Almost all process systems are nonlinear in nature. Nonlinear control is traditionally an area of interest in process systems engineering which is of great practical importance. These facts notwithstanding, many process engineers have difficulty with the paradigms and results of modern nonlinear control theory because they lack the mathematical background usually associated with such methods or because of the their computational difficulty and small-scale applicability in the general case. Analysis and Control of Nonlinear Process Systems overcomes these barriers. Features: · The necessary mathematical preliminaries for readers from a process engineering background. · Constant reference to the widely-known finite-dimensional linear time-invariant continuous case as a basis for extension to the nonlinear situation. · The most promising theories and analytical methods for nonlinear process control laid out clearly and straightforwardly with exercises to reaffirm the techniques as they are taught. · Emphasis on the importance of process knowledge and first-principles-based models in obtaining feasible and effective solutions in particular circumstances from general cases. · Illustration of applications with simple examples and case studies. Analysis and Control of Nonlinear Process Systems will interest graduate process engineers wishing to study advanced control methods either with a view to further research or application in industry as well as to academics seeking to move process control courses into more complicated but up-to-date territory. It will also be a great assistance to those in their senior undergraduate years who will form the next generation of industrial process engineers and need unfussy access to the most modern nonlinear control ideas.
Author(s): Katalin M. Hangos, József Bokor, Gábor Szederkényi
Series: Advanced Textbooks in Control and Signal Processing
Edition: 1
Publisher: Springer
Year: 2004
Language: English
Pages: 335
Contents......Page 12
List of Definitions......Page 20
List of Examples......Page 24
1.1 A Brief Overview of Nonlinear Process Control......Page 28
1.2 Aims and Objectives......Page 30
1.3 The Road Map of the Book......Page 31
2.1.1 What is a Signal?......Page 34
2.1.2 Classification of Signals......Page 36
2.1.3 Signals of Special Importance......Page 37
2.1.4 Operations on Signals......Page 39
2.1.5 L[sub(q)] Signal Spaces and Signal Norms......Page 42
2.2 Systems......Page 44
2.2.1 Classification of Systems: Important System Properties......Page 45
2.4 Questions and Exercises......Page 47
3. State-space Models......Page 50
3.1 Basic Notions of State-space Representation......Page 51
3.2.1 The General Form of State-space Models......Page 52
3.2.2 Linear Transformation of States......Page 53
3.2.3 Special Realization Forms of LTI Systems......Page 54
3.3 Linear Time-varying (LTV) Parameter Systems......Page 55
3.4 Linear Parameter-varying (LPV) Systems......Page 56
3.5 Nonlinear Systems......Page 58
3.5.2 Nonlinear Transformation of States......Page 59
3.5.3 Bilinear State-space Models......Page 60
3.6 Summary......Page 62
3.7 Questions and Exercises......Page 63
4. Dynamic Process Models......Page 66
4.1.1 General Modeling Assumptions......Page 67
4.1.2 The Principal Mechanisms in Process Systems......Page 68
4.1.4 The Model Construction Procedure......Page 69
4.1.5 Conserved Extensive and Intensive Potential Variables......Page 70
4.1.6 Conservation Balances......Page 71
4.1.7 Constitutive Equations......Page 72
4.2.1 System Variables......Page 73
4.2.2 State Equations in Input-affine Form......Page 74
4.2.3 Decomposition of the State Equations Driven by Mechanisms......Page 75
4.2.4 Balance Volumes Coupled by Convection......Page 76
4.3.1 Bilinear Process Systems......Page 78
4.3.2 Process Models in DAE Form......Page 79
4.4.1 Heat Exchanger Cells......Page 82
4.4.2 LTI State-space Model of a Heat Exchanger Cell......Page 84
4.4.4 Nonlinear State-space Model of a Heat Exchanger Cell......Page 85
4.5.1 A Simple Unstable CSTR Example......Page 87
4.5.2 A Simple Fed-batch Fermenter......Page 88
4.5.3 Simple Continuous Fermenter Models......Page 90
4.6.1 System Description......Page 92
4.6.2 Modeling Assumptions......Page 93
4.6.3 Conservation Balances......Page 94
4.6.4 Conservation Balances in Extensive Variable Form......Page 95
4.6.6 Constitutive Equations......Page 96
4.6.7 Operation Domain and System Variables......Page 97
4.8 Questions and Application Exercises......Page 98
5.1 Input–output Models of LTI Systems......Page 100
5.1.1 Time Domain Description......Page 101
5.1.2 Operator Domain Description......Page 102
5.1.3 Input–output and State-space Representations of LTI Systems......Page 103
5.2.1 Fliess's Functional Expansion......Page 105
5.2.2 Volterra Series Representation......Page 107
5.2.3 Higher-order Nonlinear Differential Equations......Page 108
5.3.1 Realization of LTI Systems......Page 109
5.3.2 Realization Theory for Nonlinear Systems......Page 112
5.3.3 Realization of Bilinear Systems......Page 115
5.4 Hankel Matrix of a 2-input–2-output Bilinear Heat Exchanger Cell model......Page 116
5.5 The Zero Dynamics......Page 117
5.5.1 The Zero Dynamics of SISO Nonlinear Systems......Page 118
5.5.2 Example: The Zero Dynamics of Continuous Fermentation Processes......Page 119
5.8 Questions and Application Exercises......Page 122
6.1 Controllability and Observability of LTI Systems......Page 124
6.1.1 State Observability......Page 125
6.1.2 State Controllability......Page 126
6.1.3 Conditions for Joint Controllability and Observability......Page 127
6.1.4 General Decomposition Theorem......Page 130
6.2.1 The Controllability Distribution, Controllable Nonlinear Systems......Page 131
6.2.2 The Observability Co-distribution, Observable Nonlinear Systems......Page 137
6.3 Controllability and Observability of Nonlinear Process Systems......Page 141
6.4 Heat Exchanger Examples......Page 142
6.4.2 Local Controllability and Observability of a Nonlinear Heat Exchanger Cell......Page 143
6.4.3 Local Controllability of a Nonlinear 2-cell Heat Exchanger......Page 145
6.5.2 Nonlinear Controllability Analysis Using Controllability Distributions......Page 147
6.6.2 Nonlinear State-space Model......Page 149
6.6.3 Reachability Analysis......Page 150
6.6.4 Calculation of the Coordinate Transformation......Page 152
6.6.5 Generalizations......Page 155
6.6.6 Engineering Interpretation......Page 158
6.6.7 Comments on Observability......Page 159
6.7 Further Reading......Page 161
6.9 Questions and Application Exercises......Page 162
7. Stability and The Lyapunov Method......Page 164
7.1.2 BIBO Stability Conditions for LTI Systems......Page 165
7.1.3 L[sub(2)]-gain of Linear and Nonlinear Systems......Page 166
7.1.4 The Small-gain Theorem......Page 167
7.1.5 Asymptotic or Internal Stability of Nonlinear Systems......Page 169
7.1.6 Asymptotic Stability of LTI Systems......Page 170
7.1.7 Relationship Between Asymptotic and BIBO Stability......Page 171
7.2 Local Stability of Nonlinear Systems......Page 172
7.2.1 Local Linearization of Nonlinear State-space Models......Page 173
7.2.2 Relationship Between Local and Global Stability of Nonlinear Systems......Page 175
7.2.3 Dependence of Local Stability on System Parameters: Bifurcation Analysis......Page 177
7.3.1 Lyapunov Function and Lyapunov Criterion......Page 179
7.3.2 Lyapunov Criterion for LTI Systems......Page 181
7.3.3 Lyapunov Criteria for LPV System Models......Page 182
7.4 Stability of Process Systems......Page 183
7.4.1 Structural Stability......Page 184
7.4.2 Conservation Matrices......Page 185
7.5.1 Stability Analysis of the Free Mass Convection Network......Page 186
7.5.2 Lyapunov Function of the Free Mass Convection Network......Page 187
7.5.3 Structural Stability Analysis of Heat Exchanger Networks......Page 188
7.5.4 Structural Stability Analysis of a Binary Distillation Column with Constant Molar Flow and Vapor–liquid Equilibrium......Page 189
7.5.5 Structural Stability of a Binary Distillation Column with Constant Molar Flows in the Non-equilibrium Case......Page 191
7.6.1 Local Stability Analysis......Page 192
7.6.3 Nonlinear Stability Analysis......Page 193
7.6.4 Stability Analysis based on an LPV Model......Page 194
7.8 Summary......Page 196
7.9 Questions and Application Exercises......Page 197
8. Passivity and the Hamiltonian View......Page 200
8.1 The Storage Function and its Properties......Page 201
8.2 Passivity Conditions and Asymptotic Stability......Page 202
8.3.1 Storage Function and the Hamiltonian View......Page 203
8.3.2 The Hamiltonian Formulation in Classical Mechanics......Page 204
8.4.1 Affine Hamiltonian Input–output Systems......Page 208
8.4.2 Simple Hamiltonian Systems......Page 209
8.5 Passivity Theory for Process Systems: a Lagrangian Description......Page 211
8.5.1 System Variables......Page 212
8.5.2 Thermodynamical Storage Function......Page 213
8.5.3 Transfer Terms......Page 214
8.5.5 Passivity Analysis......Page 216
8.6.1 State, Co-state and Input Variables......Page 217
8.6.2 Input Variables for the Hamiltonian System Model......Page 218
8.6.3 The Hamiltonian Function......Page 219
8.8 Simple Process Examples......Page 221
8.8.1 Storage Function of the Heat Exchanger Cell......Page 222
8.8.2 Hamiltonian Description of the Heat Exchanger Cell......Page 223
8.8.3 Hamiltonian Description of the Free Mass Convection Network......Page 226
8.8.4 Hamiltonian Description of a Simple Unstable CSTR......Page 227
8.10 Summary......Page 229
8.11 Questions and Application Exercises......Page 230
9.1 Control and Feedback......Page 232
9.1.2 Feedback......Page 233
9.1.3 Different Kinds of Feedback......Page 234
9.1.4 Linear Static Full State Feedback Applied to SISO LTI Systems......Page 236
9.2 Pole-placement Controller for SISO LTI Systems......Page 237
9.2.2 Solution for the SISO Case......Page 238
9.3.1 Problem Statement......Page 239
9.3.2 The Solution Method: Calculus of Variations......Page 240
9.3.3 LQR as a Full-state Feedback Controller......Page 242
9.4 Hamiltonian View on Controlled Systems......Page 243
9.5.1 Pole-placement Controller......Page 246
9.5.2 LQ Control......Page 247
9.6 Further Reading......Page 249
9.7 Summary......Page 250
9.8 Questions and Exercises......Page 251
10.1 Relative Degree......Page 254
10.2.1 Nonlinear Coordinates Transformation and State Feedback......Page 257
10.2.2 The State-space Exact Linearization Problem for SISO Systems......Page 259
10.2.3 Simple Examples for Feedback Linearization......Page 262
10.3 Input–output Linearization......Page 265
10.4 Process Systems with Maximal Relative Degree......Page 266
10.5.1 Exact Linearization via State Feedback......Page 269
10.5.2 Input–output Linearization......Page 270
10.6 Output Selection for Feedback Linearization......Page 273
10.9 Questions and Application Exercises......Page 276
11.1 The Passivation Problem and Static Feedback Design......Page 280
11.2 Stabilization Using Control Lyapunov Functions......Page 282
11.3 Control Lyapunov Function of a Continuous Fermenter......Page 284
11.4 Case Study: Direct Passivation of a Gas Turbine......Page 286
11.4.1 Nonlinear State-space Model......Page 287
11.4.2 Controller Design......Page 289
11.4.3 Simulation Results......Page 290
11.5 Further Reading......Page 292
11.7 Questions and Application Exercises......Page 293
12.1 Stabilization of Hamiltonian Systems......Page 296
12.1.1 Asymptotic Stabilization of BIBO-stable Systems......Page 297
12.1.2 Stabilization by Shaping the Potential Energy......Page 298
12.1.3 The Nonlinear PD-controller for Hamiltonian Systems......Page 299
12.2.1 Process Systems as Simple Hamiltonian Systems......Page 300
12.3.1 Hamiltonian Control of the Heat Exchanger Cell......Page 301
12.3.2 Loop-shaping Control of the Free Mass Convection Network......Page 302
12.4 Stabilization of a Simple Unstable CSTR......Page 303
12.4.2 Nonlinear Proportional Feedback Controller......Page 304
12.4.3 Stability Region......Page 305
12.5 Hamiltonian Control of a Simple Continuous Fermenter......Page 306
12.5.1 Hamiltonian Model of the Fermentation Process......Page 307
12.5.4 Controller Tuning and Stability Analysis of the Closedloop System......Page 308
12.6 Further Reading......Page 311
12.8 Questions and Application Exercises......Page 312
A.1.1 Vector Norms......Page 314
A.2 Matrix and Operator Norms......Page 315
A.3.1 Lie-derivative......Page 316
A.3.2 Lie-product......Page 317
A.4.1 Distributions......Page 319
A.4.2 Co-distributions......Page 321
References......Page 326
C......Page 330
F......Page 331
L......Page 332
N......Page 333
S......Page 334
Z......Page 335
