The attitude determination and control subsystem (ADCS) is a critical part of any satellite conducting scientific experiments that require accurate positioning (such as Earth observation and solar spectroscopy). The engineering design process of this subsystem has a long heritage; yet, it is surrounded by several limitations due to the stringent physical constraints imposed on small satellites. These limitations (e.g., limited computational capabilities, power, and volume) require an improved approach for the purpose of attitude determination (AD) and control. Previous space missions relied mostly on the extended Kalman filter (EKF) to estimate the relative orientation of the spacecraft because it yields an optimal estimator under the assumption that the measurement and process models are white Gaussian processes. However, this filter suffers from several limitations such as a high computational cost. This thesis addresses all the limitations found in small satellites by introducing a computationally efficient algorithm for AD based on a fuzzy inference system with a gradient decent optimization technique to calculate and optimize the bounds of the membership functions. Also, an optimal controller based on a fractional proportional-integral-derivative controller has been implemented to provide an energy-efficient control scheme. The AD algorithm presented in this thesis relies on the residual information of the Earth magnetic field. In contrast to current approaches, the new algorithm is immune to several limitations such as sensitivity to initial conditions and divergence problems. Additionally, its computational cost has been reduced. Simulation results illustrate a higher pointing stability, while maintaining satisfying levels of pointing accuracy and increasing reliability. Moreover, the optimal controller designed provides a shorter time delay, settling time, and steady-state error. This demonstrates that accurate attitude determination and control can be conducted in small spacecraft.

Les applications du calcul fractionnaire en automatique se sont considérablement développées ces dernières années, surtout en commande robuste. Ce mémoire est une contribution à la commande robuste des systèmes d'ordre entier à l'aide d'un correcteur PID d'ordre fractionnaire.Le conventionnel régulateur PID, unanimement apprécié pour le contrôle des processus industriels, a été adapté au cas fractionnaire sous la forme PInDf grâce à l'introduction d'un modèle de référence d'ordre non entier, réputé pour sa robustesse vis-à-vis des variations du gain statique.Cette nouvelle structure a été étendue aux systèmes à retard sous la forme d'un Prédicteur de SMITH fractionnaire. Dans leur forme standard, ces correcteurs sont adaptés à la commande des systèmes du premier et du second ordre, avec ou sans retard pur.Pour des systèmes plus complexes, deux méthodologies de synthèse du correcteur ont été proposées, grâce à la méthode des moments et à l'approche retour de sortie.Pour les systèmes dont le modèle est obtenu à partir d'une identification, la boucle fermée doit en outre être robuste aux erreurs d'estimation. Un modèle pire-cas, déduit de la matrice de covariance de l'estimateur et des domaines d'incertitudes fréquentielles, a été proposé pour la synthèse du correcteur.Les différentes simulations numériques montrent l'efficacité de cette méthodologie pour l'obtention d'une boucle fermée robuste aux variations du gain statique et aux incertitudes d'identification. / The application of fractional calculus in automatic control have received much attention these last years, mainly in robust control. This PhD dissertation is a contribution to the control of integer order systems using a fractional order PID controller.The classical PID, well known for its applications to industrial plants, has been adapted to the fractional case as a PInDf controller, thanks to a fractional order reference model, characterized by its robustness to static gain variations.This new controller has been generalized to time delay systems as a fractional SMITH Predictor. In standard case, these controllers are adapted to first and second order systems, with or without a time delay. For more complex systems, two design methodologies have been proposed, based on the method of moments and on output feedback approach.For systems whose model is obtained by an identification procedure, the closed loop has to be robust to estimation errors. So, a worst-case model, derived from the covariance matrix of the estimator and the frequency uncertainty domains, has been proposed for the design of the controller.The different numerical simulations demonstrate that this methodology is able to provide robustness to static gain variations and to identification uncertainties.

<div>In this thesis work, a novel approach for the design of a fractional order proportional integral</div><div>derivative (FOPID) controller is proposed. This design introduces a new time-varying FOPID controller</div><div>to mitigate a voltage spike at the controller output whenever a sudden change to the setpoint occurs. The</div><div>voltage spike exists at the output of the proportional integral derivative (PID) and FOPID controllers when a</div><div>derivative control element is involved. Such a voltage spike may cause a serious damage to the plant if it is</div><div>left uncontrolled. The proposed new FOPID controller applies a time function to force the derivative gain to</div><div>take effect gradually, leading to a time-varying derivative FOPID (TVD-FOPID) controller, which maintains</div><div>a fast system response and signi?cantly reduces the voltage spike at the controller output. The time-varying</div><div>FOPID controller is optimally designed using the particle swarm optimization (PSO) or genetic algorithm</div><div>(GA) to ?nd the optimum constants and time-varying parameters. The improved control performance is</div><div>validated through controlling the closed-loop DC motor speed via comparisons between the TVD-FOPID</div><div>controller, traditional FOPID controller, and time-varying FOPID (TV-FOPID) controller which is created</div><div>for comparison with all three PID gain constants replaced by the optimized time functions. The simulation</div><div>results demonstrate that the proposed TVD-FOPID controller not only can achieve 80% reduction of voltage</div><div>spike at the controller output but also is also able to keep approximately the same characteristics of the system</div><div>response in comparison with the regular FOPID controller. The TVD-FOPID controller using a saturation</div><div>block between the controller output and the plant still performs best according to system overshoot, rise time,</div><div>and settling time.</div>