Backstepping control of the one-phase stefan problem

Shumon Koga; Mamadou Diagne; Shuxia Tang; Miroslav Krstic

doi:10.1109/ACC.2016.7525300

Backstepping control of the one-phase stefan problem

Shumon Koga, Mamadou Diagne, Shuxia Tang, Miroslav Krstic

Mechanical Engineering

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

16 Scopus citations

Abstract

In this paper, a backstepping control of the one-phase Stefan Problem, which is a 1-D diffusion Partial Differential Equation (PDE) defined on a time varying spatial domain described by an ordinary differential equation (ODE), is studied. A new nonlinear backstepping transformation for moving boundary problem is utilized to transform the original coupled PDE-ODE system into a target system whose exponential stability is proved. The full-state boundary feedback controller ensures the exponential stability of the moving interface to a reference setpoint and the H1-norm of the distributed temperature by a choice of the setpint satisfying given explicit inequality between initial states that guarantees the physical constraints imposed by the melting process.

Original language	English
Title of host publication	2016 American Control Conference, ACC 2016
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	2548-2553
Number of pages	6
ISBN (Electronic)	9781467386821
DOIs	https://doi.org/10.1109/ACC.2016.7525300
State	Published - Jul 28 2016
Event	2016 American Control Conference, ACC 2016 - Boston, United States Duration: Jul 6 2016 → Jul 8 2016

Publication series

Name	Proceedings of the American Control Conference
Volume	2016-July
ISSN (Print)	0743-1619

Conference

Conference	2016 American Control Conference, ACC 2016
Country/Territory	United States
City	Boston
Period	07/6/16 → 07/8/16

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10.1109/ACC.2016.7525300

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title = "Backstepping control of the one-phase stefan problem",

abstract = "In this paper, a backstepping control of the one-phase Stefan Problem, which is a 1-D diffusion Partial Differential Equation (PDE) defined on a time varying spatial domain described by an ordinary differential equation (ODE), is studied. A new nonlinear backstepping transformation for moving boundary problem is utilized to transform the original coupled PDE-ODE system into a target system whose exponential stability is proved. The full-state boundary feedback controller ensures the exponential stability of the moving interface to a reference setpoint and the H1-norm of the distributed temperature by a choice of the setpint satisfying given explicit inequality between initial states that guarantees the physical constraints imposed by the melting process.",

author = "Shumon Koga and Mamadou Diagne and Shuxia Tang and Miroslav Krstic",

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year = "2016",

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doi = "10.1109/ACC.2016.7525300",

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Koga, S, Diagne, M, Tang, S & Krstic, M 2016, Backstepping control of the one-phase stefan problem. in 2016 American Control Conference, ACC 2016., 7525300, Proceedings of the American Control Conference, vol. 2016-July, Institute of Electrical and Electronics Engineers Inc., pp. 2548-2553, 2016 American Control Conference, ACC 2016, Boston, United States, 07/6/16. https://doi.org/10.1109/ACC.2016.7525300

Backstepping control of the one-phase stefan problem. / Koga, Shumon; Diagne, Mamadou; Tang, Shuxia et al.
2016 American Control Conference, ACC 2016. Institute of Electrical and Electronics Engineers Inc., 2016. p. 2548-2553 7525300 (Proceedings of the American Control Conference; Vol. 2016-July).

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

TY - GEN

T1 - Backstepping control of the one-phase stefan problem

AU - Koga, Shumon

AU - Diagne, Mamadou

AU - Tang, Shuxia

AU - Krstic, Miroslav

PY - 2016/7/28

Y1 - 2016/7/28

N2 - In this paper, a backstepping control of the one-phase Stefan Problem, which is a 1-D diffusion Partial Differential Equation (PDE) defined on a time varying spatial domain described by an ordinary differential equation (ODE), is studied. A new nonlinear backstepping transformation for moving boundary problem is utilized to transform the original coupled PDE-ODE system into a target system whose exponential stability is proved. The full-state boundary feedback controller ensures the exponential stability of the moving interface to a reference setpoint and the H1-norm of the distributed temperature by a choice of the setpint satisfying given explicit inequality between initial states that guarantees the physical constraints imposed by the melting process.

AB - In this paper, a backstepping control of the one-phase Stefan Problem, which is a 1-D diffusion Partial Differential Equation (PDE) defined on a time varying spatial domain described by an ordinary differential equation (ODE), is studied. A new nonlinear backstepping transformation for moving boundary problem is utilized to transform the original coupled PDE-ODE system into a target system whose exponential stability is proved. The full-state boundary feedback controller ensures the exponential stability of the moving interface to a reference setpoint and the H1-norm of the distributed temperature by a choice of the setpint satisfying given explicit inequality between initial states that guarantees the physical constraints imposed by the melting process.

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M3 - Conference contribution

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T3 - Proceedings of the American Control Conference

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BT - 2016 American Control Conference, ACC 2016

PB - Institute of Electrical and Electronics Engineers Inc.

T2 - 2016 American Control Conference, ACC 2016

Y2 - 6 July 2016 through 8 July 2016

ER -

Backstepping control of the one-phase stefan problem

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