Séminaire online à 14h00 donné par Weijia Yao de l’université de Groningen .
Abstract : With flexible structures we mean mechanisms with moving parts that can possibly show some flexible deformation behaviours. From a mathematical point of view, the flexible parts are distributed parameter systems whose dynamics are described by Partial Differential Equations (PDE), while the dynamics of the rigid parts are described by Ordinary Differential Equations (ODE). Therefore, the total model is described by a mixed set of ODE-PDE (m-ODE-PDE). For studying these dynamical models, we use the port-Hamiltonian approach combined with the infinite-dimensional semigroup theory.
In this presentation, we will consider a linear class of m-ODE-PDE that is general enough to include a large number of physical systems, but structured enough to conclude about some solutions’ properties that help in the system’s analysis. Firstly, we show the modelling procedure of a string with a tip mass and how to fit it in the defined class of m-ODE-PDE. Secondly, we introduce some mathematical tools, related to the generalization of the Lyapunov theory to infinite-dimensional systems, used to study the systems stability. Therefore, we introduce two different control laws: a classical PD controller and a “strong-dissipation” feedback controller. Finally, the closed-loop stability analysis is briefly discussed for both control laws using the previously introduced mathematical tools.