Exponential Observers for Distributed Tubular (Bio)Reactors

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. (C) 2008 American Institute of Chemical Engineers AIChE J, 54: 2943-2956, 2008