Global Asymptotic Stability of a PID Control System with Coulomb Friction

Andrea Bisoffi (1) , Mauro da Lio (1) , Andrew Teel (2) , Luca Zaccarian (1, 3)

1 Dipartimento di Ingegneria Industriale
2 CCDC - Center for Control, Dynamical-Systems, and Computation [Santa Barbara]
3 LAAS-MAC - Équipe Méthodes et Algorithmes en Commande

For a point mass subject to Coulomb friction in feedback with a PID controller, we consider a model based on a differential inclusion comprising all the possible magnitudes of static friction during the stick phase and having unique solutions. We study the set of all equilibria and we establish its global asymptotic stability using a discontinuous Lyapunov-like function, and a suitable LaSalle's invariance principle. The well-posedness of the proposed model allows to establish useful robustness results, including an ISS property from a suitable input in a perturbed context. Simulation results are also given to illustrate our statements.

Domaines: Automatique / Robotique

Andrea Bisoffi, Mauro da Lio, Andrew Teel, Luca Zaccarian. Global Asymptotic Stability of a PID Control System with Coulomb Friction. IEEE Transactions on Automatic Control, 2018, 63 (8), pp.2654-2661. ⟨10.1109/TAC.2017.2774443⟩. ⟨hal-01700168⟩