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Stability and asymptotic observers of binary distillation processes described by nonlinear convection/diffusion models

Authors: S. Dudret, K. Beauchard, F. Ammouri, P. Rouchon, American Control Conference 2012, pp. 3352 - 3358, 27-29 June 2012, Montreal, Canada.
Distillation column monitoring requires shortcut nonlinear dynamic models. On the basis of a classical wave-model and time-scale reduction techniques, we derive a one-dimensional partial differential equation describing the composition dynamics where convection and diffusion terms depend non-linearly on the internal compositions and the inputs. The Cauchy problem is well posed for any positive time and we prove that it admits, for any relevant constant inputs, a unique stationary solution. We exhibit a Lyapunov function to prove the local exponential stability around the stationary solution. For a boundary measure, we propose a family of asymptotic observers and prove their local exponential convergence. Numerical simulations indicate that these convergence properties seem to be more than local.
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BibTeX:
@Proceedings{,
author = {S. Dudret, K. Beauchard, F. Ammouri, P. Rouchon},
editor = {},
title = {Stability and asymptotic observers of binary distillation processes described by nonlinear convection/diffusion models},
booktitle = {American Control Conference 2012},
volume = {},
publisher = {},
address = {Montreal},
pages = {3352 - 3358},
year = {2012},
abstract = {Distillation column monitoring requires shortcut nonlinear dynamic models. On the basis of a classical wave-model and time-scale reduction techniques, we derive a one-dimensional partial differential equation describing the composition dynamics where convection and diffusion terms depend non-linearly on the internal compositions and the inputs. The Cauchy problem is well posed for any positive time and we prove that it admits, for any relevant constant inputs, a unique stationary solution. We exhibit a Lyapunov function to prove the local exponential stability around the stationary solution. For a boundary measure, we propose a family of asymptotic observers and prove their local exponential convergence. Numerical simulations indicate that these convergence properties seem to be more than local.},
keywords = {Biological system modeling, Boundary conditions, Equations, Liquids, Lyapunov methods, Mathematical model, Observers}}