Les Robots Parallèles à Câbles sont des robots possédant un effecteur relié à une base uniquement à l’aide de câbles, dont il est possible de modifier la longueur. Ils sont ainsi légers, capables de grandes dynamiques et peuvent présenter un énorme espace de travail.Mais ils sont sujets à des vibrations de grande amplitude et basse fréquence à cause de leur rigidité très faible. Cette thèse propose une approche originale d'amortissement actif pour atténuer efficacement ces vibrations. Le modèle dynamique du robot à câbles embarquant des roues à inertie est calculé, linéarisé autour d'un point d'équilibre et projeté dans l'espace modal dans lequel les vibrations sont découplées. Une commande par placement de pôles adapté à la fréquence naturelle de vibrations est appliquée pour chaque mode. Les résultats sur une simulation et deux prototypes sont présentés pour valider cette approche. / Cable-driven parallel robots use cables only to connect a fixed base to a mobile end-effector. Robot motion is obtained by winding the cables around pulleys to alter their length. Thus, cable-driven parallel robots are lightweight, can achieve very high dynamics and exhibit a very large workspace.Therefore, they are subject tp high magnitude and low frequency vibrations, because of their very low end-effector stiffness.This thesis proposes a novel approach for effective active damping of those vibrations.The dynamical model of a cable-driven parallel robot embedding reaction wheels is derived, lineraized around an equilibrium point and projected onto modal space, in which vibrations are decoupled.For each vibration mode, a control algorithm designed by poles placement adapted to the associated vibration natural frequency is applied for active vibration damping.Experiments conducted on a realistic simulation and two prototypes are presented to validate this approach.

The Finite Element Method (FEM) based computational mechanics is applied to simulate the optimal attenuation of vibrations in actively controlled structures. The simulation results provide the forces to be generated by actuators, as well as the structures response. Vibrations can be attenuated by applying either open loop or closed loop control strategies. In open loop control, the control forces for a given initial (or disturbed) configuration of the structure are determined in terms of time, and can be preprogrammed in advance. On the other hand, the control forces in closed loop control depend only on the current state of the system, which should be continuously monitored. Optimal attenuation is obtained by solving the optimality equations for the problem derived from the Pontryagins principle. These equations together with the initial and final boundary conditions constitute the two-point-boundary-value (TPBV) problem. <p>Here the optimal solutions are obtained by applying an analogy (referred to as the beam analogy) between the optimality equation and the equation for a certain problem of static beams in bending. The problem of analogous beams is solved by the standard FEM in the spatial domain, and then the results are converted into the solution of the optimal vibration control problem in the time domain. The concept of the independent-modal-space-control (IMSC) is adopted, in which the number of independent actuators control the same number of vibrations modes. <p>The steps of the analogy are programmed into an algorithm referred to as the Beam Analogy Algorithm (BAA). As an illustration of the approach, the BAA is used to simulate the open loop vibration control of a structure with several sets of actuators. Some details, such as an efficient meshing of the analogous beams and effective solving of the target condition are discussed. <p> Next, the BAA is modified to handle closed loop vibration control problems. The algorithm determines the optimal feedback gain matrix, which is then used to calculate the actuator forces required at any current state of the system. The methods accuracy is also analyzed.

The Finite Element Method (FEM) based computational mechanics is applied to simulate the optimal attenuation of vibrations in actively controlled structures. The simulation results provide the forces to be generated by actuators, as well as the structures response. Vibrations can be attenuated by applying either open loop or closed loop control strategies. In open loop control, the control forces for a given initial (or disturbed) configuration of the structure are determined in terms of time, and can be preprogrammed in advance. On the other hand, the control forces in closed loop control depend only on the current state of the system, which should be continuously monitored. Optimal attenuation is obtained by solving the optimality equations for the problem derived from the Pontryagins principle. These equations together with the initial and final boundary conditions constitute the two-point-boundary-value (TPBV) problem. <p>Here the optimal solutions are obtained by applying an analogy (referred to as the beam analogy) between the optimality equation and the equation for a certain problem of static beams in bending. The problem of analogous beams is solved by the standard FEM in the spatial domain, and then the results are converted into the solution of the optimal vibration control problem in the time domain. The concept of the independent-modal-space-control (IMSC) is adopted, in which the number of independent actuators control the same number of vibrations modes. <p>The steps of the analogy are programmed into an algorithm referred to as the Beam Analogy Algorithm (BAA). As an illustration of the approach, the BAA is used to simulate the open loop vibration control of a structure with several sets of actuators. Some details, such as an efficient meshing of the analogous beams and effective solving of the target condition are discussed. <p> Next, the BAA is modified to handle closed loop vibration control problems. The algorithm determines the optimal feedback gain matrix, which is then used to calculate the actuator forces required at any current state of the system. The methods accuracy is also analyzed.