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Exponential observers for distributed tubular (bio)reactors
Author(s) -
García Míriam R.,
Vilas Carlos,
Banga Julio R.,
Alonso Antonio A.
Publication year - 2008
Publication title -
aiche journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.958
H-Index - 167
eISSN - 1547-5905
pISSN - 0001-1541
DOI - 10.1002/aic.11571
Subject(s) - dissipative system , observer (physics) , control theory (sociology) , exponential function , lyapunov function , exponential stability , exponential growth , reaction–diffusion system , projection (relational algebra) , partial differential equation , mathematics , representation (politics) , process (computing) , transformation (genetics) , computer science , algorithm , mathematical analysis , physics , chemistry , artificial intelligence , thermodynamics , biochemistry , control (management) , quantum mechanics , nonlinear system , politics , political science , gene , law , operating system
The dissipative nature of spatially distributed process systems is exploited to develop efficient exponential state observers based on a low‐dimensional dynamic representation of the original set of partial differential equations. The suggested approach combines standard observer design techniques for reactors, where the reaction rates are unknown with efficient model reduction methodologies based on projection of the original concentration and temperature fields on low‐dimensional subspaces capturing the slow dynamics of the process. The global exponential stability of the resulting observer is derived combining classical Lyapunov analysis with a transformation that allows us to obtain a diffusion system from a diffusion‐convection system. In addition, aspects related to the location of sensors and their influence on the ability to reconstruct the necessary fields to feed the observer will also be considered. © 2008 American Institute of Chemical Engineers AIChE J, 2008