Control of mechanical motion systems with non-collocation of actuation and friction: a Popov criterion approach for input-to-state stability and set-valued nonlinearities

J.C.A. Bruin, de, A. Doris, N. Wouw, van de, W.P.M.H. Heemels, H. Nijmeijer

Research output: Contribution to journalArticleAcademicpeer-review

85 Citations (Scopus)
8 Downloads (Pure)

Abstract

The presence of friction in mechanical motion systems is a performance limiting factor as it induces stick–slip vibrations. To appropriately describe the stiction effect of friction, we adopt set-valued force laws. Then, the complete motion control system can be described by a Lur’e system with set-valued nonlinearities. In order to eliminate stick–slip vibrations for mechanical motion systems, a state-feedback control design is presented to stabilize the equilibrium. The proposed control design is based on an extension of a Popov-like criterion to systems with set-valued nonlinearities that guarantees input-to-state stability (ISS). The advantages of the presented controller is that it is robust to uncertainties in the friction and it is applicable to systems with non-collocation of actuation and friction where common control strategies such as direct friction compensation fail. Moreover, an observer-based output-feedback design is proposed for the case that not all the state variables are measured. The effectiveness of the proposed output-feedback control design is shown both in simulations and experiments for a typical motion control system.
Original languageEnglish
Pages (from-to)405-415
JournalAutomatica
Volume45
Issue number2
DOIs
Publication statusPublished - 2009

Fingerprint

Friction
Motion control
Feedback control
Stiction
Control systems
State feedback
Feedback
Controllers
Experiments

Cite this

@article{31835adf2eba4dffa82f446454350e15,
title = "Control of mechanical motion systems with non-collocation of actuation and friction: a Popov criterion approach for input-to-state stability and set-valued nonlinearities",
abstract = "The presence of friction in mechanical motion systems is a performance limiting factor as it induces stick–slip vibrations. To appropriately describe the stiction effect of friction, we adopt set-valued force laws. Then, the complete motion control system can be described by a Lur’e system with set-valued nonlinearities. In order to eliminate stick–slip vibrations for mechanical motion systems, a state-feedback control design is presented to stabilize the equilibrium. The proposed control design is based on an extension of a Popov-like criterion to systems with set-valued nonlinearities that guarantees input-to-state stability (ISS). The advantages of the presented controller is that it is robust to uncertainties in the friction and it is applicable to systems with non-collocation of actuation and friction where common control strategies such as direct friction compensation fail. Moreover, an observer-based output-feedback design is proposed for the case that not all the state variables are measured. The effectiveness of the proposed output-feedback control design is shown both in simulations and experiments for a typical motion control system.",
author = "{Bruin, de}, J.C.A. and A. Doris and {Wouw, van de}, N. and W.P.M.H. Heemels and H. Nijmeijer",
year = "2009",
doi = "10.1016/j.automatica.2008.09.008",
language = "English",
volume = "45",
pages = "405--415",
journal = "Automatica",
issn = "0005-1098",
publisher = "Agon Elsevier",
number = "2",

}

TY - JOUR

T1 - Control of mechanical motion systems with non-collocation of actuation and friction: a Popov criterion approach for input-to-state stability and set-valued nonlinearities

AU - Bruin, de, J.C.A.

AU - Doris, A.

AU - Wouw, van de, N.

AU - Heemels, W.P.M.H.

AU - Nijmeijer, H.

PY - 2009

Y1 - 2009

N2 - The presence of friction in mechanical motion systems is a performance limiting factor as it induces stick–slip vibrations. To appropriately describe the stiction effect of friction, we adopt set-valued force laws. Then, the complete motion control system can be described by a Lur’e system with set-valued nonlinearities. In order to eliminate stick–slip vibrations for mechanical motion systems, a state-feedback control design is presented to stabilize the equilibrium. The proposed control design is based on an extension of a Popov-like criterion to systems with set-valued nonlinearities that guarantees input-to-state stability (ISS). The advantages of the presented controller is that it is robust to uncertainties in the friction and it is applicable to systems with non-collocation of actuation and friction where common control strategies such as direct friction compensation fail. Moreover, an observer-based output-feedback design is proposed for the case that not all the state variables are measured. The effectiveness of the proposed output-feedback control design is shown both in simulations and experiments for a typical motion control system.

AB - The presence of friction in mechanical motion systems is a performance limiting factor as it induces stick–slip vibrations. To appropriately describe the stiction effect of friction, we adopt set-valued force laws. Then, the complete motion control system can be described by a Lur’e system with set-valued nonlinearities. In order to eliminate stick–slip vibrations for mechanical motion systems, a state-feedback control design is presented to stabilize the equilibrium. The proposed control design is based on an extension of a Popov-like criterion to systems with set-valued nonlinearities that guarantees input-to-state stability (ISS). The advantages of the presented controller is that it is robust to uncertainties in the friction and it is applicable to systems with non-collocation of actuation and friction where common control strategies such as direct friction compensation fail. Moreover, an observer-based output-feedback design is proposed for the case that not all the state variables are measured. The effectiveness of the proposed output-feedback control design is shown both in simulations and experiments for a typical motion control system.

U2 - 10.1016/j.automatica.2008.09.008

DO - 10.1016/j.automatica.2008.09.008

M3 - Article

VL - 45

SP - 405

EP - 415

JO - Automatica

JF - Automatica

SN - 0005-1098

IS - 2

ER -