Robustness of an Adaptive Output Feedback for an Anti-Damped Boundary Wave PDE in Presence of In-Domain Viscous Damping

Christophe Roman (1, 2) , Delphine Bresch-Pietri (1) , Christophe Prieur (2) , Olivier Sename (1)

1 GIPSA-SLR - GIPSA - Systèmes linéaires et robustesse
2 GIPSA-SYSCO - GIPSA - Systèmes non linéaires et complexité

This paper presents a robustness result for the use of a previously developed adaptive output-feedback controller designed for a pure wave PDE. This one-dimensional wave PDE has a boundary actuation opposite to an unknown anti-damping dynamics boundary. We prove that stabilization is still valid in the case of in-domain viscous damping using a controller designed neglecting the damping, provided that the damping coefficient is small enough. Our robustness proof grounds on the use of an alternative pure wave PDE, neglecting the in-domain damping. We compare these two systems and apply a tailored backstepping transformation to carry out Lyapunov analysis. Numerical simulations show the relevance of our result for drilling applications and illustrate the merits of this control design.

Mots clés: adaptive control; Robust Analysis; Output Feedback Controller; Infinite Dimensional Systems; Stick-Slip; drilling; wave pde

Domaines: Automatique / Robotique

Christophe Roman, Delphine Bresch-Pietri, Christophe Prieur, Olivier Sename. Robustness of an Adaptive Output Feedback for an Anti-Damped Boundary Wave PDE in Presence of In-Domain Viscous Damping. ACC 2016 - American Control Conference, Jul 2016, Boston, MA, United States. ⟨10.1109/ACC.2016.7525448⟩. ⟨hal-01349352⟩