Multivariable Control Systems An Engineering Approach

Index......Page 355
Preface......Page 10
Contents......Page 14
1.1 Introduction......Page 20
1.2 Process and Instrumentation......Page 22
1.3 Process Variables......Page 24
1.4 The Process Behaviour......Page 25
1.5 Control Aims......Page 27
1.6 Modes of Operation......Page 28
1.7 The Need for Feedback......Page 29
1.8 Model-free vs. Model-based Control......Page 31
1.9 The Importance of Considering Modelling Errors......Page 32
1.10 Multivariable Systems......Page 33
1.11 Implementation and Structural Issues......Page 34
1.12 Summary of the Chapters......Page 35
2.1 Introduction: Objectives of Modelling......Page 36
2.2 Types of Models......Page 37
2.3 First-principle Models: Components......Page 38
2.4 Internal Representation: State Variables......Page 41
2.5 Linear Models and Linearisation......Page 43
2.6 Input/Output Representations......Page 48
2.7 Systems and Subsystems: Interconnection......Page 54
2.8 Discretised Models......Page 58
2.9 Equivalence of Representations......Page 59
2.10 Disturbance Models......Page 61
2.11 Key Issues in Modelling......Page 65
2.12 Case Study: The Paper Machine Headbox......Page 66
3.1 Introduction......Page 72
3.2 Linear System Time-response......Page 73
3.3 Stability Conditions......Page 75
3.4 Discretisation......Page 76
3.5 Gain......Page 79
3.6 Frequency response......Page 82
3.7 System Internal Structure......Page 84
3.8 Block System Structure (Kalman Form)......Page 95
3.9 Input/Output Properties......Page 102
3.10 Model Reduction......Page 105
3.11 Key Issues in MIMO Systems Analysis......Page 109
3.12 Case Study: Simple Distillation Column......Page 110
4.1 The Control Design Problem......Page 117
4.2 Control Goals......Page 118
4.3 Variables Selection......Page 120
4.4 Control Structures......Page 124
4.5 Feedback Control......Page 125
4.6 Feedforward Control......Page 132
4.7 Two Degree of Freedom Controller......Page 137
4.8 Hierarchical Control......Page 138
4.9 Key Issues in Control Design......Page 139
4.10 Case Study: Ceramic Kiln......Page 140
5.1 Introduction......Page 143
5.2 Multi-loop Control, Pairing Selection......Page 145
5.3 Decoupling......Page 154
5.4 Enhancing SISO Loops with MIMO Techniques: Cascade Control......Page 161
5.5 Other Possibilities......Page 165
5.6 Sequential–Hierarchical Design and Tuning......Page 169
5.7 Key Conclusions......Page 172
5.8 Case Studies......Page 173
6.1 State Feedback......Page 183
6.2 Output Feedback......Page 189
6.3 Rejection of Deterministic Unmeasurable Disturbances......Page 196
6.5 Case Study: Magnetic Suspension......Page 200
7 Optimisation-based Control......Page 207
7.1 Optimal State Feedback......Page 208
7.2 Optimal Output Feedback......Page 214
7.3 Predictive Control......Page 220
7.4 A Generalised Optimal Disturbance-rejection Problem......Page 226
7.6 Case Study: Distillation Column......Page 231
8.1 The Downside of Model-based Control......Page 237
8.2 Uncertainty and Feedback......Page 239
8.3 Limitations in Achievable Performance due to Uncertainty......Page 242
8.4 Trade-o.s and Design Guidelines......Page 245
8.5 Robustness Analysis Methodologies......Page 251
8.6 Controller Synthesis......Page 258
8.8 Case Studies......Page 262
9.1 Control Implementation: Centralised vs. Decentralised......Page 267
9.2 Implementation Technologies......Page 269
9.3 Bumpless Transfer and Anti-windup......Page 275
9.4 Non-conventional Sampling......Page 278
9.5 Coping with Non-linearity......Page 281
9.6 Reliability and Fault Detection......Page 287
9.7 Supervision, Integrated Automation, Plant-wide Control......Page 290
A.1 Signals......Page 293
A.2 Continuous Systems......Page 294
A.3 Discrete Systems......Page 297
A.4 Experimental Modelling......Page 299
A.5 Tables of Transforms......Page 302
B.1 Column, Row and Null Spaces......Page 303
B.2 Matrix Inversion......Page 304
B.3 Eigenvalues and Eigenvectors......Page 305
B.4 Singular Values and Matrix Gains......Page 307
B.5 Matrix Exponential......Page 311
B.6 Polynomial Fraction Matrices......Page 312
C.2 Function Spaces......Page 315
C.3 Signals and Systems Norms......Page 317
C.4 BIBO Stability and the Small-gain Theorem......Page 318
D.1 Static Optimisation......Page 321
D.2 Discrete Linear Quadratic Regulator......Page 323
E.1 Random Variables......Page 329
E.2 Multi-dimensional Random Variables......Page 331
E.3 Linear Predictors (Regression)......Page 334
E.4 Linear Systems......Page 336
F.1 Small-gain Stability Analysis......Page 341
F.2 Structured Uncertainty......Page 343
F.3 Additional Design Techniques......Page 346
References......Page 349