Journal
SYSTEMS & CONTROL LETTERS
Volume 57, Issue 9, Pages 750-758Publisher
ELSEVIER
DOI: 10.1016/j.sysconle.2008.02.005
Keywords
delays; distributed parameter systems; backstepping
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We consider a problem of boundary feedback stabilization of first-order hyperbolic partial differential equations (PDEs). These equations serve as a model for physical phenomena such as traffic flows, chemical reactors, and heat exchangers. We design controllers 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 delay line system which converges to zero in finite time. We then apply this procedure to finite-dimensional systems with actuator and sensor delays to recover a well-known infinite-dimensional controller (analog of the Smith predictor for unstable plants). We also show that the proposed method can be used for the boundary control of a Korteweg-de Vries-like third-order PDE. The designs are illustrated with simulations. (C) 2008 Elsevier B.V. All rights reserved.
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