Design and application of state observers for exothermic fed-batch reactors with uncertain kinetics and heat transfer

First Edition

Monitoring the limiting reactant concentration is a key question to maximize the productivity and to guarantee the safety of exothermic fed-batch processes. However in most applications, the concentration cannot be measured in real-time since suitable devices do not exist or are too expensive; the concentrations are then measured by off-line analyses. In this context monitoring the concentrations via software sensors, or state observer based estimators, is an attractive option.

The presence of model uncertainties is a major limitation when applying state observers to real processes. More precisely, in fed-batch exothermic reactors the bad knowledge of both the reaction kinetics and the heat transfer may prevent the use of classical observers. In this study, we propose two different approaches to estimate the concentration of the limiting reactant in a class of single phase exothermic fed-batch reactors with uncertain kinetics and heat transfer. The first approach is based on a finite time converging observer that provides an estimate for the reaction rate via the reactor energy balance equation. The concentration is then computed from the reaction rate estimate via a material balance equation.

The main contribution of this approach is the use of a finite time observer to limit the reconstruction error by guaranteeing a small convergence time interval for the reaction rate estimate. The second approach is based on an interval observer that provides two bounds for the concentration by considering uncertainties related to both the heat transfer and the reaction kinetics. The final estimate is then computed as the mean of the bounds. A systematic tuning procedure has been developed for each of both estimation techniques. Both estimators have then been tested and validated with real data coming from the production of different kinds of resins carried out in 10 tons reactors.

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Presses universitaires de Louvain
Title Part
Numéro 172
Frédéric Sauvage,
Thèses de l'École polytechnique de Louvain
Publisher Category
Applied Sciences > Materials and procedures
BISAC Subject Heading
Onix Audience Codes
06 Professional and scholarly
CLIL (Version 2013-2019)
Title First Published
Type of Work


Publication Date
10 June 2014
Main content page count : 282
16 x 24.5 x 1.5 cm
462 grams
List Price
21.00 €
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Chapter 1 Introduction p.7
1.1 State of the art p.14
1.2 Structure p.24
Chapter 2 Reactor model p.27
2.1 A general formulation p. 29
2.2 Model for a class of fed-batch reactors p.31
2.3 A second order model p.36
Chapter 3 Finite time observer p.39
3.1. Finite time observer for LTI systems p.43
3.2 FTO for a class of nonlinear systems p.49
3.3 FTO for exothermic reactors p.63
Chapter 4 Interval observer p.73
4.1 Definition p.76
4.2 Interval observer design p.78
4.8 Interval observer for exothermic reactors p.84
Chapter 5 Application p.96
5.1 Estimation algorithms p.99
5.2 Benchmark model p.105
5.3 Numerical simulations p.108
5.4 Experimental results p.137
Chapter 6 Conclusion p.161
Chapter 7 Notation p.165
Bibliography p.171