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

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-linearl...

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Bibliographic Details
Published in2012 American Control Conference (ACC) pp. 3352 - 3358
Main Authors Dudret, Stephane, Beauchard, K., Ammouri, F., Rouchon, P.
Format Conference Proceeding
LanguageEnglish
Published IEEE 01.06.2012
Subjects
Biological system modeling
Boundary conditions
Equations
Liquids
Lyapunov methods
Mathematical model
Observers
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Summary: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.
ISBN:9781457710957
1457710951
ISSN:0743-1619
2378-5861
DOI:10.1109/ACC.2012.6315036