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Backstepping boundary control for unstable second-order hyperbolic PDEs and trajectory tracking

Vatankhah, R ; Sharif University of Technology

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  1. Type of Document: Article
  2. DOI: 10.1115/DETC2009-87038
  3. Abstract:
  4. In this paper, a problem of boundary feedback stabilization of second order hyperbolic partial differential equations (PDEs) is considered. These equations serve as a model for physical phenomena such as oscillatory systems like strings and beams. The controllers are designed using a backstepping method, which has been recently developed for parabolic PDEs. With the integral transformation and boundary feedback the unstable PDE is converted into a system which is stable in sense of Lyapunov. Then taylorian expansion is used to achieve the goal of trajectory tracking. It means design a boundary controller such that output of the system follows an arbitrary map. The designs are illustrated with simulations
  5. Keywords:
  6. Back-stepping method ; Boundary controls ; Boundary feedback ; Hyperbolic partial differential equation ; Hyperbolic PDEs ; Integral transformations ; Lyapunov ; Oscillatory system ; Parabolic PDEs ; Physical phenomena ; Second orders ; Trajectory tracking ; Controllers ; Design ; Integral equations ; Nonlinear equations ; Nonlinear feedback ; Partial differential equations ; Backstepping
  7. Source: Proceedings of the ASME Design Engineering Technical Conference, 30 August 2009 through 2 September 2009 ; Volume 4, Issue PARTS A, B AND C , 2009 , Pages 1787-1792 ; 9780791849019 (ISBN)
  8. URL: http://proceedings.asmedigitalcollection.asme.org/proceeding.aspx?articleid=1649854