Bioprocess Control

Edited by Denis Dochain

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Bioprocess Control

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Bioprocess Control

Edited by Denis Dochain

First published in France in 2001 by Hermes Science entitled “Automatique des bioprocédés” First published in Great Britain and the United States in 2008 by ISTE Ltd and John Wiley & Sons, Inc. Apart from any fair dealing for the purposes of research or private study, or criticism or review, as permitted under the Copyright, Designs and Patents Act 1988, this publication may only be reproduced, stored or transmitted, in any form or by any means, with the prior permission in writing of the publishers, or in the case of reprographic reproduction in accordance with the terms and licenses issued by the CLA. Enquiries concerning reproduction outside these terms should be sent to the publishers at the undermentioned address: ISTE Ltd John Wiley & Sons, Inc. 6 Fitzroy Square 111 River Street London W1T 5DX Hoboken, NJ 07030 UK USA www.iste.co.uk www.wiley.com © ISTE Ltd, 2008 © Hermes Science, 2001 The rights of Denis Dochain to be identified as the author of this work have been asserted by him in accordance with the Copyright, Designs and Patents Act 1988.

Library of Congress Cataloging-in-Publication Data Automatique des bioprocédés. English. Bioprocess control / edited by Denis Dochain. p. ; cm. Translation from French. Includes bibliographical references and index. ISBN: 978-1-84821-025-7 1. Biotechnological process control. 2. Biotechnological process monitoring. I. Dochain, D. (Denis), 1956- II. Title. [DNLM: 1. Biomedical Engineering. 2. Bioreactors. 3. Biotechnology. 4. Models, Biological. QT 36 A939 2008a] TP248.25.M65A9813 2008 660.6--dc22

2007046923 British Library Cataloguing-in-Publication Data A CIP record for this book is available from the British Library ISBN: 978-1-84821-025-7

Printed and bound in Great Britain by Antony Rowe Ltd, Chippenham, Wiltshire.

http://www.wiley.com

Contents

Chapter 1. What are the Challenges for the Control of Bioprocesses? . . . 11Denis DOCHAIN

1.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111.2. Specific problems of bioprocess control . . . . . . . . . . . . . . . . . . 121.3. A schematic view of monitoring and control of a bioprocess . . . . . . 121.4. Modeling and identification of bioprocesses: some key ideas . . . . . . 131.5. Software sensors: tools for bioprocess monitoring . . . . . . . . . . . . 14

151.7. Bioprocess monitoring: the central issue . . . . . . . . . . . . . . . . . . 151.8. Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161.9. Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

Chapter 2. Dynamic Models of Biochemical Processes: Properties ofModels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17Olivier BERNARD and Isabelle QUEINNEC

2.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172.2. Description of biochemical processes . . . . . . . . . . . . . . . . . . . 18

2.2.1. Micro-organisms and their use . . . . . . . . . . . . . . . . . . . . 182.2.2. Types of bioreactors . . . . . . . . . . . . . . . . . . . . . . . . . . 192.2.3. Three operating modes . . . . . . . . . . . . . . . . . . . . . . . . . 19

2.3. Mass balance modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . 212.3.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212.3.2. Reaction scheme . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212.3.3. Choice of reactions and variables . . . . . . . . . . . . . . . . . . . 232.3.4. Example 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

2.4. Mass balance models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 242.4.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 242.4.2. Example 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 242.4.3. Example 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

1.6. Bioprocess control: basic concepts and advanced control . . . . . . . .

6 Bioprocess Control

2.4.4. Matrix representation . . . . . . . . . . . . . . . . . . . . . . . . . 252.4.4.1. Example 2 (continuation) . . . . . . . . . . . . . . . . . . . . 262.4.4.2. Example 1 (continuation) . . . . . . . . . . . . . . . . . . . . 26

2.4.5. Gaseous flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 272.4.6. Electroneutrality and affinity constants . . . . . . . . . . . . . . . 272.4.7. Example 1 (continuation) . . . . . . . . . . . . . . . . . . . . . . . 282.4.8. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

2.5. Kinetics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 302.5.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 302.5.2. Mathematical constraints . . . . . . . . . . . . . . . . . . . . . . . 30

2.5.2.1. Positivity of variables . . . . . . . . . . . . . . . . . . . . . . 302.5.2.2. Variables necessary for the reaction . . . . . . . . . . . . . . 312.5.2.3. Example 1 (continuation) . . . . . . . . . . . . . . . . . . . . 312.5.2.4. Phenomenological knowledge . . . . . . . . . . . . . . . . . 31

2.5.3. Specific growth rate . . . . . . . . . . . . . . . . . . . . . . . . . . 322.5.4. Representation of kinetics by means of a neural network . . . . . 34

2.6. Validation of the model . . . . . . . . . . . . . . . . . . . . . . . . . . . 352.6.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 352.6.2. Validation of the reaction scheme . . . . . . . . . . . . . . . . . . . 35

2.6.2.1. Mathematical principle . . . . . . . . . . . . . . . . . . . . . 352.6.2.2. Example 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

2.6.3. Qualitative validation of model . . . . . . . . . . . . . . . . . . . . 372.6.4. Global validation of the model . . . . . . . . . . . . . . . . . . . . 39

2.7. Properties of the models . . . . . . . . . . . . . . . . . . . . . . . . . . . 392.7.1. Boundedness and positivity of variables . . . . . . . . . . . . . . . 392.7.2. Equilibrium points and local behavior . . . . . . . . . . . . . . . . 40

2.7.2.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 402.8. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 422.9. Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

Chapter 3. Identi cation of Bioprocess Models . . . . . . . . . . . . . . . . . 47Denis DOCHAIN and Peter VANROLLEGHEM

3.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 473.2. Structural identifiability . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

3.2.1. Development in Taylor series . . . . . . . . . . . . . . . . . . . . . 493.2.2. Generating series . . . . . . . . . . . . . . . . . . . . . . . . . . . . 503.2.3. Examples for the application of the methods of development in

series . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 503.2.4. Some observations on the methods for testing structural identifi-

ability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 513.3. Practical identifiability . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

3.3.1. Theoretical framework . . . . . . . . . . . . . . . . . . . . . . . . . 523.3.2. Confidence interval of the estimated parameters . . . . . . . . . . 54

Contents 7

3.3.3. Sensitivity functions . . . . . . . . . . . . . . . . . . . . . . . . . . 553.4. Optimum experiment design for parameter estimation (OED/PE) . . . . 57

3.4.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 573.4.2. Theoretical basis for the OED/PE . . . . . . . . . . . . . . . . . . 593.4.3. Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

3.5. Estimation algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . 633.5.1. Choice of two datasets . . . . . . . . . . . . . . . . . . . . . . . . . 633.5.2. Elements of parameter estimation: least squares estimation in the

linear case . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 643.5.3. Overview of the parameter estimation algorithms . . . . . . . . . . 65

3.6. A case study: identification of parameters for a process modeled foranaerobic digestion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68

3.6.1. The model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 693.6.2. Experiment design . . . . . . . . . . . . . . . . . . . . . . . . . . . 703.6.3. Choice of data for calibration and validation . . . . . . . . . . . . 703.6.4. Parameter identification . . . . . . . . . . . . . . . . . . . . . . . . 713.6.5. Analysis of the results . . . . . . . . . . . . . . . . . . . . . . . . . 75

3.7. Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75

Chapter 4. State Estimation for Bioprocesses . . . . . . . . . . . . . . . . . . 79Olivier BERNARD and Jean-Luc GOUZÉ

4.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 794.2. Notions on system observability . . . . . . . . . . . . . . . . . . . . . . 80

4.2.1. System observability: definitions . . . . . . . . . . . . . . . . . . . 804.2.2. General definition of an observer . . . . . . . . . . . . . . . . . . . 814.2.3. How to manage the uncertainties in the model or in the output . . 83

4.3. Observers for linear systems . . . . . . . . . . . . . . . . . . . . . . . . . 844.3.1. Luenberger observer . . . . . . . . . . . . . . . . . . . . . . . . . . 854.3.2. The linear case up to an output injection . . . . . . . . . . . . . . . 864.3.3. Local observation of a nonlinear system around an equilibrium

point . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 864.3.4. PI observer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 874.3.5. Kalman filter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 874.3.6. The extended Kalman filter . . . . . . . . . . . . . . . . . . . . . . 89

4.4. High gain observers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 894.4.1. Definitions, hypotheses . . . . . . . . . . . . . . . . . . . . . . . . 894.4.2. Change of variable . . . . . . . . . . . . . . . . . . . . . . . . . . . 904.4.3. Fixed gain observer . . . . . . . . . . . . . . . . . . . . . . . . . . 914.4.4. Variable gain observers (Kalman-like observer) . . . . . . . . . . . 914.4.5. Example: growth of micro-algae . . . . . . . . . . . . . . . . . . . 92

4.5. Observers for mass balance-based systems . . . . . . . . . . . . . . . . 944.5.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 944.5.2. Definitions, hypotheses . . . . . . . . . . . . . . . . . . . . . . . . 96

8 Bioprocess Control

4.5.3. The asymptotic observer . . . . . . . . . . . . . . . . . . . . . . . . 964.5.4. Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 984.5.5. Improvements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99

4.6. Interval observers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1014.6.1. Principle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1024.6.2. The linear case up to an output injection . . . . . . . . . . . . . . . 1034.6.3. Interval estimator for an activated sludge process . . . . . . . . . . 1054.6.4. Bundle of observers . . . . . . . . . . . . . . . . . . . . . . . . . . 107

4.7. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1104.8. Appendix: a comparison theorem . . . . . . . . . . . . . . . . . . . . . . 1114.9. Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112

Chapter 5. Recursive Parameter Estimation . . . . . . . . . . . . . . . . . . 115Denis DOCHAIN

5.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1155.2. Parameter estimation based on the structure of the observer . . . . . . . 116

5.2.1. Example: culture of animal cells . . . . . . . . . . . . . . . . . . . 1165.2.2. Estimator based on the structure of the observer . . . . . . . . . . 1175.2.3. Example: culture of animal cells (continued) . . . . . . . . . . . . 1195.2.4. Calibration of the estimator based on the structure of the observer:

theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1195.2.5. Calibration of the estimator based on the structure of the observer:

application to the culture of animal cells . . . . . . . . . . . . . . . 1245.2.6. Experimental results . . . . . . . . . . . . . . . . . . . . . . . . . . 127

5.3. Recursive least squares estimator . . . . . . . . . . . . . . . . . . . . . . 1295.4. Adaptive state observer . . . . . . . . . . . . . . . . . . . . . . . . . . . 133

5.4.1. Generalization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1385.5. Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1405.6. Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141

Denis DOCHAIN and Jérôme HARMAND

6.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143

6.2.1. Biological system dynamics . . . . . . . . . . . . . . . . . . . . . . 1446.2.2. Sources of uncertainties and disturbances of biological systems . 146

6.3. Stability of biological processes . . . . . . . . . . . . . . . . . . . . . . 1476.3.1. Basic concept of the stability of a dynamic system . . . . . . . . . 1476.3.2. Equilibrium point . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1486.3.3. Stability analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149

6.4. Basic concepts of biological process control . . . . . . . . . . . . . . . . 1506.4.1. Regulation and tracking control . . . . . . . . . . . . . . . . . . . . 1506.4.2. Strategy selection: direct and indirect control . . . . . . . . . . . . 151

�Chapter 6. Basic Concepts of Bioprocess Control . . . . . . . . . . . . . . . 143

. . . . . . . . . . . . . . . . . 1446.2. Bioprocess control: basic concepts . . . .

Contents 9

6.4.3. Selection of synthesis method . . . . . . . . . . . . . . . . . . . . . 152

6.5.1. Representation of systems . . . . . . . . . . . . . . . . . . . . . . . 153

. . . . . . . . . . . . . . . . . . . . . . . . . . . . 1606.6.1. A nonlinear PI controller . . . . . . . . . . . . . . . . . . . . . . . 1606.6.2. Robust control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162

6.7. Specific approaches . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1656.7.1. Pulse control: a dialog with bacteria . . . . . . . . . . . . . . . . . 1656.7.2. Overall process optimization: towards integrating the control

objectives in the initial stage of bioprocess design . . . . . . . . . 1676.8. Conclusions and perspectives . . . . . . . . . . . . . . . . . . . . . . . . 1706.9. Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 170

Chapter 7. Adaptive Linearizing Control and Extremum-Seeking Controlof Bioprocesses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173Denis DOCHAIN, Martin GUAY, Michel PERRIER and Mariana TITICA

7.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1737.2. Adaptive linearizing control of bioprocesses . . . . . . . . . . . . . . . 174

7.2.1. Design of the adaptive linearizing controller . . . . . . . . . . . . 1747.2.2. Example 1: anaerobic digestion . . . . . . . . . . . . . . . . . . . . 176

7.2.2.1. Model order reduction . . . . . . . . . . . . . . . . . . . . . . 1777.2.2.2. Adaptive linearizing control design . . . . . . . . . . . . . . 179

7.2.3. Example 2: activated sludge process . . . . . . . . . . . . . . . . . 1837.3. Adaptive extremum-seeking control of bioprocesses . . . . . . . . . . . 188

7.3.1. Fed-batch reactor model . . . . . . . . . . . . . . . . . . . . . . . . 1897.3.2. Estimation and controller design . . . . . . . . . . . . . . . . . . . 191

7.3.2.1. Estimation equation for the gaseous outflow rate y . . . . . . 1917.3.2.2. Design of the adaptive extremum-seeking controller . . . . . 1927.3.2.3. Stability and convergence analysis . . . . . . . . . . . . . . . 1957.3.2.4. A note on dither signal design . . . . . . . . . . . . . . . . . 196

7.3.3. Simulation results . . . . . . . . . . . . . . . . . . . . . . . . . . . 1977.4. Appendix: analysis of the parameter convergence . . . . . . . . . . . . 2027.5. Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 207

Chapter 8. Tools for Fault Detection and Diagnosis . . . . . . . . . . . . . . 211Jean-Philippe STEYER, Antoine GÉNOVÉSI and Jérôme HARMAND

8.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2118.2. General definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212

8.2.1. Terminology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2128.2.2. Fault types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213

8.3. Fault detection and diagnosis . . . . . . . . . . . . . . . . . . . . . . . . 2148.3.1. Methods based directly on signals . . . . . . . . . . . . . . . . . . 215

6.5. Synthesis of biological process control laws

6.5.2. Structure of control laws

. . . . . . . . . . . . . . . . 153

. . . . . . . . . . . . . . . . . . . . . . . . 1546.6. Advanced control laws

10 Bioprocess Control

8.3.1.1. Hardware redundancy . . . . . . . . . . . . . . . . . . . . . . 2158.3.1.2. Specific sensors . . . . . . . . . . . . . . . . . . . . . . . . . 2168.3.1.3. Comparison of thresholds . . . . . . . . . . . . . . . . . . . . 2178.3.1.4. Spectral analysis . . . . . . . . . . . . . . . . . . . . . . . . . 2178.3.1.5. Statistical approaches . . . . . . . . . . . . . . . . . . . . . . 218

8.3.2. Model-based methods . . . . . . . . . . . . . . . . . . . . . . . . . 2188.3.2.1. Parity space . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2198.3.2.2. Observers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2208.3.2.3. Parametric estimation . . . . . . . . . . . . . . . . . . . . . . 221

8.3.3. Methods based on expertise . . . . . . . . . . . . . . . . . . . . . . 2228.3.3.1. AI models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2238.3.3.2. Artificial neural networks . . . . . . . . . . . . . . . . . . . . 2248.3.3.3. Fuzzy inference systems . . . . . . . . . . . . . . . . . . . . . 225

8.3.4. Choice and combined use of diverse methods . . . . . . . . . . . . 2278.4. Application to biological processes . . . . . . . . . . . . . . . . . . . . . 227

8.4.1. “Simple” biological processes . . . . . . . . . . . . . . . . . . . . 2288.4.2. Wastewater treatment processes . . . . . . . . . . . . . . . . . . . 229

8.5. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2318.6. Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 232

List of Authors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 239

Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 241

Chapter 1

What are the Challenges for the Controlof Bioprocesses?

1.1. Introduction

In simple terms, we can define a fermentation process as the growth of microorgan-isms (bacteria, yeasts, mushrooms, etc.) resulting from the consumption of substratesor nutrients (sources of carbon, oxygen, nitrogen, phosphorus, etc.). This growth ispossible only when favorable “environmental” conditions are present. Environmentalconditions refer to physicochemical conditions (pH, temperature, agitation, ventila-tion, etc.) necessary for good microbial activity.

Techniques in the field of biotechnology can be roughly grouped into three majorcategories:

1. microbiology and genetic engineering;

2. bioprocess engineering;

3. bioprocess control.

Microbiology and genetic engineering aim to develop microorganisms, whichallow for the production of new products, or aim to choose the best microbial strains soas to obtain certain desired products or product quality. Process engineering choosesthe best operating modes or develops processes and/or reactors, which change andimprove the output and/or the productivity of bioprocesses. Automatic control aimsto increase the output and/or productivity by developing methods of monitoring

Chapter written by Denis DOCHAIN.

12 Bioprocess Control

and control, enabling real-time optimization of the bioprocess operation. Theseapproaches are obviously complementary to one another. This book discusses thematter within the context of the final approach.

1.2. Speci c problems of bioprocess control

Over the past several decades, biotechnological processes have been increasinglyused industrially, which is attributed to several reasons (improvement of profitabilityand quality in production industries, new legislative standards in processing indus-tries, etc.). The problems arising from this industrialization are generally the sameas those encountered in any processing industry and we face, in the field of biopro-cessing, almost all of the problems that are being tackled in automatic control. Thus,system requirements for supervision, control and monitoring of the processes in orderto optimize operation or detect malfunctions are on the increase. However, in reality,very few installations are provided with such systems. Two principal reasons explainthis situation:

– first of all, biological processes are complex processes involving living organ-isms whose characteristics are, by nature, very difficult to apprehend. In fact, themodeling of these systems faces two major difficulties. On the one hand, lack ofreproducibility of experiments and inaccuracy of measurements result not only in oneor several difficulties related to selection of model structure but also in difficultiesrelated to the concepts of structural and practical identifiability at the time of iden-tification of a set of given parameters. On the other hand, difficulties also occur atthe time of the validation phase of these models whose sets of parameters could haveprecisely evolved over course of time. These variations can be the consequence ofmetabolic changes of biomass or even genetic modifications that could not be fore-seen and observed from a macroscopic point of view;

– the second major difficulty is the almost systematic absence of sensors providingaccess to measurements necessary to know the internal functioning of biological pro-cesses. The majority of the key variables associated with these systems (concentrationof biomass, substrates and products) can be measured only using analyzers on a labo-ratory scale – where they exist – which are generally very expensive and often requireheavy and expensive maintenance. Thus, the majority of the control strategies usedin industries are very often limited to indirect control of fermentation processes bycontrol loops of the environmental variables such as dissolved oxygen concentration,temperature, pH, etc.

1.3. A schematic view of monitoring and control of a bioprocess

Use of a computer to monitor and control a biological process is representedschematically in Figure 1.1. In the situation outlined, the actuator is the feed rateof the reactor. Its value is the output of the control algorithm, which uses the infor-mation of the available process. This information regroups, on the one hand, the state

What are the Challenges for the Control of Bioprocesses? 13

Sample

Effluent

Screen monitor

ComputerSet point

Keyboard

Monitoringalgorithm

Softwaresensors

Controlaction

Output gas

Concentratedsubstrate

Supply ofwater

Liquid

Bioreactor Sensors: analyzers andmeasuring systems

of the process to date (i.e. measurements) and, on the other hand, available a prioriknowledge (for example, in the form of a “material balance” model type) relative toa dynamic biological process and mutual interactions of different process variables.In certain cases – and in particular, when control objectives directly use variables thatcould not be measured (certain concentrations of biomass, substrates and/or products)or key parameters of the biological process (growth rate or more generally produc-tion rate, yield coefficients, transfer parameters) – information resulting from “in-line”measurements and a priori knowledge will be combined to synthesize “software sen-sors” or “observers,” whose principles and methods will be presented in Chapters4 and 5. Thus, according to the available process knowledge and control objectivesspecified by the user, we will be able to develop and implement more or less complexcontrol algorithms.

1.4. Modeling and identi cation of bioprocesses: some key ideas

The dynamic model concept plays a central role in automatic control. It is in facton the basis of the time required for the development of the knowledge process that

Figure 1.1. Schematic representation of bioprocess control system

14 Bioprocess Control

the total design, analysis and implementation of monitoring and control methods arecarried out. Within the framework of bioprocesses, the most natural way to determinethe models that will enable the characterization of the process dynamics is to considerthe material balance (and possibly energy) of major components of the process. It isthis approach that we will consider in this work (although certain elements of hybrid

in the chapter on modeling). One of the important aspects of the balance models is thatthey consist of two types of terms representing, respectively, conversion (i.e. kinetics

substrates in terms of biomass and products) and the dynamics of transport (whichregroups transit of matter within the process in solid, liquid or gaseous form and thetransfer phenomena between phases). These models have various properties, whichcan prove to be interesting for the design of monitoring and control algorithms forbioprocesses, and which will, thus, be reviewed in Chapter 2. Moreover, we will intro-duce in Chapter 4 on state observers a state transformation that makes it possible towrite part of the bioprocess equations in a form independent of the process kinetics.This transformation is largely related to the concept of reaction invariants, which arewell known in the literature in chemistry and chemical engineering.

An important stage of modeling consists not only of choosing a model suitableand appropriate for describing the bioprocess dynamics studied but also of calibratingthe parameters of this model. This stage is far from being understood and thereforeno solution has been obtained, given the complexity of models as well as the (fre-quent) lack of sufficiently numerous and reliable experimental data. Chapter 3 willattempt to introduce the problem of identification of the parameters of the models ofthe bioprocess (in dealing with questions of structural and practical identifiability aswell as experiment design for its identification) and suitable methods to carry out thisidentification.

1.5. Software sensors: tools for bioprocess monitoring

As noted above, sometimes many important variables of the process are not acces-sible to be measured online. Similarly, many parameters remain unclear and/or arelikely to vary with time. There is, thus, a fundamental need to develop a model, whichmakes it possible to carry out a real-time follow-up of variables and key parameters ofthe bioprocess. Thus, Chapters 4 and 5 will attempt, respectively, to develop softwaretools to rebuild the evolution of these parameters and variables in the course of time.Insofar as their design gives reliable values to these parameters and variables, they playthe role of sensors and will thus be called “software sensors”. The material is dividedbetween the two chapters on the basis of distinction between state variables (i.e. pri-marily, component concentrations) whose evolution in time is described by differen-tial equations and parameters (kinetic, conversion and transfer parameters), which areeither the functions of process variables (as is typically the case for kinetic parameters

modeling, which combines balance equations and neural networks, will be addressed

of various biochemical reactions of the process and conversion yields of various

What are the Challenges for the Control of Bioprocesses? 15

such as specific growth rates) or constants (output parameters, transfer parameters)1.For state variables, we will proceed with the design of “software sensors” called stateobservers (Chapter 4), whereas for estimating the unknown or unclear parametersonline, parameter estimators will be used (Chapter 5). Due to space considerations,Chapter 5 will deal exclusively with the estimation of kinetic parameters, which provesto be a more crucial problem to be solved. However, the methods which are developedare also applicable to other parameters.

1.6.

profile compatible with an optimal operating condition. Chapter 6 will attempt todevelop the basic concepts of automatic control applied to bioprocesses, particularly

portional and integral actions. We can also initiate certain control methods specificto bioprocesses. The following chapter will concentrate on the development of moresophisticated control methods with the objective of guaranteeing the best possiblebioprocess operation while accounting, in particular, for disturbances and modelinguncertainties. Emphasis will be placed, particularly, on optimal control and adaptivecontrol methods based on the balance model as developed in the chapter on model-ing. The objective is clearly to obtain control laws, which seek the best compromisebetween what is well known in bioprocess dynamics (for example, the reaction schemeand the material balance) and what is less understood (for example, the kinetics).

1.7. Bioprocess monitoring: the central issue

With the exception of real-time monitoring of state variables and parameters, therehas been little consideration of bioprocess monitoring. In particular, how to managebioprocesses with respect to various operation problems, which are about malfunction-ing or broken down sensors, actuators (valves, pumps, agitators, etc.), or even morebasically malfunction of the bioprocess itself, if it starts to deviate from the nomi-nal state (let us not forget that the process implements living organisms, which canpossibly undergo certain, at least partial, transformations or changes, which are likelyto bring the process to a different state from that expected). This issue is obviouslyimportant and cannot be ignored if we wish to guarantee a good real time processoperation. This problem calls for all the process information (which is obtained frommodeling, physical and software sensors or control). This will be covered in the finalchapter.

1. The models used in practice are often so simplified with respect to reality that these param-eters can “apparently” undergo certain variations with time. However, it is important to notethat these variations are nothing but a reflection of the inaccuracy or inadequacy of the selectedmodel.

Bioprocess control: basic concepts and advanced control

operation, less susceptible to various disturbances, close to a certain state or desiredAn important aspect of bioprocess control is to lay down a stable real time

the concepts of control and setpoint tracking, feedback, feedforward control and pro-

16 Bioprocess Control

1.8. Conclusions

A certain number of works exist in the literature, which deal with the application ofautomatic control in bioprocesses. This book is largely based on the following books:[BAS 90, VAN 98]. However, we should also mention other reference works worthyof interest: [MOS 88, PAV 94, PON 92, SCH 00]. Due to lack of space, we have notconsidered certain topics, which could, however, legitimately have had a place in thisbook. Initially, the informed reader would have noted that there is no chapter on instru-mentation, which is, however, an essential link in monitoring and control. Fortunately,the reader will be able to complement the reading of this work with that (in French)of Boudrant, Corrieu, and Coulet [BOU 94] or that (in English) of Pons [PON 92]. Inaddition, we did not have the space for approaches such as metabolic engineering, atype of approach, which is already playing a growing role in bioprocess control. Wesuggest the reader consult the following book on metabolic engineering: [STE 98].

1.9. Bibliography

[BAS 90] G. BASTIN and D. DOCHAIN, On-line Estimation and Adaptive Control of Biore-actors, Elsevier, Amsterdam, 1990.

[BOU 94] J. BOUDRANT, G. CORRIEU and P. COULET, Capteurs et Mesures en Biotechnolo-gie, Lavoisier, Paris, 1994.

[MOS 88] A. MOSER, Bioprocess Technology. Kinetics and Reactors, Springer Verlag, NewYork, 1988.

[PAV 94] A. PAVÉ, Modélisation en Biologie et en Ecologie, Aléas, Lyon, 1994.

[PON 92] M.N. PONS, Bioprocess Monitoring and Control, Hanser, Munich, 1992.

[SCH 00] K. SCHÜGERL and K.H. BELLGARDT, Bioreaction Engineering. Modeling andControl, Springer, Berlin, 2000.

[STE 98] G. STEPHANOPOULOS, J. NIELSEN and A. ARISTIDOU, Metabolic Engineering,Academic Press, Boston, 1998.

[VAN 98] J. VAN IMPE, P. VANROLLEGHEM and D. ISERENTANT, Advanced Instrumenta-tion, Data Interpretation and Control of Biotechnological Processes, Kluwer, Amsterdam,1998.

Chapter 2

Dynamic Models of Biochemical Processes:Properties of Models

2.1. Introduction

Modeling biochemical processes is a delicate exercise. Contrary to physics, wherethere are laws that have been known to man for centuries (Ohm’s law, ideal gas law,Newton’s second law, the principles of thermodynamics, etc.) the majority of the mod-els in biology depend on empirical laws. As it is not possible to base them only onavailable (and validated) knowledge, it is very important to be able to characterize thereliability of the laws used in the construction of the model. This implies hierarchismin the construction of biochemical models. In this chapter, we will see how to organizeknowledge in the model in order to distinguish a reliable part established on the basisof a mass balance, and a more fragile part which will describe the bacterial kinetics.

The quality of the model and, above all, its structure must correspond to the objec-tive for which the model was built. In fact, a model can be developed for very differentpurposes, which will have to be clearly identified from the beginning. Thus, the modelcould be used to:

– reproduce an observed behavior;

– explain an observed behavior;

– predict the evolution of a system;

– help in understanding the mechanisms of the studied system;

– estimate variables which are not measured;

Chapter written by Olivier BERNARD and Isabelle QUEINNEC.

18 Bioprocess Control

– estimate parameters of the process;

– act on the system to steer and control its variables;

– detect an anomaly in the functioning of the process;

– etc.

The modeling objectives will generally lead to a formalism for designing themodel. If we want to explain spatial heterogenity in a fermentor, it will be necessaryto resort to a spatialized model (generally described by partial derivative equations).If the objective is to improve the production of a metabolite during the transitionalstages, it will be necessary to represent the dynamics of the system. In the same way,the tools that we want to use to achieve the goal will guide us in choosing the modeltype (continuous/discrete, deterministic/stochastic, etc.).

Furthermore, within the limit of these objectives, the model will also have to beadapted to the data available. In fact, a complex model implying a great number ofparameters will require a large quantity of data to be identified and validated.

Finally, considering the lack of validated laws in biology, the key stage of modelingis the validation of the model. This will be the subject of a special section. It is in factfundamental to be able to show, on the basis of experimental data, that the modelcorrectly achieves the assigned goals; we invite the reader to refer to [PAV 94] for athorough reflection on modeling.

2.2. Description of biochemical processes

2.2.1. Micro-organisms and their use

Microbial fermentation is a process in which a population of micro-organisms(bacteria, yeasts, moulds, etc.) are grown using certain nutritive elements (nutrients)under favorable surrounding conditions (temperature, pH, agitation, aeration, etc.).It schematically corresponds to the transformation of substances (generally carbona-ceous substrates) into products, resulting from the metabolic activity of cells.

The main components of the reaction are as follows:

– substrates, denoted as Si, which are necessary for the growth of micro-organ-isms, or even which are precursors of a compound to be produced. These substratesgenerally contain a source of carbon (glucose, ethanol, etc.) and sometimes nitrogen(NO3, NH4, etc.) and phosphorus (PO4, etc.);

– microbial biomasses, denoted as Xi;

– end products, denoted as Pi, for agri-foods (oils, cheese, beer, wines, etc.), chem-istry (solvents, enzymes, amino acids, etc.), the pharmaceutical industry (antibiotics,hormones, vitamins, etc.) or for the production of energy (ethanol, biogas, etc.) etc.

Dynamic Models of Biochemical Processes: Properties of Models 19

Mineral salt and vitamins are added to these main components, which, althoughthey seldom appear in the models, are essential for growth.

Each type of micro-organism contains some characteristics related to its geneticinheritance and to its regulating systems and fermentation can have various uses:

– microbial growth: the primary objective is the growth of the micro-organismitself. This is the case of fermentations aiming to produce baking yeast;

– metabolic production: the objective is to synthesize a preferred metabolite(ethanol, penicillin, etc.) using the cell;

– substrate consumption: in this case, it is the degradation of the substrate whichis desired. In this category, we will primarily find depollution processes (biologicaltreatment of wastewater, breakdown of specific pollutants, etc.);

– phenomenologic study: here, the purpose of fermentation is the study of themicro-organism. This can, for example, be to better understand how the micro-organ-ism develops in the natural environment.

The majority of biotechnological processes developed at an industrial level usemicrobial cultures made up of a single species of micro-organism for the possiblesynthesis of a well defined product (pure culture). However, in certain cases, severalspecies can be made to grow simultaneously, but this is possible only if they are nottoo competitive.

2.2.2. Types of bioreactors

From the view point of mathematical modeling, biological reactors can be dividedinto two major classes [BAI 86]:

– stirred tank reactors (STR) for which the reacting medium is homogenous andthe reaction is described by ordinary differential equations;

– reactors with a spatial concentration gradient, such as fixed beds, fluidized beds,air lifts, etc., for which the reaction is described by partial derivative equations.

In this chapter, we are interested only in the first class of stirred tank reactors, andany reader interested in the second class should see [JAC 96, DOC 94], etc.

2.2.3. Three operating modes

Operating modes of bioreactors are generally characterized by liquid exchanges,i.e. by the type of substrate supply of the reactor. We can distinguish three main modes(Figure 2.1).

Discontinuous (or batch) mode

All the nutritive elements necessary for biological growth are introduced at thebeginning of the reaction. Neither supply nor removal (except for some measurements)

20 Bioprocess Control

Semi-continuousBatch Continuous

Figure 2.1. Various operating modes of biological processes

is carried out thereafter, and the reaction takes place at constant volume. The onlypossible actions of the operator relate specifically to the environmental variables (pH,temperature, stirring velocity, aeration, etc.). Thus, few means are necessary for itsimplementation, which in fact is its attraction, from the industrial point of view. Thesecond advantage is to guarantee the purity of cultures because the risks of culturecontamination are less. A disadvantage is the minimal means which make it possi-ble to operate the fermentor to optimize the use of micro-organisms. It also suffersfrom a major disadvantage: the initial supply of a high quantity of substrate generallyinhibits the growth of micro-organisms which consume it, which results in lengtheneddurations of the process, and limit the acceptable initial load.

Semi-continuous (or fed-batch) mode

This operating mode is distinguished from the preceding mode by a supply of vari-ous nutritive elements as and when there is a need by the micro-organisms. It primarilymakes it possible to eliminate the inhibition problems associated with the precedingmode, and to function at specific growth rates close to their maximum value [QUE 99].From a previously inoculated initial volume the reactor is supplied by a flow controlledin a closed loop. In addition, it is the latter point which strongly limits the use of fed-batch at an industrial scale. Lastly, this operating mode, just like the previous one, ismore particularly recommended when the recovery of the products is carried out atintervals (intracellular accumulation for example) or when it is dangerous to releaseresidual toxic matters (which may happen in the continuous mode).

Continuous (or chemostat) mode

This is the most widely used mode in the field of the biological treatment of water.Characterized by a constant reaction volume, it reaches a state where the extractionof reaction medium equals the nutritive flow rate. The continuous processes work atsteady state for fixed supply conditions, by maintaining the system in a stationarystate, while avoiding any inhibiting phenomenon owing to the dilution effect due tothe supply. Although it generally works in open loop, it is perhaps the richest operatingmode from a dynamic point of view, because it makes it possible to study transitory

Dynamic Models of Biochemical Processes: Properties of Models 21

phenomena [GUI 96], the characteristics of a micro-organism over long periods ofgrowth, optimization problems, etc. Moreover, it enables significant productions insmall-sized reactors.

Sequencing batch reactors (SBR)

This is in fact a combination at one time of various operating modes. The ideais to recover the biomass by sedimentation or the supernatant product between twoproduction (or treatment) sequences. The succession of various stages is representedin Figure 2.2.

1–Filling up 2–Reaction 3–Sedimentation 4–Withdrawal of a fraction of the sludge

5–Drain and return to step 1

Figure 2.2. SBR (sequencing batch reactors): time sequence of various stages

In the same way, the SFBR (sequencing fed-batch reactor) differs from the SBRonly in the way in which the first filling stage is carried out, as and when there is aneed and not in a single action.

2.3. Mass balance modeling

2.3.1. Introduction

Modeling biological systems is a delicate task because there are no laws character-izing the evolution of micro-organisms. Nevertheless, these systems, like all physicalsystems, must comply with rules such as the conservation of mass, electroneutralityof solutions, etc. In this chapter, we will see how to frame the model around thesephysical laws, so as to guarantee some robustness.

2.3.2. Reaction scheme

At the macroscopic level, the reaction scheme of a biochemical process describesthe set of the main biological and chemical reactions. For this we adopt [BAS 90]formalism similar to that of chemistry, by simply defining the transformation of tworeactants A and B into a product C in the following form:

A + B −→ C

22 Bioprocess Control

By convention, contrary to chemistry, we do not consider stoichiometric coeffi-cients in these reactions. In general the reaction rate corresponds to the growing rateof the implied biomass.

At the macroscopic level, the reaction scheme is in fact a synthetic way of sum-marizing all reactions which are supposed to determine the dynamics of the process.Thus, a reaction scheme is generally based on assumptions related to the phenomeno-logical details available. Unlike in chemistry, all the compounds intervening in thereaction are not strictly represented (which is fortunate, because it would be difficultto make a complete balance of compounds (Fe, Pb, F, etc.) necessary for microbialgrowth).

The principal transformation reactions of the mass in a bioprocess are as follows:

– growth of micro-organisms and biosynthesis (related to secondary metabolism)

S1 + S2 + · · ·+ Sp −→ X + P1 + · · ·+ Pkwhen the growth is aerobic, we find in the substrates of the reaction a source of carbon,nitrogen, phosphorus and mineral salts, as well as oxygen. In the products, there isCO2;

– synthesis of a product via primary metabolism

S1 + S2 + · · ·+ Sq −→ P1 + · · ·+ PlIn this case, the manufacture of products is not dependent on the bacterial growth,

but generally depends on enzymes produced by micro-organisms;

– mortality

X −→ Xdwhere, Xd corresponds to a dead biomass (whereas X is the living biomass).

However, this equation can be completed only by adding the reaction rate andstoichiometric coefficients to it. This is why we will prefer to express the reactionscheme in a more complete form:

kAA + kBBϕ−−→ kCC + X

where ϕ is the reaction rate, here corresponding to the rate of biomass formation. Theconsumption yield of A is kA, that of B, is kB , and kC is the production yield of C.The production rate of C is therefore KCϕ and the consumption rates of A and B arerespectively kAϕ and kBϕ.

Thereafter, we will assume that the reaction scheme is described by a set of kbiological or chemical reactions. We will consider n variables (substrates, products,biomasses, etc.).

Dynamic Models of Biochemical Processes: Properties of Models 23

2.3.3. Choice of reactions and variables

The choice of the number of reactions to be considered and components whichintervene in these reactions is very important for modeling. It will be carried out basedon the knowledge that we have on the process and measurements which could havebeen carried out. The reaction scheme, as we will see thereafter, will condition thestructure of the model. It will thus have to be chosen with parsimony, bearing in mindthe objectives of the model and the precision which is expected. The required numberof reactions and the reaction scheme can be determined directly from a set of availableexperimental data [BER 05a, BER 05b].

In addition, in section 2.6 we will present a means of validating the reactionscheme. When we write the mass balance, we make the following assumptions:

– the reaction scheme summarizes the distribution of mass and flows between var-ious reactions intervening in the process;

– yield coefficients are constant.

2.3.4. Example 1

Here, we will consider the example of anaerobic digestion. This wastewater treat-ment process uses anaerobic bacteria to degrade organic matter (S1). It is in fact avery complex process, in which a great number of bacterial populations intervene[MOS 83, DEL 01]. If the objective is to control this ecosystem, we will need a rela-tively simple model. We will also limit ourselves to considering two bacterial popu-lations. Thus, we assume that the dynamics of the system can be summarized in twomain stages:

– acidogenesis stage (at rate r1(·)), during which substrate S1 is degraded by aci-dogenic bacteria (X1) and is transformed into volatile fatty acids (S2) and into CO2:

k1S1r1(·)−−−−→ X1 + k2S2 + k4CO2 (2.1)

– methanogenesis stage (at rate r2(·)), where the volatile fatty acids (VFA) aredegraded into CH4 and CO2 by methanogenic bacteria (X2).

k3S2r2(·)−−−−→ X2 + k5CO2 + k6CH4 (2.2)

The constants k1, k2 and k4 respectively represent stoichiometric coefficients asso-ciated with consumption of substrate S1, production of VFA and CO2 in the acidoge-nesis process. k3, k5 and k6 respectively represent stoichiometric coefficients in theconsumption of VFA and in the production of CO2 and CH4 during the methanogen-esis process.

It should be noted that this reaction scheme has no biological reality insofar asbiomasses X1 and X2 represent a flora of different species. This is the same forsubstrates S1 and S2 which gather a group of heterogenous compounds. There are