Andrea MATTIONI : "Modelling and stability analysis of flexible robots: a distributed parameter port-Hamiltonian approach"

Andrea MATTIONI PhD works :"Modelling and stability analysis of flexible robots: a distributed parameter port-Hamiltonian approach"

Abstract  : The objective of this thesis is to provide a mathematical framework that allows to explicit the dynamical model of a class of flexible mechanisms, to design their control law and to analyze the resulting closed loop asymptotic behaviour. From a mathematical point of view, the flexible parts are distributed parameter systems whosedynamics are described by Partial Differential Equations (PDE), while the dynamics of the rigid parts are described by Ordinary Differential Equation (ODE). Therefore, the total model is described by a mixed set of ODEPDE (m-PDE-ODE). For studying these dynamic models, this thesis uses the port-Hamiltonian framework combined with the infinite-dimensional semigroup theory. First, we define a rigorous procedure based on the Least Action Principle for deriving the model of mechanisms with possible flexible components, providing several illustrative examples. The general class of nonlinear systems enclosing all the proposed examples is shown to be passive with respect to its mechanical energy. In this class of systems, the distributed parameter parts are modelled as one dimensional boundary control systems. Second, we restrict ourselves to a linear class of m-ODEPDE systems for which we propose different control laws. We show that the proposed control laws allow achieving asymptotic or exponential stability. Finally, a rotating arm that enters in contact with the external environment is studied in case the link is considered as being both rigid or flexible. Since this system exhibits instant changes in the impact times, we study this problem with the help of switching theory applied to infinite dimensional systems.

Jury Composition :

Yann LE GORREC PR1 Université Bourgogne Franche-Comté PhD Director

Christophe PRIEUR Directeur de recherche Gipsa-lab Reporter

Lassi PAUNONEN Associate Professor Tampere University Reporter

Yongxin WU Maître de conférences Université Bourgogne Franche-Comté  PhD Co-director

Hans ZWART Professor University of Twente Reviewer

Mme Birgit JACOB Professor University of Wuppertal Reviewer

Alessandro MACCHELLI Associate Professor University of Bologna Reviewer

M. Bao-Zhu GUO Professor Chinese Academy of Science Reviewer

Localization : Salle de réunion AS2M, ENSMM - 26, Rue de l'Epitaphe - 25000 BESANCON