Hybrid model formulation and stability analysis of a PID-controlled motion system with Coulomb friction

Andrea Bisoffi (1) , Ruud Beerens (2) , Luca Zaccarian (3, 4) , Maurice Heemels (2) , Henk Nijmeijer (2) , N. van de Wouw (2)

1 KTH - KTH Royal Institute of Technology [Stockholm]
2 TU/e - Eindhoven University of Technology [Eindhoven]
3 Dipartimento di Ingegneria Industriale [Trento]
4 LAAS-MAC - Équipe Méthodes et Algorithmes en Commande

For a PID-controlled motion system under Coulomb friction described by a differential inclusion, we present a hybrid model comprising logical states indicating whether the closed loop is in stick or in slip, thereby resembling a hybrid automaton. A key step for this description is the addition of a timer exploiting a peculiar semiglobal dwell time of the original dynamics, which then removes defective and unwanted nonconverging Zeno solutions from the hybrid model. Through it, we then revisit an existing proof of global asymptotic stability, which is significantly simplified by way of a smooth weak Lyapunov function. The relevance of the proposed hybrid representation is also illustrated on a novel control strategy resetting the PID integrator and hinging upon the proposed hybrid model.

Mots clés: hybrid systems; nonlinear systems; Coulomb friction; Lyapunov methods; global asymptotic stability; PID control

Domaines: Automatique / Robotique

Andrea Bisoffi, Ruud Beerens, Luca Zaccarian, Maurice Heemels, Henk Nijmeijer, et al.. Hybrid model formulation and stability analysis of a PID-controlled motion system with Coulomb friction. IFAC Symposium on Nonlinear Control Systems (NOLCOS), Sep 2019, Wien, Austria. pp.84-89, ⟨10.1016/j.ifacol.2019.11.760⟩. ⟨hal-03028141⟩