Model Predictive Control

Foreword xv
Preface xxv
Acknowledgments xxvii

1 Introduction 1
1.1 What Is MPC? 1
1.2 Why MPC? 5
1.3 Historical Overview 10
1.4 Impact of MPC on Control Research 13
1.5 A Typical Industrial Control Problem 17
1.6 Organization of This Book 20

Part I Early Industrial MPC Algorithms 23

2 Step Response Modeling and Identification 25
2.1 Linear Time-invariant Systems 26
2.2 Impulse/Step Response Models 28
2.3 Multi-step Prediction 34
2.4 Examples 39
2.5 Identification 41

3 Dynamic Matrix Control: The Basic Algorithm 51
3.1 The Concept of Moving Horizon Control 51
3.2 Multi-step Prediction 52
3.3 Objective Function 56
3.4 Constraints 57
3.5 Quadratic Programming Solution of the Control Problem 60
3.6 Implementation 62
3.7 Examples: Analysis and Guidelines 71
3.8 Case Study: Control of the "Shell Heavy Oil Fractionator" Using DMC 83

4 Dynamic Matrix Control-Extensions and Variations 99
4.1 Features Found in Other Industrial Algorithms 99
4.2 Connection with Internal Model Control 104
4.3 Some Possible Enhancements to DMC 106

Part II Basics of Linear Systems, Optimal Control, and System Identification 117

5 Linear Time Invariant System Models 119
5.1 Sampling and Reconstruction 120
5.2 Introduction to z-transform 124
5.3 Transfer Function Models 125
5.4 State-space Model 130
5.5 Conversion Between Discrete-time Models 134

6 Discrete-time State Space Models 145
6.1 State-coordinate Transformation 145
6.2 Stability 146
6.3 Controllability, Reachability, and Stabilizability 148
6.4 Observability, Reconstructability, and Detectability 156
6.5 Kalman Decomposition and Minimal Realization 160
6.6 Disturbance Modeling 163

7 State Estimation 171
7.1 Linear Estimator Structure 172
7.2 Observer Pole Placement 173
7.3 Kalman Filter 176
7.4 Extensions 185
7.5 Least Squares Formulation of State Estimation 192

8 Unconstrained Quadratic Optimal Control 201
8.1 Linear State Feedback Controller Design 202
8.2 Finite-horizon Quadratic Optimal Control 203
8.3 Infinite-horizon Quadratic Optimal Control 208
8.4 Analysis 214
8.5 Stochastic LQ Control 216

9 Constrained Quadratic Optimal Control 223
9.1 Finite-horizon Problem 223
9.2 Infinite-horizon Problem 224
9.3 Constraint Softening 231
9.4 Derivation of an Explicit Form of the Optimal Control Law via Multi-parametric Programming 232
9.5 Analysis 235
9.6 Stochastic Case (*) 243

10 System Identification 249
10.1 Problem Overview 249
10.2 Model Structures 250
10.3 Parametric Identification Methods 255
10.4 Nonparametric Identification 270
10.5 Subspace Identification 275
10.6 Practice of System Identification: A User's Perspective 284

Part III Advanced MPC 297

11 Linear MPC: State-space Formulation 299
11.1 Model Construction 300
11.2 The Background: Deterministic State-space MPC 310
11.3 The Workhorse: MPC with State Estimation 316xii Contents
11.4 Inferential Control 335
11.5 Sequential Linearization-based MPC (for Nonlinear Systems) 341

12 Nonlinear Model Predictive Control 359
12.1 NMPC Formulation 360
12.2 Solution via NLP 362
12.3 Stability and Other Properties 368
12.4 Nonlinear State Estimation 372
12.5 Case Study 379
12.6 Conclusions and Future Directions 382

13 Repetitive MPC for Batch and Periodic Systems 387
13.1 Historical Background 387
13.2 General Framework 388
13.3 Iterative Learning Model Predictive Control for Batch Systems 391
13.4 Repetitive Model Predictive Control for Continuous Systems with Periodic Operations 397
13.5 Future Outlook 405
Exercises 406

Appendix A Review of Linear Transformation 409
Appendix B Random Variables and Stochastic Processes 433
Appendix C Model Reduction 455
Appendix D Optimality of Kalman Filter and LQG Controller for Linear Gaussian Systems 463
Appendix E Internal Model Control Basics 479
Appendix F MPC Toolbox Tutorial: Shell Oil Fractionator 495
Appendix G A Brief Tutorial on Simulink 513

Bibliography 517
Index 523