Relay-based hybrid control of minimal-order mechanical systems with applications

Andrea Bisoffi (1) , Fulvio Forni (2) , Mauro da Lio (1) , Luca Zaccarian (3, 4)

1 Dipartimento di Ingegneria Industriale
2 CAM - University of Cambridge [UK]
3 Dipartimento di Ingegneria Industriale [Trento]
4 LAAS-MAC - Équipe Méthodes et Algorithmes en Commande

This work explores the potential of relay-based control on a one-degree-of-freedom nonlinear mechanical system, in the contexts of both sustaining and damping oscillations. For both cases we state our main results building upon a simple reset formulation (relay feedback) and providing intuitive basic equations from classical mechanics. With a more rigorous description following a hybrid system formalism, we establish then the global asymptotic stability of the corresponding (compact-set) attractors through hybrid Lyapunov tools. The aspects of sustaining and damping oscillation are seen as complementary, because they reduce to a suitable mirroring of the reset surface. Finally, we discuss two applications of our results to the case of a hopping mass and an automotive suspension.

Mots clés: Nonlinear control systems; nonlinear systems; relay control; reset actions; discontinuous control; forced oscillations; periodic motion; limit cycles; global stability; asymptotic stability; Lyapunov stability; stability analysis; Lyapunov methods; mechanical systems

Domaines: Automatique / Robotique

Andrea Bisoffi, Fulvio Forni, Mauro da Lio, Luca Zaccarian. Relay-based hybrid control of minimal-order mechanical systems with applications. Automatica, 2018, 97, pp.104-114. ⟨10.1016/j.automatica.2018.07.033⟩. ⟨hal-01970879⟩