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The main objective of this study is to propose a methodology to build a parametric linear model of Flexible Multibody Systems for control design. This approach uses a combined Finite Element - State Space Approach based on component modes synthesis and double-port approach. The proposed scheme offers the advantage of automatic assembly of substructures, preserving the elastic dynamical behavior of the whole system. Substructures are connected following the double-port approach; i.e, through the transfer of accelerations and loads at the connection points, which take into account the dynamic coupling among them. In addition, parametric variations can be included in the model for accomplishing integrated control/structure design purposes. The method can be applied to combinations of chain-like or/and star-like flexible systems, and it is validated through its comparison with the assumed modes method for the case of a rotatory spacecraft., This paper has been withdrawn by the author due to significant changes in the article's content

International audience; This paper proposes an anti-windup strategy to deal with stability and performance requirements for a class of hybrid systems, such as those including a reset controller and subject to input saturation. The computation of the anti-windup compensator aiming at ensuring both $\mathcal{L}_2$ input-to-state stability and internal stability of the closed-loop system is carried out from the solution of matrix inequalities. Depending on the way chosen to describe reset rules, the conditions for designing the anti-windup compensator are expressed through nonlinear matrix inequalities or linear matrix inequalities. Some optimization criteria in both cases are considered for the synthesis purpose: maximization of the $\mathcal{L}_2$-norm upper bound on the admissible disturbances for which the trajectories are assured to be bounded; minimization of the $\mathcal{L}_2$-gain of the disturbance to the system to-be-controlled output; and the maximization of an estimate of the domain of attraction of the origin.

For a class of reset control systems, we reconsider the piecewise quadratic Lyapunov function construction proposed in Zaccarian et al. [2005]. In particular, we propose an alternative construction that addresses an analysis subtlety overlooked in that preliminary result. An example illustrates the potential pitfalls of ignoring this analysis subtlety. Another example is used to show that the new statement leads to numerical results that are similar to the ones that come from Zaccarian et al. [2005].

This study presents a generic TITOP (Two-Input Two-Output Port) model of a substructure actuated with embedded piezoelectric materials as actuators (PEAs), previously modeled with the FE technique. This allows intuitive assembly of actuated flexible substructures in large flexible multi-body systems. The modeling technique is applied to an illustrative example of a flexible beam with bonded piezoelectric strip and vibration attenuation of a chain of flexible beams., submitted to IFAC ACA 2016

International audience; This study presents the integrated control/structure design of a large flexible structure, the Extra Long Mast Observatory (ELMO). The integrated design is performed using structured Hinfinity control tools, developing the Two-Input Two-Output Port (TITOP) model of the flexible multi-body structure and imposing integrated design specifications as Hinfinity constraints. The integrated control/structure design for ELMO consists of optimizing simultaneously its payload mass and control system for low-frequency perturbation rejection respecting bandwidth requirements.

This paper is dedicated to the study of specific hybrid systems: reset control systems. A reset system is a system whose states are reset whenever its output and input satisfy an appropriate relationship. Stability analysis and L2-performance are studied for systems (and in particular for systems in closed-loop with reset controller) in presence of perturbations and parametric uncertainties. Based on the use of quadratic and piecewise quadratic Lyapunov functions, constructive conditions into LMI form are proposed. The potentialities of the approach are illustrated on a numerical example borrowed from the literature.

This paper proposes a double input output port transfer to model complex mechanical systems composed of several sub-systems. The sub-structure decomposition is revisited from the control designer point of view. The objective is to develop modelling tools to be used for mechanical/control co-design of large space flexible structures involving various substructures (boom, links of robotic arm,...) connected one to each other through dynamics local (actuated) mechanisms inducing complex boundary conditions. The double input output port model of each substructure is a transfer where accelerations and external forces at the connection points are both on the model inputs and outputs. Such a model : * allows to the boundary conditions linked to interactions with the other substructures to be externalized outside the model, * is defined by the only substructure own dynamic parameters, * allows to build the dynamic model of the whole structure by just assembling the double port models of each substructure. The principle is first introduced on a single axis spring-mass system and then extented to the 6 degress-of-freedom case. This generalization uses the clamped-free substructure dynamic parameters such as finite element softwares can provide.

This work presents a method to build a linear dynamic model of openchain assembly of spacecraft flexible appendages for future Attitude Control System (ACS)/Structure co-design. This kind of modeling takes into account the flexible interactions between all the spacecraft substructures, called bodies or appendages, to finally provide the loads (forces and torques) induced to the main body. More generally, this method can be applied to any open mechanical chain, such as segments of robotic arms, segments of antenna mast or masts linking solar panels to the main hub. Therefore, the dynamics model of the entire spacecraft can be derived easily in order to design the spacecraft ACS. The method is based on the Craig-Bampton modal synthesis, from which a state-space representation is obtained.

International audience; The study presents and validates a flexible appendage model to be used in an integrated control/structure spacecraft design. The integrated design methodology needs an accurate LFT representation of spacecraft flexible appendages so that parametric variations can be included. This requirement can be met using the Interconnected Flexible Appendage model studied in Perez et al. (2015). The model suitability is validated through the modeling of a real deployable boom, obtaining the same frequency modes and dynamical behavior.

This paper introduces an innovative method for the design of Earth Observation satellites with large flexible appendages that combines performance of the attitude control system and the structural sizing of the satellite itself. Such process is a structure-control co-design, obtained via a constrained optimisation. The objective is to determine a satellite structural model that minimises a cost function while preserving a controller performance index. The free parameters for optimisation are directly defined on the satellite Finite Element Model (FEM). For each optimisation step, the continuous dynamical model, in terms of mass, stiffness, and damping matrices, is obtained by performing FE analysis with commercial FEM software, and a linear robust control is synthesized. The control performance index is computed to evaluate whether the solution is compliant with the control requirements or not. A Genetic Algorithm is chosen as optimisation strategy to deal with the non-convexity of the search space, and both single and multi-objective optimisations are performed. The whole process has been tested and validated using as benchmark the Biomass satellite (selected for implementation as Earth Explorer Core Mission 7). The work described in this paper has been carried out in the frame of the study ”Modern attitude control of Earth Observation satellites with large flexible elements”, funded by the European Space Agency.

In this paper, a multi-model H1 synthesis scheme for fixed-structure controller design is developed and applied to the attitude control of a highly flexible earth-observation satellite. The particularity of the proposed approach is that the decision variables optimized by the fixed-structure Hinfinity solver include the structured controller parameters but also some parameters which characterize the avionics. Furthermore the proposed control scheme can be very easily adapted to a new configuration of sensors and thus can handle gyro or gyroless configurations. This way, various avionics configurations can be easily evaluated. The avionics characteristics for a given configuration and the control law can be simultaneously optimized avoiding time-consuming iterations between the definition of avionics and the design of the controller on the basis of the current avionics. The approach is applied on a earth observation satellite for two different study cases. The first one aims to design an improved controller in order to meet the nominal requirements with a poor avionics. The second ones aims to find a controller and an improved avionics to meet very challenging requirements.

In this paper, the modeling of flexible multi-body systems (typically a satellite), the design of a reduced-order robust controller and the closed-loop system robustness analysis are considered. First, we present a generic tool developed to build the model of a multi- body dynamic system taking into account parametric uncertainties for robust control and analysis purpose. Satellites are typically composed of a main body (hub of the satellite) and cantilevered appendages (flexible or not). Based on the description of each element(mechanical and geometrical properties, uncertain parameters ...), a linear model between torques applied to the hub (control or perturbation inputs) and angular accelerations is built using the Linear Fractional Representation framework. Second, based on this model, a control design method is proposed: from a basic standard scheme and the latest H_infinity solver, a low order H1 controller can be derived. Roll-off requirements and worst-case parametric configurations can also be taken into account in a multi-model design approach. Third, robustness analysis of the design on the full order model is considered. A numerical example illustrate the relevance and effectiveness of the proposed approach.