Tracking control of mechanical systems with a unilateral position constraint inducing dissipative impacts

J.J.B. Biemond, N. Wouw, van de, W.P.M.H. Heemels, R.G. Sanfelice, H. Nijmeijer

Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

7 Citations (Scopus)
2 Downloads (Pure)

Abstract

In this paper, the tracking control problem is considered for mechanical systems with unilateral constraints with dissipative impacts. In these systems, impacts are triggered at the exact moment when the constraint becomes active. Typically, a small time mismatch is introduced between the impacts of the plant and the reference, even if this trajectory is arbitrarily close to the reference. Consequently, the Euclidean tracking error cannot behave stable in the sense of Lyapunov, such that standard tracking control approaches are unfeasible. However, desirable tracking behaviour does not imply that the Euclidean error vanishes asymptotically over time. We design continuous-time controllers that can handle the impact time mismatch and achieve accurate tracking of reference trajec- tories containing dissipative impacts for mechanical systems with a unilateral constraint. The behaviour of the resulting closed-loop dynamical system is illustrated with an exemplary bouncing ball system.
Original languageEnglish
Title of host publicationProceedings of the 51st IEEE Conference on Decision and Control (CDC), 10-13 December 2012, Maui, Hawaii, USA
Place of PublicationPiscataway
PublisherInstitute of Electrical and Electronics Engineers
Pages4223-4228
Publication statusPublished - 2012

Fingerprint

Trajectories
Dynamical systems
Controllers

Cite this

Biemond, J. J. B., Wouw, van de, N., Heemels, W. P. M. H., Sanfelice, R. G., & Nijmeijer, H. (2012). Tracking control of mechanical systems with a unilateral position constraint inducing dissipative impacts. In Proceedings of the 51st IEEE Conference on Decision and Control (CDC), 10-13 December 2012, Maui, Hawaii, USA (pp. 4223-4228). Piscataway: Institute of Electrical and Electronics Engineers.
Biemond, J.J.B. ; Wouw, van de, N. ; Heemels, W.P.M.H. ; Sanfelice, R.G. ; Nijmeijer, H. / Tracking control of mechanical systems with a unilateral position constraint inducing dissipative impacts. Proceedings of the 51st IEEE Conference on Decision and Control (CDC), 10-13 December 2012, Maui, Hawaii, USA. Piscataway : Institute of Electrical and Electronics Engineers, 2012. pp. 4223-4228
@inproceedings{89643f85d3744abda1646d4b4337a16b,
title = "Tracking control of mechanical systems with a unilateral position constraint inducing dissipative impacts",
abstract = "In this paper, the tracking control problem is considered for mechanical systems with unilateral constraints with dissipative impacts. In these systems, impacts are triggered at the exact moment when the constraint becomes active. Typically, a small time mismatch is introduced between the impacts of the plant and the reference, even if this trajectory is arbitrarily close to the reference. Consequently, the Euclidean tracking error cannot behave stable in the sense of Lyapunov, such that standard tracking control approaches are unfeasible. However, desirable tracking behaviour does not imply that the Euclidean error vanishes asymptotically over time. We design continuous-time controllers that can handle the impact time mismatch and achieve accurate tracking of reference trajec- tories containing dissipative impacts for mechanical systems with a unilateral constraint. The behaviour of the resulting closed-loop dynamical system is illustrated with an exemplary bouncing ball system.",
author = "J.J.B. Biemond and {Wouw, van de}, N. and W.P.M.H. Heemels and R.G. Sanfelice and H. Nijmeijer",
year = "2012",
language = "English",
pages = "4223--4228",
booktitle = "Proceedings of the 51st IEEE Conference on Decision and Control (CDC), 10-13 December 2012, Maui, Hawaii, USA",
publisher = "Institute of Electrical and Electronics Engineers",
address = "United States",

}

Biemond, JJB, Wouw, van de, N, Heemels, WPMH, Sanfelice, RG & Nijmeijer, H 2012, Tracking control of mechanical systems with a unilateral position constraint inducing dissipative impacts. in Proceedings of the 51st IEEE Conference on Decision and Control (CDC), 10-13 December 2012, Maui, Hawaii, USA. Institute of Electrical and Electronics Engineers, Piscataway, pp. 4223-4228.

Tracking control of mechanical systems with a unilateral position constraint inducing dissipative impacts. / Biemond, J.J.B.; Wouw, van de, N.; Heemels, W.P.M.H.; Sanfelice, R.G.; Nijmeijer, H.

Proceedings of the 51st IEEE Conference on Decision and Control (CDC), 10-13 December 2012, Maui, Hawaii, USA. Piscataway : Institute of Electrical and Electronics Engineers, 2012. p. 4223-4228.

Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

TY - GEN

T1 - Tracking control of mechanical systems with a unilateral position constraint inducing dissipative impacts

AU - Biemond, J.J.B.

AU - Wouw, van de, N.

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

AU - Sanfelice, R.G.

AU - Nijmeijer, H.

PY - 2012

Y1 - 2012

N2 - In this paper, the tracking control problem is considered for mechanical systems with unilateral constraints with dissipative impacts. In these systems, impacts are triggered at the exact moment when the constraint becomes active. Typically, a small time mismatch is introduced between the impacts of the plant and the reference, even if this trajectory is arbitrarily close to the reference. Consequently, the Euclidean tracking error cannot behave stable in the sense of Lyapunov, such that standard tracking control approaches are unfeasible. However, desirable tracking behaviour does not imply that the Euclidean error vanishes asymptotically over time. We design continuous-time controllers that can handle the impact time mismatch and achieve accurate tracking of reference trajec- tories containing dissipative impacts for mechanical systems with a unilateral constraint. The behaviour of the resulting closed-loop dynamical system is illustrated with an exemplary bouncing ball system.

AB - In this paper, the tracking control problem is considered for mechanical systems with unilateral constraints with dissipative impacts. In these systems, impacts are triggered at the exact moment when the constraint becomes active. Typically, a small time mismatch is introduced between the impacts of the plant and the reference, even if this trajectory is arbitrarily close to the reference. Consequently, the Euclidean tracking error cannot behave stable in the sense of Lyapunov, such that standard tracking control approaches are unfeasible. However, desirable tracking behaviour does not imply that the Euclidean error vanishes asymptotically over time. We design continuous-time controllers that can handle the impact time mismatch and achieve accurate tracking of reference trajec- tories containing dissipative impacts for mechanical systems with a unilateral constraint. The behaviour of the resulting closed-loop dynamical system is illustrated with an exemplary bouncing ball system.

M3 - Conference contribution

SP - 4223

EP - 4228

BT - Proceedings of the 51st IEEE Conference on Decision and Control (CDC), 10-13 December 2012, Maui, Hawaii, USA

PB - Institute of Electrical and Electronics Engineers

CY - Piscataway

ER -

Biemond JJB, Wouw, van de N, Heemels WPMH, Sanfelice RG, Nijmeijer H. Tracking control of mechanical systems with a unilateral position constraint inducing dissipative impacts. In Proceedings of the 51st IEEE Conference on Decision and Control (CDC), 10-13 December 2012, Maui, Hawaii, USA. Piscataway: Institute of Electrical and Electronics Engineers. 2012. p. 4223-4228