On-line Estimation and Adaptive Control of Bioreactors (eBook)

Front Cover 1
On-line Estimation and Adaptive Control of Bioreactors 4
Copyright Page 5
Table of Contents 12
Dedication 6
PREFACE 8
CHAPTER 1. DYNAMICAL MODELS OF BIOREACTORS 16
1.0. Introduction 16
1.1. The Basic Dynamics of Microbial Growth in Stirred Tank Reactors 18
1.2. Extensions to the Basic Dynamics 22
1.3. Models of the Specific Growth Rate 25
1.4. The Reaction Scheme of a Biotechnological Process 33
1.5 General Dynamical Model of Bioreactors 44
1.6. Examples of State Space Models 55
1.7. A Basic Structural Property of the General Dynamical Model 58
1.8. Reduction of the General Dynamical Model 61
1.9. Stability Analysis 67
1.10. Extending the General Dynamical Model 86
1.11. References and Bibliography 92
CHAPTER 2. KINETIC MODELLING, ESTIMATION AND CONTROL IN BIOREACTORS : AN OVERVIEW 98
2.0. Introduction 98
2.1. Difficulties in Modelling the Reaction Kinetics 99
2.2. Minimal Modelling of Reaction Kinetics 104
2.3. Software Sensors for Bioreactors 106
2.4. Adaptive Control of Bioreactors 109
2.5. Conclusions and Perspectives 111
2.6. References and Bibliography 111
CHAPTER 3. STATE AND PARAMETER ESTIMATION WITH KNOWN YIELD COEFFICIENTS 116
3.0. Introduction 116
3.1. On State Observation in Bioreactors 118
3.2. Extended Luenberger and Kalman Observers 124
3.3. Asymptotic Observers for State Estimation when the Reaction Rates are Unknown 131
3.4. On-line Estimation of Reaction Rates 161
3.5. References and Bibliography 210
CHAPTER 4. STATE AND PARAMETER ESTIMATION WITH UNKNOWN YIELD COEFFICIENTS 216
4.0. Introduction 216
4.1. On-line Estimation of the Specific Reaction Rates 217
4.2. Joint Estimation of Yield Coefficients and Specific Reaction Rates 231
4.3. Adaptive Observers 246
4.4. Estimation of Yield Coefficients 249
4.5. Other Parameter Estimation Issues in Bioreactors 259
4.6. References and Bibliography 263
CHAPTER 5. ADAPTIVE CONTROL OF BIOREACTORS 266
5.0. Introduction 266
5.1. Principle of Linearizing Control and Remarks on Closed Loop Stability 272
5.2. Singular Perturbation Design of Linearizing Controllers 281
5.3. Adaptive Linearizing Control (Known Yield Coefficients) 302
5.4. A General Solution to the Linearizing Control Problem for a Class of CST Bioreactors 311
5.5. Adaptive Linearizing Control (Unknown Yield Coefficients) 316
5.6. Practical Aspects of Implementation 320
5.7. Case Study : Adaptive Linearizing Control of Fed-Batch Reactors 326
5.8. Case Study : Adaptive Control of the Gaseous Production Rate of a Synthesis Product 338
5.9. References and Bibliography 347
APPENDIX 1: MODELS OF THE SPECIFIC GROWTH RATE 354
1. Dependence on the Substrate Concentration : µ(S) 354
2. Dependence on the Biomass Concentration : µ(.) 357
3. Dependence on the Substrate Concentration S(t) and on the Biomass Concentration X(t) : µ(S,.) 358
4. Dependence on the Product Concentration P(t) : µ(.) 359
5. Dependence on the Substrate Concentration S(t) and the Product Concentration P(t) : µ(S,.) 360
6. Dependence on the Substrate Concentration S(t) and the Dissolved Oxygen Concentration C(t) : µ(S,C) 362
7. Dependence on the Substrate Concentration S(t), the Dissolved Oxygen Concentration C(t) and the Product Concentration P(t) : µ(S,C,.) 362
8. Dependence on the Substrate Concentration S(t) and the Inhibitory Metabolite Concentration l(t) :µ(S,.) 363
9. Dependence on the pH : µ (pH) 363
10. Dependence on the pH and the Temperature : µ(.., .) 363
11. Dependence on the pH and the Substrate Concentration S(t) : µ(..,S) 364
12. Dependence on the Temperature . : µ(.) 365
13. Dependence on the Temperature . and the Biomass Concentration X(t) : µ(., X) 366
14. Dependence on the Light Intensity l(t) and the Biomass Concentration X(t) : µ(., X) 366
References 367
APPENDIX 2: ELEMENTS OF STABILITY THEORY 372
A2.1. Nonlinear Systems 372
A2.2. Linear Time-Varying Systems 375
APPENDIX 3: PERSISTENCE OF EXCITATION. CONVERGENCE OF ADAPTIVE ESTIMATORS 382
NOMENCLATURE 386
INDEX 392