Dead-time compensation for wave/string PDEs / Krstic, Miroslav in Transactions of the ASME . Journal of dynamic systems, measurement, and control, Vol. 133 N° 3 (Mai 2011)  

Dead-time compensation for wave/string PDEs [texte imprimé] / Krstic, Miroslav, Auteur . - 2011 . - 13 p.
Systèmes dynamiques
Langues : Anglais (eng)
in Transactions of the ASME . Journal of dynamic systems, measurement, and control > Vol. 133 N° 3 (Mai 2011) . - 13 p.

Mots-clés :	Asymptotic stability Delays Feedback Multidimensional systems Parabolic equations Partial differential
Index. décimale :	629.8
Résumé :	Smith predictorlike designs for compensation of arbitrarily long input delays are commonly available only for finite-dimensional systems. Only very few examples exist, where such compensation has been achieved for partial differential equation (PDE) systems, including our recent result for a parabolic (reaction-diffusion) PDE. In this paper, we address a more challenging wave PDE problem, where the difficulty is amplified by allowing all of this PDE's eigenvalues to be a distance to the right of the imaginary axis. Antidamping (positive feedback) on the uncontrolled boundary induces this dramatic form of instability. We develop a design that compensates an arbitrarily long delay at the input of the boundary control system and achieves exponential stability in closed-loop. We derive explicit formulae for our controller's gain kernel functions. They are related to the open-loop solutions of the antistable wave equation system over the time period of input delay (this simple relationship is the result of the design approach).
DEWEY :	629.8
ISSN :	0022-0434
En ligne :	http://asmedl.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=JDSMAA00013300 [...]