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

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.
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https://hal-mines-paristech.archives-ouvertes.fr/hal-00738684
Contributor : François Chaplais <>
Submitted on : Thursday, October 4, 2012 - 6:50:18 PM
Last modification on : Thursday, September 24, 2020 - 5:04:18 PM

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  • HAL Id : hal-00738684, version 1

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Stéphane Dudret, Karine Beauchard, Fouad Ammouri, Pierre Rouchon. Stability and asymptotic observers of binary distillation processes described by nonlinear convection/diffusion models. American Control Conference 2012, Jun 2012, Montreal, Canada. pp.3352 - 3358. ⟨hal-00738684⟩

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