Author Biography xiii
Preface xv
Acknowledgments xxi
List of Symbols and Acronyms xxiii
About the Companion Website xxv
Part I Continuous-time State Feedback Control 1
1 State Feedback Controller and Observer Design 3
1.1 Introduction 3
1.2 Motivation for Going Beyond PID Control 4
1.3 Basics in State Feedback Control 12
1.3.1 State Feedback Control 12
1.3.2 Controllability 18
1.3.3 Food for Thought 21
1.4 Pole-assignment Controller 21
1.4.1 The Design Method 21
1.4.2 Similarity Transformation for Controller Design 24
1.4.3 MATLAB Tutorial on Pole-assignment Controller 27
1.4.4 Food for Thought 29
1.5 Linear Quadratic Regulator (LQR) Design 29
1.5.1 Motivational Example 29
1.5.2 Linear Quadratic Regulator Design 32
1.5.3 Selection of Q and R Matrices 34
1.5.4 LQR with Prescribed Degree of Stability 39
1.5.5 Food for Thought 46
1.6 Observer Design 47
1.6.1 Motivational Example for Observer 47
1.6.2 Observer Design 50
1.6.3 Observability 53
1.6.4 Duality between Controller and Observer 55
1.6.5 Observer Implementation 56
1.6.6 Food for Thought 57
1.7 State Estimate Feedback Control System 58
1.7.1 State Estimate Feedback Control 58
1.7.2 Separation Principle 59
1.7.3 Food for Thought 60
1.8 Summary 61
1.9 Further Reading 62
Problems 63
2 Practical Multivariable Controllers in Continuous-time 67
2.1 Introduction 67
2.2 Practical Controller I: Integral Action via Controller Design 68
2.2.1 The Original Control Law 68
2.2.2 Integrator Windup Scenarios 69
2.2.3 Proposed Practical Multivariable Controller 71
2.2.4 Anti-windup Implementation 74
2.2.5 MATLAB Tutorial on Design and Implementation 77
2.2.6 Application to Drum Boiler Control 85
2.2.7 Food for Thought 91
2.3 Practical Controller II: Integral Action via Observer Design 92
2.3.1 Integral Control via Disturbance Estimation 92
2.3.2 Anti-windup Mechanism 95
2.3.3 MATLAB Tutorial on Design and Implementation 96
2.3.4 Application to Sugar Mill Control 102
2.3.5 Design for Systems with Known States 103
2.3.6 Food for Thought 106
2.4 Drive Train Control of aWind Turbine 107
2.4.1 Modelling of Wind Turbine’s Drive Train 107
2.4.2 Configuration of The Control System 110
2.4.3 Design Method I 111
2.4.4 Design Method II 115
2.4.5 MATLAB Tutorial on Design Method II 116
2.4.6 Food for Thought 121
2.5 Summary 121
2.6 Further Reading 122
Problems 122
Part II Discrete-time State Feedback Control 127
3 Introduction to Discrete-time Systems 129
3.1 Introduction 129
3.2 Discretization of Continuous-time Models 130
3.2.1 Sampling of a Continuous-time Model 130
3.2.2 Stability of Discrete-time System 133
3.2.3 Examples of Discrete-time Models from Sampling 134
3.2.4 Food for Thoughts 141
3.3 Input and Output Discrete-time Models 142
3.3.1 Input and Output Models 142
3.3.2 Finite Impulse Response and Step Response Models 144
3.3.3 Non-minimal State Space Realization 148
3.3.4 Food for Thought 148
3.4 z-Transforms 149
3.4.1 z-Transforms for Commonly Used Signals 149
3.4.2 z-Transfer Functions 152
3.4.3 Food for Thought 154
3.5 Summary 155
3.6 Further Reading 156
Problems 156
4 Discrete-time State Feedback Control 161
4.1 Introduction 161
4.2 Discrete-time State Feedback Control 161
4.2.1 Basic Ideas 161
4.2.2 Controllability in Discrete-time 165
4.2.3 Food for Thought 167
4.3 Discrete-time Observer Design 167
4.3.1 Basic Ideas about Discrete-time Observer 167
4.3.2 Observability in Discrete-time 171
4.3.3 Food for Thought 173
4.4 Discrete-time Linear Quadratic Regulator (DLQR) 173
4.4.1 Objective Function for DLQR 173
4.4.2 Optimal Solution 174
4.4.3 Observer Design using DLQR 176
4.4.4 Food for Thought 176
4.5 Discrete-time LQR with Prescribed Degree of Stability 177
4.5.1 Basic Ideas about a Prescribed Degree of Stability 177
4.5.2 Case Studies 180
4.5.3 Food for Thought 186
4.6 Summary 186
4.7 Further Reading 187
Problems 188
5 Disturbance Rejection and Reference Tracking via Observer Design 195
5.1 Introduction 195
5.2 Disturbance Models 195
5.2.1 Commonly Encountered Disturbance Signals 196
5.2.2 State Space Model with Input Disturbance 199
5.2.3 Food for Thought 200
5.3 Compensation of Input and Output Disturbances in Estimation 200
5.3.1 Motivational Example 200
5.3.2 Input Disturbance Observer Design 202
5.3.3 MATLAB Tutorial for Augmented State Space Model 206
5.3.4 The Observer Error System 207
5.3.5 Output Disturbance Observer Design 209
5.3.6 Food for Thought 213
5.4 Disturbance-Observer-based State Feedback Control 214
5.4.1 The Control Law 214
5.4.2 MATLAB Tutorial for Control Implementation 217
5.4.3 Food for Thought 222
5.5 Analysis of Disturbance-Observer-based Control System 223
5.5.1 Controller Transfer Function 223
5.5.2 Disturbance Rejection 225
5.5.3 Reference Tracking 227
5.5.4 A Case Study 228
5.5.5 Food for Thought 232
5.6 Anti-windup Implementation of the Control Law 233
5.6.1 Algorithm for Anti-windup Implementation 233
5.6.2 Heating Furnace Control 236
5.6.3 Example for Bandlimited Disturbance 239
5.6.4 Food for Thought 241
5.7 Summary 242
5.8 Further Reading 243
Problems 243
6 Disturbance Rejection and Reference Tracking via Control Design 253
6.1 Introduction 253
6.2 Embedding Disturbance Model into Controller Design 254
6.2.1 Formulation of Augmented State Space Model 254
6.2.2 MATLAB Tutorial 256
6.2.3 Controllability and Observability 258
6.2.4 Food for Thought 259
6.3 Controller and Observer Design 260
6.3.1 Controller Design and Control Signal Calculation 260
6.3.2 Adding Reference Signal 262
6.3.3 Observer Design and Implementation 262
6.3.4 MATLAB Tutorial for Control Implementation 264
6.3.5 Food for Thought 268
6.4 Practical Issues 269
6.4.1 Reducing Overshoot in Reference Tracking 269
6.4.2 Anti-windup Implementation 272
6.4.3 Control System using NMSS Realization 276
6.4.4 Food for Thought 282
6.5 Repetitive Control 283
6.5.1 Basic Ideas about Repetitive Control 283
6.5.2 Determining the Disturbance Model D(z) 285
6.5.3 Robotic Arm Control 290
6.5.4 Food for Thought 295
6.6 Summary 295
6.7 Further Reading 296
Problems 296
Part III Kalman Filtering 309
7 The Kalman Filter 311
7.1 Introduction 311
7.2 The Kalman Filter Algorithm 312
7.2.1 State Space Models in the Kalman Filter 312
7.2.2 An Intuitive Computational Procedure 313
7.2.3 Optimization of Kalman Filter Gain 315
7.2.4 Kalman Filter Examples with MATLAB Tutorials 317
7.2.5 Compensation of Sensor Bias and Load Disturbance 325
7.2.6 Food for Thought 330
7.3 The Kalman Filter in Multi-rate Sampling Environment 331
7.3.1 KF Algorithm for Missing Data Scenarios 331
7.3.2 Case Studies with MATLAB Tutorial 333
7.3.3 Food for Thought 344
7.4 The Extended Kalman Filter (EKF) 344
7.4.1 Linearization in Extended Kalman Filter 344
7.4.2 The Extended Kalman Filter Algorithm 348
7.4.3 Case Studies with MATLAB Tutorial 351
7.4.4 Food for Thought 359
7.5 The Kalman Filter with Fading Memory 359
7.5.1 The Algorithm for KF with Fading Memory 360
7.5.2 Food for Thought 363
7.6 Relationship between Kalman Filter and Observer 364
7.6.1 One-step Kalman Filter Algorithm 364
7.6.2 Kalman Filter and Observer 365
7.6.3 Food for Thought 370
7.7 Summary 371
7.8 Further Reading 372
Problems 372
8 Addressing Computational Issues in KF 377
8.1 Introduction 377
8.2 The Sequential Kalman Filter 377
8.2.1 Basic Ideas about Sequential Kalman Filter 377
8.2.2 Non-diagonal R 382
8.2.3 MATLAB Tutorial for Sequential Kalman Filter 383
8.2.4 Food for Thought 387
8.3 The Kalman Filter using UDUT Factorization 388
8.3.1 Gram-Schmidt Orthogonalization Procedure 388
8.3.2 Basic Ideas 390
8.3.3 Sequential Kalman Filter with UDUT Decomposition 393
8.3.4 MATLAB Tutorial 395
8.3.5 Food for Thought 398
8.4 Summary 398
8.5 Further Reading 399
Problems 399
Bibliography 403
Index 413
