the control problems such as satellite attitude control and model reference adaptive control. A comparative study of the performance of these neural structures compared to that of the conventional linear controllers has been presented. The simulation results obtained in this research were applicable only for the simplified model presented in the simulation studies.

Neural networks play an important role in the execution of goal-oriented paradigms. They offer flexibility, adaptability and versatility, so that a variety of approaches may be used to meet a specific goal, depending upon the circumstances and the requirements of the design specifications. Development of higher-order neural units with higher-order synaptic operations will open a new window for some complex problems such as control of aerospace vehicles, pattern recognition, and image processing. The neural models described in this thesis consider the behavior of a single neuron as the basic computing unit in neural information processing operations. Each computing unit in the network is based on the concept of an idealized neuron in the central nervous system (CNS). Most recent mathematical models and their architectures for neuro-control systems have generated many theoretical and industrial interests. Recent advances in static and dynamic neural networks have created a profound impact in the field of neuro-control. Neural networks consisting of several layers of neurons, with linear synaptic operation, have been extensively used in different applications such as pattern recognition, system identification and control of complex systems such as flexible structures, and intelligent robotic systems. The conventional linear neural models are highly simplified models of the biological neuron. Using this model, many neural morphologies, usually referred to as multilayer feedforward neural networks (MFNNs), have been reported in the literature. The performance of the neurons is greatly affected when a layer of neurons are implemented for system identification, pattern recognition and control problems. Through simulation studies of the XOR logic it was concluded that the neurons with linear synaptic operation are limited to only linearly separable forms of pattern distribution. However, they perform a variety of complex mathematical operations when they are implemented in the form of a network structure. These networks suffer from various limitations such as computational efficiency and learning capabilities and moreover, these models ignore many salient features of the biological neurons such as time delays, cross and self correlations, and feedback paths which are otherwise very important in the neural activity. In this thesis an effort is made to develop new mathematical models of neurons that belong to the class of higher-order neural units (HONUs) with higher-order synaptic operations such as quadratic and cubic synaptic operations. The advantage of using this type of neural unit is associated with performance of the neurons but the performance comes at the cost of exponential increase in parameters that hinders the speed of the training process. In this context, a novel method of representation of weight parameters without sacrificing the neural performance has been introduced. A generalised representation of the higher-order synaptic operation for these neural structures was proposed. It was shown that many existing neural structures can be derived from this generalized representation of the higher-order synaptic operation. In the late 1960s, McCulloch and Pitts modeled the stimulation-response of the primitive neuron using the threshold logic. Since then, it has become a practice to implement the logic circuits using neural structures. In this research, realization of the logic circuits such as OR, AND, and XOR were implemented using the proposed neural structures. These neural structures were also implemented as neuro-controllers for the control problems such as satellite attitude control and model reference adaptive control. A comparative study of the performance of these neural structures compared to that of the conventional linear controllers has been presented. The simulation results obtained in this research were applicable only for the simplified model presented in the simulation studies.

This thesis addresses the attitude control of satellites with similar and dissimilar actuators and control allocation methods on maneuvering. In addition, the control moment gyro (CMG) steering with gyroscopes having limited gimbal angle travel is also addressed. Full Momentum envelopes for a cluster of four CMG&#039 / s are obtained in a pyramid type mounting arrangement. The envelopes when gimbal travel is limited to plus-minus 90 degree are also obtained. The steering simulations using Moore Penrose (MP) pseudo inverse as well as blended inverse are presented and success of the pre planned blended inverse steering in avoiding gimbal angle limits is demonstrated through satellite slew maneuver simulations, showing the completion of the maneuver without violating gimbal angle travel restrictions. Dissimilar actuators, CMG and magnetic torquers are used as an approach of overactuated system. Steering simulations are carried out using different steering laws for constant torque and desired satellite slew maneuver scenarios. Success of the blended inverse steering algorithm over MP pseudo inverse is also demonstrated

Cette thèse porte sur la commande variant dans le temps avec comme fil directeur l’application au contrôle d’attitude de satellites. Nous avons étudié trois types de commande: une commande à commutation, une commande LPV et une commande adaptative directe. Pour cette dernière nous avons proposé des résultats théoriques nouveaux portant sur la structuration du gain et de l’adaptation. Les résultats ont été validés en simulation et sont testés à bord d’un satellite. En partant de la loi à commutation actuellement utilisée sur les satellites Myriade, une première partie de nos travaux est dédiée à la commande LPV. Notre approche, basée sur la spécification des objectifs de commande à travers un modèle de référence LPV, permet d'obtenir de nouveaux algorithmes exprimés dans ce formalisme. Testées en simulation, ces lois de commande répondent à la problématique de notre application. Toutefois, le choix du modèle de référence LPV s'avère délicat. Cette difficulté a été levée en utilisant la commande adaptative. Dans cette approche, les spécifications sur le comportement temps-variant sont traduites par des contraintes au niveau des lois d'adaptation des gains de commande. Nous introduisons ainsi une nouvelle méthode de synthèse de lois adaptatives structurées. Les preuves de stabilité établies s'appuient sur des outils de la théorie de Lyapunov. Les résultats obtenus sur un simulateur complet montrent l'intérêt de tels algorithmes adaptatifs. Ils permettent en particulier de modifier la dynamique du satellite selon les capacités disponibles des actionneurs. Sur la base de ces résultats, une campagne d’essai en vol sur le satellite PICARD est actuellement en cours. / This manuscript considers time varying control, with a strong emphasis on a satellite attitude control application. Three types of control structures have been studied: a switch-based approach, LPV control and direct adaptive control. In this last field we have introduced new theoretical results which allow structuring the gain and the adaptation law. The results have been validated in simulation and are currently tested on board a satellite. Starting from the switch-based control law currently implemented on the Myriade satellites, a first part of our work isdedicated to LPV control. Based on the specification of the control objectives by using of an LPV reference model, our approach allows obtaining new control algorithms expressed within this framework. The simulations carried out with theLPV algorithms obtained by using this method show that they meet the needs of our application. Nonetheless, the choice of a reference model proves to be difficult. This obstacle has been surpassed by using direct adaptive control. In this approach, specifications regarding the timevarying behaviour are added through constraints on the laws defining the control gains adaptation. We thus introduce anew synthesis method, based on which structured adaptive control laws are obtained. Stability proofs are established based on tools of the Lyapunov theory.The results obtained on a complete simulator show the interest of using such adaptive algorithms, which allow in particular to modify the satellite dynamics depending on the available capacity of the actuators. Based on these positive results, a fight-test campaign on the PICARD satellite is underway.

Studies aimed at the development of indigenous low cost star tracker and gyroless attitude and angular rate estimation is presented in the thesis. This study is required for the realization of low cost micro satellites. A target specification of determining the attitude with accuracy (3σ) of 0.05 degrees and attitude rate with accuracy (3σ) in the range of 50rad/sec at a rate of 10 samples/second in all the axes is set as a goal for the study. Different sensor arrays available in the market are evaluated on the basis of their noise characteristics, resolution of the analog-to-digital converter (ADC) present and ability to work in low light conditions, for possible use in the hardware realization of star tracker. STAR1000 APS CMOS array, manufactured by Cypress Semiconductors, qualified these performance criteria, is used for the simulation study. An algorithm is presented for scanning the sensor array, detection of star image and retrieving the information concerning the photoelectron counts corresponding to a star image. The exact designation of the center of the star image becomes crucial as it has direct implications on the accuracy of the estimated attitude. Various algorithms concerning the centroid estimation of a defocused star image on the sensor array to subpixel accuracy are studied and Gaussian Weighed Center of Gravity algorithm is adapted with some modifications and an accuracy of 0.039 pixels is obtained in both horizontal and vertical direction of the array. A one-to-one relationship is established between the stars obtained in the field-of-view (FOV) of the star tracker with the stars present in the star catalog resident in the star tracker through star identification algorithm. A star identification algorithm which relies on the interstar angles and brightness of the stars is developed in this thesis. The interstar angles of the stars visible in the FOV of the star sensor is recorded, compared with the inter-star angles made by the stars selected in the catalog, based on initial brightness match with stars formed on image plane. After identification at the initial epoch, consequent instants can drive information from the previous matches so as to decrease the computational complexity and storage requirement for the subsequent instants. The memory constraints and computational overhead on the processor and the dynamic range of the image detector used in the star tracker are the limiting factors. The stars thus identified with the stars in the catalog are used for the estimation of attitude. A point solution to the attitude estimation problem is computed using a least square based algorithm called ESOQ-2. The algorithm for centroiding of star images and ESOQ-2 for finding the point solution satellite attitude is coded and tested on Da Vinci based emulator. This exercise shows that it is possible to implement above algorithm for real time operations. Estimation of attitude at a given epoch using algorithms like ESOQ-2 does not minimize the noise and error covariance as the attitude estimated at each instant of time depends only on the measurement taken at that particular instant. So a Kalman Filter (KF) based estimation using Integrated Rate Parameter (IRP) formulation called SIAVE algorithm, is adapted, with some modifications, for the estimation of incremental angle and attitude rates from vector observations of stars. From the point solution of attitude estimation problem of the satellite, the incremental angle and angular rate at successive time steps are predicted using a linear KF and refined with the measurements from the stand alone star tracker, taken at discrete time steps, using the SIAVE algorithm. The sensor noise is modeled from the characteristics of STAR1000 sensor array used in the algorithm in order to make the simulations more realistic in nature. The optimality of Kalman filter is based on the assumption that the state and measurement noises are white gaussian random processes and the state dynamics of the plant is completely known. However, for most real systems, modeling uncertainties are present. So a robust state estimator based on H∞ norm minimization is devised. The H∞ filter, based on game theory approach is used to minimize the worst case variance of noise signals with the only assumption on the noise signals that they are energy bounded. The aim is to find the feasibility of using H∞ filter for the estimation of incremental angle and attitude rate of the satellite. The studies shows that H∞ filter with proper tuning can serve as potential estimation scheme for the attitude and angular rate estimation of the satellite. It is found that both Kalman filter and H∞ are able to meet the specified accuracy desired from low cost accurate star sensor.

This thesis presents the design of Kalman filter based attitude determination algorithms for a hypothetical LEO satellite and for a satellite attitude control test setup. For the hypothetical LEO satellite, an Extended Kalman Filter based attitude determination algorithms are formed with a multi-mode structure that employs the different sensor combinations and as well as online switching between these combinations depending on the sensor availability. The performance of these different attitude determination modes are investigated through Monte Carlo simulations. New attitude determination algorithms are prepared for the satellite attitude control test setup by considering the constraints on the selection of the suitable sensors. Here, performances of the Extended Kalman Filter and Unscented Kalman Filter are investigated. It is shown that robust and sufficiently accurate attitude estimation for the test setup is achievable by using the Unscented Kalman Filter.

Cette thèse porte sur la commande adaptative directe robuste et son application au contrôle d’attitude des satellites de la filière Myriade du CNES. Après avoir présenté les différents types de commande variant dans le temps, nous rappelons les caractéristiques d’un contrôleur adaptatif direct, en particulier le fait que la seule connaissance d’un retour de sortie stabilisant le système à contrôler suffit pour concevoir un contrôleur adaptatif direct. Parallèlement, nous présentons la théorie des systèmes descripteurs. Modéliser un système sous forme descripteur est non conventionnel mais présente de nombreux avantages dans le contexte de la commande adaptative directe robuste. A l’aide des résultats existants sur la commande adaptative directe d’une part, et de la théorie des systèmes descripteurs d’autre part, nous fournissons une méthode permettant de calculer, connaissant un retour de sortie constant, les paramètres d’un contrôleur adaptatif direct robuste stabilisant. Cette méthode repose sur la résolution d’inégalités matricielles linéaires. Le contrôleur adpatatif est plus robuste que le contrôleur constant, mais on ne peut prouver que la stabilité globale que vers un voisinage du point d’équilibre. Nous présentons ensuite une méthode, également basée sur la résolution d’inégalités matricielles linéaires, permettant de concevoir un contrôleur adaptatif direct robuste de meilleur niveau de rejet des perturbations extérieures que le contrôleur constant à partir duquel il est construit. L’ensemble de ces résultats théoriques est ensuite appliqué au contrôle d’attitude des satellites de la filière Myriade du CNES. En particulier, nous concevons un contrôleur d’attitude stabilisant le satellite quelle que soit la valeur de son inertie. Ce contrôleur d’attitude est également capable d’éviter aux roues à réaction du satellite de saturer. Nous concevons ensuite un contrôleur d’attitude adaptatif, robuste, et qui rejette mieux les perturbations extérieures que le contrôleur constant à partir duquel il est construit. Ce contrôleur constant est d’ailleurs actuellement implémenté à bord des satellites de la filière Myriade du CNES. Enfin, nous validons l’ensemble des résultats de cette thèse à l’aide d’un simulateur SCAO du CNES, où nous simulons le déploiement des mâts d’un satellite, ainsi que des scénarii de sauts de guidage. / This manuscript deals with robust direct adaptive control, and its application to CNES microsatellites attitude control. After listing the different types of time-varying controllers, we recall the characteristics of direct adaptive control. In particular, we recall that the knowledge of a stabilizing static output feedback is sufficient to design a direct adaptive controller. In parallel, we introduce the descriptor system theory. Modelizing a system into descriptor form is not usual but fits well with robust direct adaptive control. Starting from existing results about adaptive control and descriptor system theory, we provide an LMI based method which allows to compute, with the knowledge of a stabilizing static output feedback, the parameters of a stabilizing direct adaptive controller. A first result proves that the adaptive controller is at least as robust as the static output feedback. The second result allows to prove improved robustness at the expense of relaxing stability of the equilibrium point to practical stability, that is convergence to a neighborhood of the equilibrium. Then, we provide a method, LMI based as well, which allows to design a robust direct adaptive controller which has a better level of rejection of the perturbations than the static output feedback from which it is designed. All these theoretical results are applied to the attitude control of CNES microsatellites. We design a controller which stabilizes the attitude of the satellite whatever the value of its inertia. This attitude controller can also avoid the satellite reaction wheels to saturate. We design another robust adaptive attitude controller which has a better level of rejection of the perturbations than the static controller which is currently implemented aboard CNES satellites. Finally, we validate all the results of this manuscript by simulating on a AOCS CNES simulator the deployment of the satellite masts and some guiding jumps.