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Hybrid model formulation and stability analysis of a PID-controlled motion system with Coulomb friction
KTH, School of Electrical Engineering and Computer Science (EECS), Intelligent systems, Decision and Control Systems (Automatic Control).ORCID iD: 0000-0001-5495-4481
Eindhoven Univ Technol, Dept Mech Engn, POB 513, NL-5600 MB Eindhoven, Netherlands..
Univ Toulouse, CNRS, LAAS, F-31400 Toulouse, France.;Univ Trento, Dept Ind Engn, I-38122 Trento, Italy..
Eindhoven Univ Technol, Dept Mech Engn, POB 513, NL-5600 MB Eindhoven, Netherlands..
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2019 (English)In: IFAC PAPERSONLINE, ELSEVIER , 2019, Vol. 52, no 16, p. 84-89Conference paper, Published paper (Refereed)
Abstract [en]

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.

Place, publisher, year, edition, pages
ELSEVIER , 2019. Vol. 52, no 16, p. 84-89
Keywords [en]
hybrid systems, nonlinear systems, Coulomb friction, Lyapunov methods, global asymptotic stability, PID control
National Category
Control Engineering
Identifiers
URN: urn:nbn:se:kth:diva-266519DOI: 10.1016/j.ifacol.2019.11.760ISI: 000503828500016Scopus ID: 2-s2.0-85077461534OAI: oai:DiVA.org:kth-266519DiVA, id: diva2:1391692
Conference
8th International-Federation-of-Automatic-Control (IFAC) Symposium on Mechatronic Systems (MECHATRONICS) / 11th International-Federation-of-Automatic-Control (IFAC) Symposium on Nonlinear Control Systems (NOLCOS), SEP 04-06, 2019, Tech Univ Wien, Vienna, AUSTRIA
Note

QC 20200205

Available from: 2020-02-05 Created: 2020-02-05 Last updated: 2020-02-05Bibliographically approved

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