Singular perturbations for hyperbolic port-Hamiltonian and non-hyperbolic systems

Séminaire le 13 Juillet 2016, 10h30 à CentraleSupelec (Gif-sur-Yvette) Salle du conseil du L2S - B4.40
Prof. Jacquelien Scherpen, University of Groningen

In this talk we explore the methodology of model order reduction based on singular perturbations for a fexible-joint robot within the port-Hamiltonian framework. We show that a fexible-joint robot has a port-Hamiltonian representation which is also a singularly perturbed ordinary differential equation. Moreover, the associated reduced slow subsystem corresponds to a port-Hamiltonian model of a rigid-joint robot. To exploit the usefulness of the reduced models, we provide a numerical example where an existing controller for a rigid robot is implemented. In addition, we provide ideas on how to expand this to planar slow-fast systems at a non-hyperbolic point.  At these type of points, the classical theory of singular perturbations is not applicable and new techniques need to be introduced in order to design a controller that stabilizes such a point. We show for some class of nonlinear systems that using geometric  desingularization (also known as blow up), it is possible to design, in a simple way, controllers that stabilize non-hyperbolic equilibrium points of slow-fast systems. The results are exemplified on the Van der Pol oscillator.