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PDE Boundary Control for Euler-Bernoulli Beam Using a Two Stage Perturbation Observer

Paranjape, Aditya A. and Guan, Jinyu and Chung, Soon-Jo and Krstic, Miroslav (2012) PDE Boundary Control for Euler-Bernoulli Beam Using a Two Stage Perturbation Observer. In: 51st IEEE Conference on Decision and Control (CDC). IEEE Conference on Decision and Control . IEEE , New York, NY, pp. 4442-4448. ISBN 978-1-4673-2066-5. http://resolver.caltech.edu/CaltechAUTHORS:20161109-084215066

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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.


Item Type:Book Section
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1109/CDC.2012.6426058DOIArticle
http://ieeexplore.ieee.org/document/6426058/PublisherArticle
ORCID:
AuthorORCID
Chung, Soon-Jo0000-0002-6657-3907
Additional Information:© 2012 IEEE. Date Added to IEEE Xplore: 04 February 2013. This project was supported by the U.S. Army Research Office (ARO) under Award No W911NF-10-1-0296.
Group:GALCIT
Funders:
Funding AgencyGrant Number
Army Research Office (ARO)W911NF-10-1-0296
Record Number:CaltechAUTHORS:20161109-084215066
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20161109-084215066
Official Citation:A. A. Paranjape, J. Guan, S. J. Chung and M. Krstic, "PDE boundary control for euler-bernoulli beam using a two stage perturbation observer," 2012 IEEE 51st IEEE Conference on Decision and Control (CDC), Maui, HI, 2012, pp. 4442-4448. doi: 10.1109/CDC.2012.6426058
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:71869
Collection:CaltechAUTHORS
Deposited By: Ruth Sustaita
Deposited On:09 Nov 2016 18:13
Last Modified:04 Jan 2017 19:14

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