Further results on sliding manifold design and observation for a heat equation

Enrique Barbieri; Sergey Drakunov; J. Fernando Figueroa

Kybernetika (2000)

  • Volume: 36, Issue: 1, page [133]-147
  • ISSN: 0023-5954

Abstract

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This article presents new extensions regarding a nonlinear control design framework that is suitable for a class of distributed parameter systems with uncertainties (DPS). The control objective is first formulated as a function of the distributed system state. Then, a control is sought such that the set in the state space where this relation is true forms an integral manifold reachable in finite time. The manifold is called a Sliding Manifold. The Sliding Mode controller implements a theoretically infinite gain but with finite control amplitudes serving as an effective tool to suppress the influence of matched disturbances and uncertainties in the system behavior. The theory is developed generically for a finite dimensional Jordan Canonical representation of the DPS. The controller manifold design is described in detail and the observer manifold design can be described in a dual manner. Finally, the control law is expressed in terms of the distributed state. However, in a temperature field control problem motivated by a robotic arc- welding application, the simulations presented are done in the standard manner: a reduced-order finite-dimensional model is used to design the controller which is then implemented on a higher-order, still finite- dimensional (truth) model of the system. An analysis of the potential spillover problem shows the effectiveness of our approach. The article concludes with a brief description of the development of an experimental setup that is underway in our Control Systems Lab.

How to cite

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Barbieri, Enrique, Drakunov, Sergey, and Figueroa, J. Fernando. "Further results on sliding manifold design and observation for a heat equation." Kybernetika 36.1 (2000): [133]-147. <http://eudml.org/doc/33474>.

@article{Barbieri2000,
abstract = {This article presents new extensions regarding a nonlinear control design framework that is suitable for a class of distributed parameter systems with uncertainties (DPS). The control objective is first formulated as a function of the distributed system state. Then, a control is sought such that the set in the state space where this relation is true forms an integral manifold reachable in finite time. The manifold is called a Sliding Manifold. The Sliding Mode controller implements a theoretically infinite gain but with finite control amplitudes serving as an effective tool to suppress the influence of matched disturbances and uncertainties in the system behavior. The theory is developed generically for a finite dimensional Jordan Canonical representation of the DPS. The controller manifold design is described in detail and the observer manifold design can be described in a dual manner. Finally, the control law is expressed in terms of the distributed state. However, in a temperature field control problem motivated by a robotic arc- welding application, the simulations presented are done in the standard manner: a reduced-order finite-dimensional model is used to design the controller which is then implemented on a higher-order, still finite- dimensional (truth) model of the system. An analysis of the potential spillover problem shows the effectiveness of our approach. The article concludes with a brief description of the development of an experimental setup that is underway in our Control Systems Lab.},
author = {Barbieri, Enrique, Drakunov, Sergey, Figueroa, J. Fernando},
journal = {Kybernetika},
keywords = {nonlinear control design; sliding mode control; heat equation; nonlinear control design; sliding mode control; heat equation},
language = {eng},
number = {1},
pages = {[133]-147},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Further results on sliding manifold design and observation for a heat equation},
url = {http://eudml.org/doc/33474},
volume = {36},
year = {2000},
}

TY - JOUR
AU - Barbieri, Enrique
AU - Drakunov, Sergey
AU - Figueroa, J. Fernando
TI - Further results on sliding manifold design and observation for a heat equation
JO - Kybernetika
PY - 2000
PB - Institute of Information Theory and Automation AS CR
VL - 36
IS - 1
SP - [133]
EP - 147
AB - This article presents new extensions regarding a nonlinear control design framework that is suitable for a class of distributed parameter systems with uncertainties (DPS). The control objective is first formulated as a function of the distributed system state. Then, a control is sought such that the set in the state space where this relation is true forms an integral manifold reachable in finite time. The manifold is called a Sliding Manifold. The Sliding Mode controller implements a theoretically infinite gain but with finite control amplitudes serving as an effective tool to suppress the influence of matched disturbances and uncertainties in the system behavior. The theory is developed generically for a finite dimensional Jordan Canonical representation of the DPS. The controller manifold design is described in detail and the observer manifold design can be described in a dual manner. Finally, the control law is expressed in terms of the distributed state. However, in a temperature field control problem motivated by a robotic arc- welding application, the simulations presented are done in the standard manner: a reduced-order finite-dimensional model is used to design the controller which is then implemented on a higher-order, still finite- dimensional (truth) model of the system. An analysis of the potential spillover problem shows the effectiveness of our approach. The article concludes with a brief description of the development of an experimental setup that is underway in our Control Systems Lab.
LA - eng
KW - nonlinear control design; sliding mode control; heat equation; nonlinear control design; sliding mode control; heat equation
UR - http://eudml.org/doc/33474
ER -

References

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  8. Drakunov S., Utkin V., 10.1080/00207179208934270, Internat. J. Control 55 (1992), 4, 1029–1037 (1992) Zbl0745.93031MR1154664DOI10.1080/00207179208934270
  9. Meirovitch L., Analytical Methods in Vibrations, MacMillan, New York 1967 Zbl0166.43803
  10. Oden J. T., Applied Functional Analysis, Prentice–Hall, Englewood Cliffs, N.J. 1979 Zbl1200.46001
  11. Russell D., Observability of linear distributed–parameter systems, In: The Control Handbook (W. S. Levine, ed.), CRC Press, Boca Raton, Fl. 1996, pp. 1169–1175 (1996) 
  12. Segel L. A., Mathematics Applied to Continuum Mechanics, MacMillan, New York 1977 Zbl1142.74001MR0502508

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