A time-stepping method for relay systems

W.P.M.H. Heemels; M.K. Camlibel; J.M. Schumacher

doi:10.1109/CDC.2001.914610

A time-stepping method for relay systems

W.P.M.H. Heemels
, M.K. Camlibel
, J.M. Schumacher

Control Systems

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

11 Citations (Scopus)

2 Downloads (Pure)

Abstract

In this paper we will analyze a time-stepping method for the numerical simulation of dynamical systems containing Coulomb friction or relay characteristics. Time-stepping techniques replace the original dynamical system by a sequence of algebraic problems, that have to be solved for each time-step. For relay systems the one-step problem can be reformulated as a linear complementarity problem for which a wide range of solution algorithms already exists. As the event times at which the relay switches are "overstepped", the consistency of the method in the sense of the convergence of a sequence of approximations to an actual solution of the relay system can be put into question. However, in this paper we show that the proposed method is consistent even in the case that the event times accumulate (Zeno behavior). By an example we will illustrate how the method deals with Zeno trajectories

Original language	English
Title of host publication	Proceedings of the 39th IEEE conference on decision and control, Sydney, Australia, December 2000, vol. 5
Place of Publication	Piscataway
Publisher	Institute of Electrical and Electronics Engineers
Pages	4461-4466
ISBN (Print)	0-7803-6638-7
DOIs	https://doi.org/10.1109/CDC.2001.914610
Publication status	Published - 2000
Event	39th IEEE Conference on Decision and Control (CDC 2000) - Sydney, Australia Duration: 12 Dec 2000 → 15 Dec 2000

Conference

Conference	39th IEEE Conference on Decision and Control (CDC 2000)
Abbreviated title	CDC 2000
Country/Territory	Australia
City	Sydney
Period	12/12/00 → 15/12/00
Other

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10.1109/CDC.2001.914610

Cite this

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title = "A time-stepping method for relay systems",

abstract = "In this paper we will analyze a time-stepping method for the numerical simulation of dynamical systems containing Coulomb friction or relay characteristics. Time-stepping techniques replace the original dynamical system by a sequence of algebraic problems, that have to be solved for each time-step. For relay systems the one-step problem can be reformulated as a linear complementarity problem for which a wide range of solution algorithms already exists. As the event times at which the relay switches are {"}overstepped{"}, the consistency of the method in the sense of the convergence of a sequence of approximations to an actual solution of the relay system can be put into question. However, in this paper we show that the proposed method is consistent even in the case that the event times accumulate (Zeno behavior). By an example we will illustrate how the method deals with Zeno trajectories",

author = "W.P.M.H. Heemels and M.K. Camlibel and J.M. Schumacher",

year = "2000",

doi = "10.1109/CDC.2001.914610",

language = "English",

isbn = "0-7803-6638-7",

pages = "4461--4466",

booktitle = "Proceedings of the 39th IEEE conference on decision and control, Sydney, Australia, December 2000, vol. 5",

publisher = "Institute of Electrical and Electronics Engineers",

address = "United States",

note = "39th IEEE Conference on Decision and Control (CDC 2000), CDC 2000 ; Conference date: 12-12-2000 Through 15-12-2000",

}

Heemels, WPMH, Camlibel, MK & Schumacher, JM 2000, A time-stepping method for relay systems. in Proceedings of the 39th IEEE conference on decision and control, Sydney, Australia, December 2000, vol. 5. Institute of Electrical and Electronics Engineers, Piscataway, pp. 4461-4466, 39th IEEE Conference on Decision and Control (CDC 2000), Sydney, Australia, 12/12/00. https://doi.org/10.1109/CDC.2001.914610

A time-stepping method for relay systems. / Heemels, W.P.M.H.; Camlibel, M.K.; Schumacher, J.M.
Proceedings of the 39th IEEE conference on decision and control, Sydney, Australia, December 2000, vol. 5. Piscataway: Institute of Electrical and Electronics Engineers, 2000. p. 4461-4466.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

TY - GEN

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AU - Camlibel, M.K.

AU - Schumacher, J.M.

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N2 - In this paper we will analyze a time-stepping method for the numerical simulation of dynamical systems containing Coulomb friction or relay characteristics. Time-stepping techniques replace the original dynamical system by a sequence of algebraic problems, that have to be solved for each time-step. For relay systems the one-step problem can be reformulated as a linear complementarity problem for which a wide range of solution algorithms already exists. As the event times at which the relay switches are "overstepped", the consistency of the method in the sense of the convergence of a sequence of approximations to an actual solution of the relay system can be put into question. However, in this paper we show that the proposed method is consistent even in the case that the event times accumulate (Zeno behavior). By an example we will illustrate how the method deals with Zeno trajectories

AB - In this paper we will analyze a time-stepping method for the numerical simulation of dynamical systems containing Coulomb friction or relay characteristics. Time-stepping techniques replace the original dynamical system by a sequence of algebraic problems, that have to be solved for each time-step. For relay systems the one-step problem can be reformulated as a linear complementarity problem for which a wide range of solution algorithms already exists. As the event times at which the relay switches are "overstepped", the consistency of the method in the sense of the convergence of a sequence of approximations to an actual solution of the relay system can be put into question. However, in this paper we show that the proposed method is consistent even in the case that the event times accumulate (Zeno behavior). By an example we will illustrate how the method deals with Zeno trajectories

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DO - 10.1109/CDC.2001.914610

M3 - Conference contribution

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BT - Proceedings of the 39th IEEE conference on decision and control, Sydney, Australia, December 2000, vol. 5

PB - Institute of Electrical and Electronics Engineers

CY - Piscataway

T2 - 39th IEEE Conference on Decision and Control (CDC 2000)

Y2 - 12 December 2000 through 15 December 2000

ER -

A time-stepping method for relay systems

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