Nonlinear control of a coupled PDE/ODE system modeling a switched power converter with a transmission line

Jamal Daafouz (1) , Marius Tucsnak (2, 3) , Julie Valein (3)

1 CRAN - Centre de Recherche en Automatique de Nancy
2 CORIDA - Robust control of infinite dimensional systems and applications
3 IECL - Institut Élie Cartan de Lorraine

We consider an infinite dimensional system modelling a boost converter connected to a load via a transmission line. The governing equations form a system coupling the telegraph partial differential equation with the ordinary differential equations model-ing the converter. The coupling is given by the boundary conditions and the nonlinear controller we introduce. We design a nonlinear saturating control law using a Lya-punov function for the averaged model of the system. The main results give the well-posedness and stability properties of the obtained closed loop system.

Mots clés: stabilization; telegraph equations; power converters; infinite dimensional system; coupled system

Domaines: Equations aux dérivées partielles [math.AP]; Mathématiques [math]; Optimisation et contrôle [math.OC]; Mathématiques générales [math.GM]

Jamal Daafouz, Marius Tucsnak, Julie Valein. Nonlinear control of a coupled PDE/ODE system modeling a switched power converter with a transmission line. Systems and Control Letters, 2014, 70, pp.92-99. ⟨10.1016/j.sysconle.2014.05.009⟩. ⟨hal-01095237⟩