| Titre : | Dead-time compensation for wave/string PDEs (2011) |
| Auteurs : | Krstic, Miroslav, Auteur |
| Type de document : | Article : texte imprimé |
| Dans : | Transactions of the ASME . Journal of dynamic systems, measurement, and control (Vol. 133 N° 3, Mai 2011) |
| Article en page(s) : | 13 p. |
| Note générale : | Systèmes dynamiques |
| Langues : | Anglais |
| Index. décimale : | 629.8 |
| Tags : | Asymptotic stability Delays Feedback Multidimensional systems Parabolic equations Partial differential |
| 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=JDSMAA000133000003031004000001&idtype=cvips&gifs=Yes&ref=no |
