Reset PID design for motion systems with Stribeck friction

Ruud Beerens (1) , A. Bisoffi (2, 3) , Luca Zaccarian (4, 5) , H. Nijmeijer (6) , W P M H Heemels (7) , N. van de Wouw (7, 8)

1 ASML - ASML [VELDHOVEN]
2 KTH - KTH Royal Institute of Technology [Stockholm]
3 Rijksuniversiteit Groningen
4 UNITN - Università degli Studi di Trento = University of Trento
5 LAAS-MAC - Équipe Méthodes et Algorithmes en Commande
6 Department of Mechanical Engineering [Eindhoven]
7 TU/e - Eindhoven University of Technology [Eindhoven]
8 Department of Civil, Environmental and Geo-Engineering [Minneapolis]

We present a reset control approach to achieve setpoint regulation of a motion system with a proportional-integral-derivative (PID) based controller, subject to Coulomb friction and a velocity-weakening (Stribeck) contribution. While classical PID control results in persistent oscillations (hunting), the proposed reset mechanism induces asymptotic stability of the setpoint, and significant overshoot reduction. Moreover, robustness to an unknown static friction level and an unknown Stribeck contribution is guaranteed. The closed-loop dynamics are formulated in a hybrid systems framework, using a novel hybrid description of the static friction element, and asymptotic stability of the setpoint is proven accordingly. The working principle of the controller is demonstrated experimentally on a motion stage of an electron microscope, showing superior performance over classical PID control.

Domaines: Génie mécanique [physics.class-ph]

Ruud Beerens, A. Bisoffi, Luca Zaccarian, H. Nijmeijer, W P M H Heemels, et al.. Reset PID design for motion systems with Stribeck friction. IEEE Transactions on Control Systems Technology, 2022, 30 (1), pp.294 - 310. ⟨10.1109/TCST.2021.3063420⟩. ⟨hal-02454405v3⟩