PDE boundary control for Euler-Bernoulli beam using a two stage perturbation observer

Aditya A. Paranjape; Jinyu Guan; Soon Jo Chung; Miroslav Krstic

doi:10.1109/CDC.2012.6426058

PDE boundary control for Euler-Bernoulli beam using a two stage perturbation observer

Aditya A. Paranjape
, Jinyu Guan
, Soon Jo Chung
, Miroslav Krstic

Research output: Chapter in Book/Report/Conference proceeding › Conference Paper › Other

6 Citations (Scopus)

Abstract

A novel perturbation observer-based PDE boundary control law for beam bending is derived based on a combination of perturbation observers and polynomial trajectory planning. The perturbation observer consists of two components. The first stage employs the “particular” solution of the original dynamics with disturbances while its boundary conditions are set to zero. In contrast, the dynamics of the “homogeneous component” are independent of the beam dynamics, but its boundary conditions are identical to those of the beam. A tracking boundary control law, based on trajectory planning, is designed for the homogeneous component, and the same control signal is also applied to the beam. The stability of the adaptive perturbation-observer is proven by Lyapunov stability in the spatial L₂ sense, while stability conditions are derived for a finite dimensional ODE analogue of the infinite dimensional closed loop PDE system. This paper also reports on one of the first experimental demonstrations of a controller designed entirely using a PDE boundary control formulation.

Original language	English
Title of host publication	2012 IEEE 51st IEEE Conference on Decision and Control (CDC)
Publisher	IEEE, Institute of Electrical and Electronics Engineers
Pages	4442-4448
Number of pages	7
DOIs	https://doi.org/10.1109/CDC.2012.6426058
Publication status	Published - 2012
Externally published	Yes
Event	IEEE Conference on Decision and Control 2012 - Grand Wailea, Maui, United States of America Duration: 10 Dec 2012 → 13 Dec 2012 Conference number: 51st https://ieeexplore.ieee.org/xpl/conhome/6416474/proceeding (Proceedings)

Publication series

Name	Proceedings of the IEEE Conference on Decision and Control
ISSN (Print)	0743-1546

Conference

Conference	IEEE Conference on Decision and Control 2012
Abbreviated title	CDC 2012
Country/Territory	United States of America
City	Maui
Period	10/12/12 → 13/12/12
Internet address	https://ieeexplore.ieee.org/xpl/conhome/6416474/proceeding (Proceedings)

Access to Document

10.1109/CDC.2012.6426058

Cite this

Paranjape, A. A., Guan, J., Chung, S. J., & Krstic, M. (2012). PDE boundary control for Euler-Bernoulli beam using a two stage perturbation observer. In 2012 IEEE 51st IEEE Conference on Decision and Control (CDC) (pp. 4442-4448). (Proceedings of the IEEE Conference on Decision and Control). IEEE, Institute of Electrical and Electronics Engineers. https://doi.org/10.1109/CDC.2012.6426058

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title = "PDE boundary control for Euler-Bernoulli beam using a two stage perturbation observer",

abstract = "A novel perturbation observer-based PDE boundary control law for beam bending is derived based on a combination of perturbation observers and polynomial trajectory planning. The perturbation observer consists of two components. The first stage employs the “particular” solution of the original dynamics with disturbances while its boundary conditions are set to zero. In contrast, the dynamics of the “homogeneous component” are independent of the beam dynamics, but its boundary conditions are identical to those of the beam. A tracking boundary control law, based on trajectory planning, is designed for the homogeneous component, and the same control signal is also applied to the beam. The stability of the adaptive perturbation-observer is proven by Lyapunov stability in the spatial L2 sense, while stability conditions are derived for a finite dimensional ODE analogue of the infinite dimensional closed loop PDE system. This paper also reports on one of the first experimental demonstrations of a controller designed entirely using a PDE boundary control formulation.",

author = "Paranjape, \{Aditya A.\} and Jinyu Guan and Chung, \{Soon Jo\} and Miroslav Krstic",

note = "Funding Information: This project was supported by the U.S. Army Research Office (ARO) under Award No W911NF-10-1-0296. Publisher Copyright: {\textcopyright} 2012 IEEE.; IEEE Conference on Decision and Control 2012, CDC 2012 ; Conference date: 10-12-2012 Through 13-12-2012",

year = "2012",

doi = "10.1109/CDC.2012.6426058",

language = "English",

series = "Proceedings of the IEEE Conference on Decision and Control",

publisher = "IEEE, Institute of Electrical and Electronics Engineers",

pages = "4442--4448",

booktitle = "2012 IEEE 51st IEEE Conference on Decision and Control (CDC)",

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url = "https://ieeexplore.ieee.org/xpl/conhome/6416474/proceeding",

}

Paranjape, AA, Guan, J, Chung, SJ & Krstic, M 2012, PDE boundary control for Euler-Bernoulli beam using a two stage perturbation observer. in 2012 IEEE 51st IEEE Conference on Decision and Control (CDC). Proceedings of the IEEE Conference on Decision and Control, IEEE, Institute of Electrical and Electronics Engineers, pp. 4442-4448, IEEE Conference on Decision and Control 2012, Maui, Hawaii, United States of America, 10/12/12. https://doi.org/10.1109/CDC.2012.6426058

PDE boundary control for Euler-Bernoulli beam using a two stage perturbation observer. / Paranjape, Aditya A.; Guan, Jinyu; Chung, Soon Jo et al.
2012 IEEE 51st IEEE Conference on Decision and Control (CDC). IEEE, Institute of Electrical and Electronics Engineers, 2012. p. 4442-4448 (Proceedings of the IEEE Conference on Decision and Control).

Research output: Chapter in Book/Report/Conference proceeding › Conference Paper › Other

TY - GEN

T1 - PDE boundary control for Euler-Bernoulli beam using a two stage perturbation observer

AU - Paranjape, Aditya A.

AU - Guan, Jinyu

AU - Chung, Soon Jo

AU - Krstic, Miroslav

N1 - Conference code: 51st

PY - 2012

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N2 - A novel perturbation observer-based PDE boundary control law for beam bending is derived based on a combination of perturbation observers and polynomial trajectory planning. The perturbation observer consists of two components. The first stage employs the “particular” solution of the original dynamics with disturbances while its boundary conditions are set to zero. In contrast, the dynamics of the “homogeneous component” are independent of the beam dynamics, but its boundary conditions are identical to those of the beam. A tracking boundary control law, based on trajectory planning, is designed for the homogeneous component, and the same control signal is also applied to the beam. The stability of the adaptive perturbation-observer is proven by Lyapunov stability in the spatial L2 sense, while stability conditions are derived for a finite dimensional ODE analogue of the infinite dimensional closed loop PDE system. This paper also reports on one of the first experimental demonstrations of a controller designed entirely using a PDE boundary control formulation.

AB - A novel perturbation observer-based PDE boundary control law for beam bending is derived based on a combination of perturbation observers and polynomial trajectory planning. The perturbation observer consists of two components. The first stage employs the “particular” solution of the original dynamics with disturbances while its boundary conditions are set to zero. In contrast, the dynamics of the “homogeneous component” are independent of the beam dynamics, but its boundary conditions are identical to those of the beam. A tracking boundary control law, based on trajectory planning, is designed for the homogeneous component, and the same control signal is also applied to the beam. The stability of the adaptive perturbation-observer is proven by Lyapunov stability in the spatial L2 sense, while stability conditions are derived for a finite dimensional ODE analogue of the infinite dimensional closed loop PDE system. This paper also reports on one of the first experimental demonstrations of a controller designed entirely using a PDE boundary control formulation.

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M3 - Conference Paper

AN - SCOPUS:85045266183

T3 - Proceedings of the IEEE Conference on Decision and Control

SP - 4442

EP - 4448

BT - 2012 IEEE 51st IEEE Conference on Decision and Control (CDC)

PB - IEEE, Institute of Electrical and Electronics Engineers

T2 - IEEE Conference on Decision and Control 2012

Y2 - 10 December 2012 through 13 December 2012

ER -

PDE boundary control for Euler-Bernoulli beam using a two stage perturbation observer

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