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Publication# H∞ and μ-Synthesis for Nanosatellites Rendezvous and Docking

Résumé

In this brief, the nanosatellite rendezvous and docking problem is tackled. It was never attempted for small spacecraft, as critical technologies, such as six-degree-of-freedom (DoF) micropropulsion systems, have only recently become available due to advances in MEMS. The typical level of noise in nanosatellites' sensors and actuators combined with the dynamics uncertainties, low actuation capabilities, and reliability requirements makes the use of robust control appropriate. The system is described by a linearized rotation/translation, six DoFs, and coupled dynamics, including fuel sloshing. An H∞ controller is first designed, in which robust stability and performance are assessed using structured singular values. The controller robustness is then improved using μ-synthesis. Nonlinear Monte Carlo simulations for both controllers, including realistic sensors and actuators models, are provided allowing a thorough assessment of the complete guidance, navigation and control (GNC). The sought GNC schemes are shown to be robust to the modeled uncertainties and to satisfy the docking requirements.

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Concepts associés (12)

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Actionneur

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Ingénierie de fiabilité

L'ingénierie de fiabilité est un domaine de l'ingénierie, qui traite de l'étude, de l'évaluation et du Product Lifecycle Management de la fiabilité : l'habilité d'un système ou d'un composant à rempli

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Chargement

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Gorka Galdos Sanz de Galdeano, Alireza Karimi

The flexible transmission benchmark was proposed in the European Journal of Control to evaluate some robust digital control approaches in 1995. With progress in convex optimization algorithms new methods for robust controller design are developed. A recently proposed fixed-order robust controller design method is applied to this benchmark problem and the results are compared with the existing results. The proposed method is based on open-loop shaping with frequency-domain constraints on the closed-loop sensitivity functions in the Nyquist diagram. The method needs only the frequency response of the model and can consider the multimodel uncertainty. A controller is designed by a convex optimization algorithm that meets all the required performance specifications for the benchmark with the lowest controller complexity.

A global approach to the problem of model-based control of fast parallel robots is proposed in this work. Fundamental differences between the well-known serial arms and parallel manipulators are first explained. A formalism inspired from Denavit-Hartenberg's makes it possible to parametrize any parallel manipulator by handling it as two tree robots connected through six standard links. Then, it is shown that kinematics and dynamics modeling is greatly simplified when the robot's state is represented both by the variables associated to the actuated joints and the variables specifying the end-effector's position in operational space. The inverse dynamics model of any parallel manipulator can then be put under a standard form called "in the two spaces". A Newton-Euler based algorithm is proposed for the real-time computation of the model in the two spaces its complexity is shown not to be much larger than for serial arms. Through Lagrangian mechanics, the model in the two spaces allows analysis of the robot's dynamics properties, such as passivity. These properties are shown to be equivalent to those of serial arms, except that parallel robots offer good performances only in a restricted workspace in which their Jacobian matrix remains bounded. Various control strategies for the trajectory tracking problem for fast robots are then examined. The advantages of model-based approaches combined with robust feedback laws in operational space are described. It is shown that a control loop in operational space requires less computations than in joint space for a parallel robot. Moreover, such a scheme can be very efficiently be implemented on a multiprocessor control unit that exploits the intrinsically parallel and pipeline structure of the required algorithms. Finally, the proposed approach is applied to the Delta parallel manipulator. A systematic approach leads to the kinematics and dynamics models of this robot, which are expressed under a very compact form. The analysis of the Delta's Jacobian matrix as well as some simulation results reveal the advantages and weak points of this manipulator. The implementation of a model-based control law for the Delta on a control unit with four Transputers is described. Some results obtained on a Delta with a crank belt reduction are presented and discussed.

Michael Amrhein, Vinicius De Oliveira, Alireza Karimi

This paper addresses the control of the blending process in cement industries. This process can be modeled by a nonlinear multivariable system with large parametric uncertainty. Using a specific transformation, a linear parameter varying (LPV) model with set-points as scheduling parameters is developed. Moreover, the model uncertainty originated from the stochastic variation of the composition of the input materials is represented as a polytopic multimodel uncertainty. Then a multivariable gain-scheduled robust controller is designed by convex optimization to control the quality of the raw mix in the blending process. The control performance is illustrated by simulation and compared with a robust controller based on a nominal model.