Multivariable Control Systems: An Engineering Approach

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
2.6.1 Polynomial Representation......Page 48
2.6.2 Transfer Matrix......Page 49
2.7 Systems and Subsystems: Interconnection......Page 54
2.7.1 Series, Parallel and Feedback Connection......Page 55
2.7.2 Generalised Interconnection......Page 56
2.8 Discretised Models......Page 58
2.9 Equivalence of Representations......Page 59
2.10.1 Deterministic Signals......Page 61
2.10.2 Randomness in the Signals......Page 62
2.10.3 Discrete Stochastic Processes......Page 63
2.11 Key Issues in Modelling......Page 65
2.12.1 Simplified Models......Page 66
2.12.2 Elaborated Models......Page 69
3.1 Introduction......Page 72
3.2 Linear System Time-response......Page 73
3.3 Stability Conditions......Page 75
3.4 Discretisation......Page 76
3.5.1 Static Gain......Page 79
3.5.3 Directional Gain......Page 80
3.6 Frequency response......Page 82
3.7 System Internal Structure......Page 84
3.7.1 Reachability (State Controllability)......Page 85
3.7.2 Observability......Page 89
3.7.3 Output Reachability......Page 90
3.7.4 Remarks on Reachability and Observability......Page 91
3.7.5 Canonical Forms......Page 92
3.8 Block System Structure (Kalman Form)......Page 95
3.8.1 Minimal Realisation......Page 96
3.8.2 Balanced Realisation......Page 99
3.8.3 Poles and Zeros......Page 100
3.9 Input/Output Properties......Page 103
3.9.1 Input/Output Controllability......Page 104
3.10.1 Time Scale Decomposition......Page 106
3.10.2 Balanced Reduction......Page 108
3.11 Key Issues in MIMO Systems Analysis......Page 110
3.12 Case Study: Simple Distillation Column......Page 111
4.1 The Control Design Problem......Page 118
4.2 Control Goals......Page 119
4.3 Variables Selection......Page 121
4.4 Control Structures......Page 125
4.5 Feedback Control......Page 126
4.5.1 Closed-loop Stability Analysis......Page 127
4.5.2 Interactions......Page 129
4.5.3 Generalised Plant......Page 130
4.5.4 Performance Analysis......Page 132
4.6.1 Manual Control......Page 133
4.6.3 Feedforward Rejection of Measurable Disturbances......Page 135
4.7 Two Degree of Freedom Controller......Page 138
4.8 Hierarchical Control......Page 139
4.9 Key Issues in Control Design......Page 140
4.10 Case Study: Ceramic Kiln......Page 141
5.1 Introduction......Page 144
5.1.1 Plant Decomposition, Grouping of Variables......Page 145
5.2 Multi-loop Control, Pairing Selection......Page 146
5.2.1 The Relative Gain Array Methodology......Page 148
5.2.2 Integrity (Fault Tolerance)......Page 153
5.3 Decoupling......Page 155
5.3.1 Feedforward Decoupling......Page 156
5.3.2 Feedback Decoupling......Page 158
5.3.3 SVD Decoupling......Page 161
5.4 Enhancing SISO Loops with MIMO Techniques: Cascade Control......Page 162
5.4.1 Case I: Extra Measurements......Page 163
5.4.2 Case II: Extra Actuators......Page 164
5.5.1 Indirect and Inferential Control......Page 166
5.5.2 Override, Selectors......Page 168
5.5.3 Split-range Control......Page 169
5.6 Sequential–Hierarchical Design and Tuning......Page 170
5.6.1 Combined Strategies for Complex Plants......Page 172
5.7 Key Conclusions......Page 173
5.8.1 Steam Boiler......Page 174
5.8.2 Mixing Process......Page 181
6.1 State Feedback......Page 184
6.1.1 Stabilisation and Pole-placement......Page 186
6.1.2 State Feedback PI Control......Page 189
6.2 Output Feedback......Page 190
6.2.1 Model-based Recurrent Observer......Page 191
6.2.3 Reduced-order Observer......Page 194
6.2.4 Separation Principle......Page 196
6.3 Rejection of Deterministic Unmeasurable Disturbances......Page 197
6.3.1 Augmented Plants: Process and Disturbance Models......Page 198
6.3.2 Disturbance rejection......Page 199
6.5 Case Study: Magnetic Suspension......Page 201
7 Optimisation-based Control......Page 208
7.1 Optimal State Feedback......Page 209
7.1.1 Linear Regulators......Page 211
7.2 Optimal Output Feedback......Page 215
7.2.1 Kalman Observer......Page 216
7.2.2 Linear Quadratic Gaussian Control......Page 220
7.3 Predictive Control......Page 221
7.3.1 Calculating Predictions......Page 222
7.3.2 Objective Function......Page 224
7.3.3 Constraints......Page 225
7.3.4 Disturbance rejection......Page 226
7.4 A Generalised Optimal Disturbance-rejection Problem......Page 227
7.4.1 Design Guidelines: Frequency Weights......Page 229
7.6 Case Study: Distillation Column......Page 232
8.1 The Downside of Model-based Control......Page 238
8.1.1 Sources of Uncertainty in Control......Page 239
8.2 Uncertainty and Feedback......Page 240
8.2.1 Model Validity Range......Page 241
8.2.2 High Gain Limitations......Page 242
8.3.1 Amplitude and Frequency of Actuator Commands......Page 243
8.3.2 Unstable and Non-minimum-phase Systems......Page 244
8.4.1 Selection of Design Parameters in Controller Synthesis......Page 246
8.4.3 Generalised 2-DoF Control Structure......Page 248
8.5.1 Sources and Types of Uncertainty......Page 252
8.5.2 Determination of Uncertainty Bounds......Page 254
8.5.3 Unstructured Robust Stability Analysis......Page 255
8.5.4 Structured Uncertainty......Page 258
8.6 Controller Synthesis......Page 259
8.6.1 Mixed Sensitivity......Page 260
8.8.1 Cascade Control......Page 263
8.8.2 Distillation Column......Page 264
9.1 Control Implementation: Centralised vs. Decentralised......Page 268
9.2.2 Digital Implementation......Page 270
9.3 Bumpless Transfer and Anti-windup......Page 276
9.4 Non-conventional Sampling......Page 279
9.5 Coping with Non-linearity......Page 282
9.5.1 Basic Techniques......Page 283
9.5.2 Gain-scheduling......Page 284
9.5.3 Global Linearisation......Page 285
9.6 Reliability and Fault Detection......Page 288
9.7 Supervision, Integrated Automation, Plant-wide Control......Page 291
A.1 Signals......Page 294
A.2 Continuous Systems......Page 295
A.2.1 System Analysis......Page 296
A.2.2 Frequency response......Page 297
A.3 Discrete Systems......Page 298
A.3.1 System Analysis......Page 299
A.4 Experimental Modelling......Page 300
A.5 Tables of Transforms......Page 303
B.1 Column, Row and Null Spaces......Page 304
B.2 Matrix Inversion......Page 305
B.3 Eigenvalues and Eigenvectors......Page 306
B.4 Singular Values and Matrix Gains......Page 308
B.4.1 Condition number......Page 309
B.5 Matrix Exponential......Page 312
B.6 Polynomial Fraction Matrices......Page 313
C.2 Function Spaces......Page 316
C.3.1 Signal Norms......Page 318
C.4 BIBO Stability and the Small-gain Theorem......Page 319
D.1 Static Optimisation......Page 322
D.2 Discrete Linear Quadratic Regulator......Page 324
D.2.1 Multi-step Optimisation (Dynamic Programming)......Page 326
D.2.2 Stationary Regulator......Page 328
E.1 Random Variables......Page 330
E.1.1 Linear Operations with Random Variables......Page 331
E.2 Multi-dimensional Random Variables......Page 332
E.3 Linear Predictors (Regression)......Page 335
E.4.1 Simulation......Page 337
E.4.2 Prediction: The Kalman Filter......Page 338
F.1 Small-gain Stability Analysis......Page 342
F.2 Structured Uncertainty......Page 344
F.2.1 Robust Performance......Page 346
F.3 Additional Design Techniques......Page 347
F.3.2 McFarlane-Glover Loop Shaping......Page 348
D......Page 356
M......Page 357
R......Page 358
Z......Page 359