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Feedback Linearization of the Lorenz System: Stabilization and Tracking Control

[+] Author Affiliations
L. G. Crespo, J. Q. Sun

University of Delaware, Newark, DE

Paper No. IMECE2002-32404, pp. 481-492; 12 pages
doi:10.1115/IMECE2002-32404
From:
  • ASME 2002 International Mechanical Engineering Congress and Exposition
  • Design Engineering
  • New Orleans, Louisiana, USA, November 17–22, 2002
  • Conference Sponsors: Design Engineering Division
  • ISBN: 0-7918-3628-2 | eISBN: 0-7918-1691-5, 0-7918-1692-3, 0-7918-1693-1
  • Copyright © 2002 by ASME

abstract

This paper presents a control study of the Lorenz system by using feedback linearization. The effects of the state transformation on the dynamics of the Lorenz system are studied first. Then, composite controllers are developed for both stabilization and tracking of the system. The controls are designed to overcome the barrier in controllability imposed by the state transformation. The transition through the manifold defined by such a singularity is achieved by inducing the chaotic response within a boundary layer that contains the singularity. Outside this region, a conventional feedback nonlinear control is applied. In this fashion, the authority of the control is enlarged to the whole state space and the need for high control efforts is substantially mitigated. Tracking problems that involve single and cooperative objectives are studied by using the differential flatness property of the system. A good understanding of the system dynamics proves to be invaluable in the design of better controls. In all numerical examples, the proposed approach led to excellent control performances.

Copyright © 2002 by ASME

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