Table Of ContentOptimal State Estimation for Process Monitoring,
Fault Diagnosis and Control
Optimal State Estimation for
Process Monitoring, Fault
Diagnosis and Control
Ch. Venkateswarlu
Chief Scientist (Retd.), Indian Institute of Chemical Technology (CSIR-IICT), Hyderabad, India
Rama Rao Karri
Petroleum and Chemical Engineering, Faculty of Engineering, Universiti Teknologi Brunei, Gadong,
Brunei Darussalam
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Contents
Abouttheauthors xiii 2.6.3 Stochasticfilteringapproachfor
Preface xv stateestimation 19
2.7 Summary 20
References 20
Part I
Basic details and state estimation 3. Linear filtering and observation
algorithms 1 techniques 21
3.1 Introduction 21
1. Optimal state estimation and its
3.2 Representationofasystemand
importance in process systems associatedvariables 21
engineering 3 3.2.1 Definitionofsystemstate 21
3.2.2 Systemvariables 21
1.1 Introduction 3
3.2.3 Statespacerepresentationof
1.2 Significanceofstateestimation 3
linearsystems 22
1.3 Roleofstateestimationinprocesssystems
3.2.4 Outputequations 22
engineering 4
3.2.5 Discretetimerepresentationof
1.4 Outlineofthisbook 4
linearsystems 23
1.5 Summary 4
3.3 Conceptsofobservabilityand
controllability 24
2. Introduction to stochastic processes
3.3.1 Observabilityofacontinuoussystem 24
and state estimation filtering 5
3.3.2 Observabilityofadiscretesystem 25
2.1 Introduction 5 3.3.3 Controllabilityofacontinuoussystem 25
2.2 Probabilityandstochasticvariables 5 3.3.4 Controllabilityofadiscretesystem 25
2.2.1 Probabilitytheorems 6 3.4 Recursiveweightedleastsquares
2.2.2 Conditionalprobability 7 estimator 27
2.3 Probabilitydistributionsanddistribution 3.4.1 Estimationprocedure 30
functions 7 3.5 Luenbergerobserverforstateestimation 31
2.3.1 Discreterandomvariablesand 3.5.1 Discreteformofobserverdesign 32
discreteprobabilitydistributions 8 3.5.2 Discreteobserverbasedstate
2.3.2 Continuousrandomvariablesand feedbackcontrol 32
continuousprobabilitydistributions 10 3.5.3 Continuousformofobserver 37
2.4 WhiteGaussiannoiseandcolorednoise 13 3.5.4 Continuousobserverbasedstate
2.5 Stochastic/randomprocesses 14 feedbackcontrol 38
2.5.1 Stochasticmodelscheme 15 3.6 ReducedorderLuenbergerobserver
2.5.2 Stochasticrepresentationofreal forstateestimation 41
processes 16 3.7 Kalmanfilterforstateestimation 44
2.5.3 Stochasticrepresentationofgeneral 3.7.1 DiscreteKalmanfilter 44
dynamicmodels 18 3.7.2 Filtercovariancematrices 46
2.6 Filtering,estimation,andprediction 3.7.3 ContinuousKalmanfilter 52
problem 18 3.8 Stateestimationapplicationsoflinear
2.6.1 Filtering,prediction,andsmoothing 18 filteringandobservationtechniques 56
2.6.2 Bayesfilteringapproachforstate 3.9 Summary 56
estimation 19 References 56
v
vi Contents
4. Mechanistic model-based nonlinear 5.3 Projectiontolatentstructures 94
filtering and observation techniques 5.3.1 Theregressionproblem 94
for optimal state/parameter 5.3.2 Scalingandcenteringthedata 94
estimation 59 5.3.3 PLSmodel 94
5.4 Artificialneuralnetworks 95
4.1 Introduction 59 5.4.1 ANNstructureanditscomponents 95
4.2 Generalnonlinearsystemandsystem 5.4.2 Neuronprocessingfunctions 97
models 59 5.4.3 Learningparadigms 97
4.2.1 Mechanistic/firstprinciplemodels 59 5.4.4 Learningalgorithmsandtraining
4.2.2 Generalrepresentationofdynamic procedure 97
models 61 5.4.5 Informationprocessing 100
4.3 Observabilityofnonlinearsystems 61 5.4.6 ANNarchitectures 100
4.3.1 Localobservability 62 5.5 Radialbasisfunctionnetworks 102
4.3.2 Globalobservability 64 5.5.1 StructureofRBFN 103
4.4 ExtendedKalmanfilter 65 5.5.2 AutomaticconfigurationofRBFN 105
4.4.1 Processrepresentationforstate 5.5.3 Implementationprocedure 106
estimation 66 5.6 Nonlineariterativepartialleastsquares 107
4.4.2 Processrepresentationforstateand 5.6.1 NIPALSalgorithmforPLS 107
parameterestimation 66 5.6.2 NonlinearPLSwithinPLS
4.4.3 ExtendedKalmanfilterfor framework 108
continuoustimenonlinearsystems 66 5.6.3 NIPALSalgorithmforRBFN 108
4.4.4 ExtendedKalmanfilterfordiscrete 5.7 Stateestimationapplicationsof
timenonlinearsystems 68 data-drivenmodelingtechniques 110
4.4.5 Emphasisoncovariancematricesof 5.8 Summary 110
extendedKalmanfilter 68 References 110
4.5 SteadystateextendedKalmanfilter 73
4.6 Two-levelextendedKalmanfilter 74 6. Optimal sensor configuration
4.6.1 Stateestimationfilter 74 methods for state estimation 113
4.6.2 Parameteridentificationfilter 75
4.7 AdaptivefadingextendedKalmanfilter 75 6.1 Introduction 113
4.8 UnscentedKalmanfilter 76 6.2 Briefreviewonsensorconfiguration
4.9 SquarerootunscentedKalmanfilter 78 methods 113
4.10 EnsembleKalmanfilter 80 6.3 Optimalsensorconfiguration:classical
4.11 Particlefilter 81 methods 114
4.12 ReducedorderLuenbergerobserver 84 6.3.1 Sensitivityindex 114
4.12.1 Determinationofobserver 6.3.2 Singularvaluedecomposition 114
coefficientmatrices 84 6.3.3 Principalcomponentanalysis 115
4.13 ReducedorderextendedLuenberger 6.4 Optimalsensorconfiguration:
observer 85 gramian-basedmethodsforlinear
4.14 Nonlinearobserver 86 systems 116
4.15 Stateestimationapplicationsofnonlinear 6.4.1 Observabilitygramianforlinear
filteringandobservationtechniques 88 systems 116
4.16 Summary 88 6.4.2 Observabilitygramian-basedsensor
References 88 selectionprocedure 117
6.5 Optimalsensorconfigurationfor
5. Data-driven modeling techniques for nonlinearsystems 117
state estimation 91 6.5.1 Empiricalobservabilitygramianfor
nonlinearsystems 118
5.1 Introduction 91 6.5.2 Empiricalobservabilitygramian
5.2 Principalcomponentanalysis 91 metrics 119
5.2.1 Basicprinciples 91 6.5.3 Empiricalobservabilitygramian-based
5.2.2 GeometricinterpretationofPCA 92 sensorselectionprocedure 119
5.2.3 Eigenstructurefordatamatrix 92 6.6 Summary 119
5.2.4 PCAmodelestablishment 93 References 121
Contents vii
Part II
8.5 Sensorconfigurationforstateestimation 145
Optimal state estimation for 8.5.1 Sensorconfigurationusing
sensitivityindex 146
process monitoring 123
8.5.2 Sensorconfigurationusing
singularvaluedecomposition 147
7 Application of mechanistic
8.5.3 Sensorconfigurationusing
model-based nonlinear filtering and principalcomponentanalysis 149
observation techniques for optimal 8.6 Performancecriteria 152
state estimation in multicomponent 8.6.1 Meanintegralsquarederror 152
batch distillation 125 8.7 ExtendedKalmanfilterforcompositions
estimation 152
7.1 Introduction 125
8.7.1 DesignofextendedKalmanfilter
7.2 Batchdistillationprocessandits
estimator 154
dynamicmodel 125
8.7.2 ExtendedKalmanfilter
7.3 Simplifieddynamicmodelofbatch
implementationresults 155
distillation 128
8.8 Summary 160
7.3.1 Equilibriumrelations 128
References 161
7.4 Theapplicationsystem 128
7.5 Measurementsconfigurationforstate
9 Application of mechanistic
estimation 129
model-based nonlinear filtering and
7.6 Performancecriteria 132
observation techniques for optimal
7.7 ExtendedKalmanfilterforcompositions
state estimation in complex
estimation 132
nonlinear dynamical systems 163
7.7.1 DesignofEKFestimator 132
7.7.2 EKFimplementationresults 134
9.1 Introduction 163
7.8 SteadystateKalmanfilterfor
9.2 NonlineardynamicalCSTR 164
compositionsestimation 136
9.2.1 Mathematicalmodel 164
7.8.1 DesignofSSKFestimator 136
9.2.2 Stabilityanalysis 165
7.8.2 SSKFimplementationresults 136
9.2.3 Bifurcationanalysis 166
7.9 AdaptivefadingextendedKalman
9.3 Optimalstateestimationinnonlinear
filterforcompositionsestimation 137
dynamicalCSTR 166
7.9.1 DesignofAFEKFestimator 137
9.3.1 Stateestimatordesign 166
7.9.2 AFEKFimplementationresults 137
9.3.2 Stateestimationresults 170
7.10 Comparativeperformanceof
9.4 Nonlineardynamical
compositionestimators 137
homopolymerizationreactor 170
7.11 Summary 139
9.4.1 Mathematicalmodel 171
References 140
9.4.2 Stabilityanalysis 173
9.4.3 Steadystatesolution 174
8 Application of mechanistic
9.4.4 Bifurcationanalysis 177
model-based nonlinear filtering and 9.5 Optimalstateestimationinnonlinear
observation techniques for optimal dynamicalhomopolymerizationreactor 177
state estimation in multicomponent 9.5.1 Stateestimatordesign 179
reactive batch distillation with 9.5.2 Stateestimationresults 181
optimal sensor configuration 141 9.6 Summary 181
References 183
8.1 Introduction 141
8.2 Reactivebatchdistillationprocessandits
10 Application of mechanistic
dynamicmodel 142
model-based nonlinear filtering and
8.2.1 Equilibriumrelations 144
observation techniques for optimal
8.2.2 Enthalpyrelations 144
state estimation of a kraft pulping
8.3 Simplifieddynamicmodelofreactive
digester 185
batchdistillation 144
8.4 Theapplicationsystem 145
10.1 Introduction 185
viii Contents
10.2 Experimentalsystemanddynamic 12.2.1 Process 218
modeling 186 12.2.2 Mathematicalmodel 218
10.2.1 Batchpulpingprocess 186 12.3 Methodofsolution 219
10.2.2 Developmentofadynamic 12.4 Resultsofnumericalsolution 221
modelforkraftpulpingdigester 188 12.5 Optimalsensorconfigurationin
10.3 Optimalstateestimationofkraft acatalytictubularreactor 222
pulpingdigester 191 12.5.1 Significanceofsensor
10.3.1 DesignofEKF 191 configurationinatubular
10.3.2 Designofnonlinearobserver 193 reactor 223
10.4 Stateestimationresults 193 12.5.2 Empiricalobservability
10.5 Summary 196 Grammians 223
References 198 12.5.3 Optimalsensorconfiguration
usingempiricalobservability
11 Application of mechanistic Grammians 223
model-based nonlinear filtering and 12.5.4 Sensorconfigurationresults 224
observation techniques for optimal 12.6 Optimalstateestimationusing
state estimation of a continuous unscentedKalmanfilter 226
12.6.1 Stateestimatordesign 227
reactive distillation column with
12.6.2 Stateestimationresults 227
optimal sensor configuration 201
12.7 Summary 229
11.1 Introduction 201 References 229
11.2 Theprocessanditsmathematical
model 202
11.2.1 Totalmassbalance 202
11.2.2 Componentbalance 202
13 Applications of data-driven
11.2.3 Energybalance 203
model-based methods for process
11.2.4 Trayhydraulics 203
state estimation 231
11.3 Optimalsensorconfigurationusing
empiricalobservabilitygrammians 204 13.1 Introduction 231
11.3.1 Significanceofoptimalsensor 13.2 Projectiontolatentstructures
configurationinareactive model-basedcompositionsestimator
distillationcolumn 204 formulticomponentbatch
11.3.2 Measurementspecificempirical distillation 231
observabilitygrammians 204 13.2.1 Stateestimatordevelopment 232
11.3.3 Optimalsensorconfiguration 13.2.2 Stateestimationresults 234
usingempiricalobservability 13.3 Artificialneuralnetworkmodel-based
grammians 206 compositionsestimatorfor
11.4 Stateestimatordesign 207 multicomponentbatchdistillation 236
11.5 Estimatorperformancemeasurefor 13.3.1 Stateestimatordevelopment 236
optimalityofsensorconfiguration 210 13.3.2 Stateestimationresults 238
11.6 Analysisofresults 211 13.4 Radialbasisfunctionnetwork
11.7 Summary 214 model-basedcompositions
References 215 estimatorformulticomponentbatch
distillation 238
12 Application of mechanistic 13.4.1 Stateestimatordevelopment 238
model-based nonlinear filtering and 13.4.2 Stateestimationresults 239
observation techniques for optimal 13.5 NIPALS(cid:1)RBFNmodel-based
state estimation of a catalytic tubular compositionsestimatorfor
multicomponentbatchdistillation 243
reactor with optimal sensor
13.5.1 Stateestimatordevelopment 243
configuration 217
13.5.2 Stateestimationresults 243
12.1 Introduction 217 13.6 Summary 246
12.2 Theprocessanditsmathematicalmodel 218 References 246
Contents ix
Part III
15.3.1 Mathematicalmodel 272
Application of data driven 15.3.2 Faultcasesinbatchbeer
fermentation 273
model-based methods for
15.4 MethodofextendedKalmanfilter 273
process state estimation 247
15.4.1 Designstrategy 273
15.4.2 Analysisofresults 274
14 Optimal state and parameter 15.5 Methodofreduced-orderextended
estimation for fault detection and Luenbergerobserverandextended
diagnosis in continuous stirred Kalmanfilter 276
tank reactor 249 15.5.1 Designstrategy 276
15.5.2 Analysisofresults 279
14.1 Introduction 249 15.6 Methodoftwo-levelextended
14.2 Generalstructureofmodel-based Kalmanfilter 279
faultdetectionanddiagnosis 250 15.6.1 Designstrategy 279
14.3 Generalprocessdescriptionforfault 15.6.2 Analysisofresults 282
detectionanddiagnosis 251 15.7 Methodofdiscreteversionofextended
14.4 NonlinearCSTR,itsmathematical Kalmanfilterandsequentialleast
modelandfaultcasesconsidered 252 squares 284
14.5 MethodofextendedKalmanfilter 253 15.7.1 Designstrategy 284
14.5.1 Designstrategy 253 15.7.2 Analysisofresults 284
14.5.2 Analysisofresults 255 15.8 Methodofdiscreteversionof
14.6 Methodofreducedorderextended extendedKalmanfilterand
Luenbergerobserverandextended simultaneousleastsquares 285
Kalmanfilter 257 15.8.1 Designstrategy 286
14.6.1 Designstrategy 257 15.8.2 Analysisofresults 287
14.6.2 Analysisofresults 260 15.9 Summary 287
14.7 Methodoftwo-levelextendedKalman References 287
filter 261
14.7.1 Designstrategy 261 16 Optimal state and parameter
14.7.2 Analysisofresults 263
estimation for fault detection and
14.8 Methodofadiscreteversionof
diagnosis of a high-dimensional
extendedKalmanfilterand
fluid catalytic cracking unit 289
sequentialleastsquares 264
14.8.1 Designstrategy 264 16.1 Introduction 289
14.8.2 Analysisofresults 266 16.2 Processrepresentation 290
14.9 Methodofdiscreteversionof 16.3 Fluidcatalyticcrackingunit 290
extendedKalmanfilterand 16.4 Mathematicalmodeloffluidcatalytic
simultaneousleastsquares 267 crackingunit 291
14.9.1 Designstrategy 267 16.4.1 Feedandpreheatsystems 291
14.9.2 Analysisofresults 269 16.4.2 Reactor 292
14.10 Summary 269 16.4.3 Regenerator 296
References 270 16.4.4 Airblowers 300
16.4.5 Catalystcirculation 302
15 Optimal state and parameter 16.4.6 Nomenclatureandnumerical
estimation for fault detection and data 303
16.5 Fluidcatalyticcrackingunitsystem
diagnosis of a nonlinear batch beer
variables 305
fermentation process 271
16.5.1 Statevariables 305
15.1 Introduction 271 16.5.2 Algebraicvariables 305
15.2 Generalstructureandgeneralprocess 16.5.3 Measuredvariables 305
descriptionformodel-basedfault 16.6 Faultcasesconsideredinfluid
detectionanddiagnosis 271 catalyticcrackingunit 306
15.3 Batchbeerfermentationprocess,its 16.7 Designofdiscreteversionofextended
mathematicalmodelandfaultcases 272 Kalmanfilter 306
x Contents
16.8 DesignofunscentedKalmanfilter 307 18.2.5 Analysisofresults 335
16.9 Analysisofresults 308 18.3 Optimalstateestimationand
16.10 Summary 310 estimator-basedcontrolof
References 311 homopolymerizationreactor 338
18.3.1 Homopolymerizationreactor
anditsmathematicalmodel 338
18.3.2 Estimatordesignandestimation
Part IV
results 338
Optimal state estimation for 18.3.3 Controllerdesign 338
18.3.4 Analysisofresults 339
process control 313
18.4 Summary 342
References 342
17 Optimal state estimator-based
inferential control of continuous
reactive distillation column 315 19 Optimal state estimator based
control of an exothermic batch
17.1 Introduction 315
chemical reactor 343
17.2 Processandthedynamicmodel 315
17.2.1 Processdescription 316 19.1 Introduction 343
17.2.2 Thedynamicmodelofthe 19.2 Experimentalsystemandits
process 317 mathematicalmodel 343
17.3 Theprocesscharacteristics 317
19.2.1 Experimentalbatchreactor 344
17.3.1 Nonlinearityanalysis 317
19.2.2 Analysisofreaction
17.3.2 Interactionandstabilityaspects 317
components 345
17.4 Classicalproportional-integral/
19.2.3 Esterificationreactormodel 345
proportional-integral-derivative 19.3 State/parameterestimation 347
controllersfordistillationcolumn 319 19.4 Controlalgorithms 348
17.5 Briefdescriptionofgeneticalgorithms 319
19.4.1 ExtendedKalmanfiltercontrol 348
17.6 Designofgeneticallytuned
19.4.2 Genericmodelcontrol 349
proportional-integralcontrollers 320
19.4.3 Modelpredictivecontrol 349
17.6.1 Controllertuning 320 19.5 Designofestimatorbasedcontrollers
17.6.2 Formulationoftheobjective fortheesterificationreactor 350
function 320 19.5.1 ExtendedKalmanfiltercontrol 350
17.6.3 Desiredresponsespecifications 19.5.2 Genericmodelcontrol 350
forgenetic-algorithmtuning 321 19.5.3 Modelpredictivecontrol 351
17.7 Designofcompositionestimator 322
19.6 Analysisofresults 352
17.8 Analysisofresults 325
19.7 Summary 356
17.9 Summary 330
References 357
References 330
18 Optimal state estimation for
nonlinear control of complex Part V
dynamic systems 333
Optimal state estimation for
18.1 Introduction 333 online optimization 359
18.2 Optimalstateestimationand
estimator-basedcontrolofchaotic 20 Optimal state and parameter
chemicalreactor 333 estimation for online optimization
18.2.1 Chaoticchemicalreactorandits
of an uncertain biochemical
mathematicalmodel 333
reactor 361
18.2.2 Estimatordesignandestimation
results 334 20.1 Introduction 361
18.2.3 Controlleralgorithm 334 20.2 Theprocessanditsmathematical
18.2.4 Controllerdesign 334 model 362
