# Model Predictive Control

Wiley - IEEE

1. Edition May 2024

304 Pages, Hardcover*Wiley & Sons Ltd*

**978-1-119-47139-4**

Model Predictive Control

Understand the practical side of controlling industrial processes

Model Predictive Control (MPC) is a method for controlling a process according to given parameters, derived in many cases from empirical models. It has been widely applied in industrial units to increase revenue and promoting sustainability. Systematic overviews of this subject, however, are rare, and few draw on direct experience in industrial settings.

Assuming basic knowledge of the relevant mathematical and algebraic modeling techniques, the book's title combines foundational theories of MPC with a thorough sense of its practical applications in an industrial context. The result is a presentation uniquely suited to rapid incorporation in an industrial workplace.

Model Predictive Control readers will also find:

* Two-part organization to balance theory and applications

* Selection of topics directly driven by industrial demand

* An author with decades of experience in both teaching and industrial practice

This book is ideal for industrial control engineers and researchers looking to understand MPC technology, as well as advanced undergraduate and graduate students studying predictive control and related subjects.

Preface xiii

Acronyms xv

Introduction xvii

1 Concepts 1

1.1 PID and Model Predictive Control 1

1.2 Two-Layered Model Predictive Control 4

1.3 Hierarchical Model Predictive Control 7

2 Parameter Estimation and Output Prediction 11

2.1 Test Signal for Model Identification 11

2.1.1 Step Test 11

2.1.2 White Noise 11

2.1.3 Pseudo-Random Binary Sequence 13

2.1.4 Generalized Binary Noise 14

2.2 Step Response Model Identification 15

2.2.1 Model 15

2.2.2 Data Processing 17

2.2.2.1 Marking or Interpolation of Bad Data 17

2.2.2.2 Smoothing Data 18

2.2.3 Model Identification 19

2.2.3.1 Case Grouping 19

2.2.3.2 Cased Data Preparation for Stable Dependent Variables 19

2.2.3.3 Cased Data Preparation for Integral Dependent Variables 21

2.2.3.4 Least Square Solution to Parameter Regression 22

2.2.3.5 Least Square Solution by SVD Decomposition 24

2.2.3.6 Filtering Pulse Response Coefficients 24

2.2.4 Numerical Example 27

2.3 Prediction Based on Step Response Model and Kalman Filter 30

2.3.1 Steady-State Kalman Filter and Predictor 31

2.3.2 Steady-State Kalman Filter and Predictor Based on Step Response Model 32

2.3.2.1 Open-Loop Prediction of Stable CV 33

2.3.2.2 Open-Loop Prediction of Integral CV 36

3 Steady-State Target Calculation 39

3.1 RTO and External Target 39

3.2 Economic Optimization and Target Tracking Problem 40

3.2.1 Economic Optimization 41

3.2.1.1 Optimization Problem 41

3.2.1.2 Minimum-Move Problem 42

3.2.2 Target Tracking Problem 46

3.3 Judging Feasibility and Adjusting Soft Constraint 46

3.3.1 Weight Method 47

3.3.1.1 An Illustrative Example 47

3.3.1.2 Weight Method 50

3.3.2 Priority-Rank Method 51

3.3.2.1 Ascending-Number Method 52

3.3.2.2 Descending-Number Method 52

3.3.3 Compromise Between Adjusting Soft Constraints and Economic Optimization 55

4 Two-Layered DMC for Stable Processes 57

4.1 Open-Loop Prediction Module 59

4.2 Steady-State Target Calculation Module 61

4.2.1 Hard and Soft Constraints 61

4.2.2 Priority Rank of Soft Constraints 63

4.2.3 Feasibility Stage 64

4.2.4 Economic Stage 66

4.3 Dynamic Calculation Module 67

4.4 Numerical Example 70

5 Two-Layered DMC for Stable and Integral Processes 73

5.1 Open-Loop Prediction Module 74

5.2 Steady-State Target Calculation Module 77

5.2.1 Hard and Soft Constraints 78

5.2.2 Priority Rank of Soft Constraints 80

5.2.3 Feasibility Stage 81

5.2.4 Economic Stage 83

5.3 Dynamic Calculation Module 85

5.4 Numerical Example 87

6 Two-Layered DMC for State-Space Model 95

6.1 Artificial Disturbance Model 95

6.1.1 Basic Model 96

6.1.2 Controlled Variable as Additional State 97

6.1.3 Manipulated Variable as Additional State 98

6.1.4 Kalman Filter 100

6.2 Open-Loop Prediction Module 103

6.3 Steady-State Target Calculation Module 104

6.3.1 Constraints on Steady-State Perturbation Increment 104

6.3.2 Feasibility Stage 106

6.3.3 Economic Stage Without Soft Constraint 107

6.4 Dynamic Calculation Module 108

6.5 Numerical Example 110

7 Offset-Free, Nonlinearity and Variable Structure in Two-Layered MPC 115

7.1 State Space Steady-State Target Calculation with Target Tracking 115

7.1.1 Case all External Targets Having Equal Importance 117

7.1.2 Case CV External Target Being More Important Than MV External Target 117

7.2 QP-Based Dynamic Control and Offset-Free 119

7.3 Static Nonlinear Transformation 125

7.3.1 Principle of Nonlinear Transformation 125

7.3.2 Usual Nonlinear Transformations 127

7.3.2.1 Nonlinear Transformation of Valve Output 127

7.3.2.2 Piecewise Linear Transformation 128

7.4 Two-Layered MPC with Varying Degree of Freedom 129

7.4.1 Numerical Example Without Varying Structure 130

7.4.2 Numerical Example with Varying Number of Manipulated Variables 131

7.5 Numerical Example with Output Collinearity 135

8 Two-Step Model Predictive Control for Hammerstein Model 141

8.1 Two-Step State Feedback MPC 142

8.2 Stability of Two-Step State Feedback MPC 144

8.3 Region of Attraction for Two-Step MPC: Semi-Global Stability 147

8.3.1 System Matrix Having No Eigenvalue Outside of Unit Circle 147

8.3.2 System Matrix Having Eigenvalues Outside of Unit Circle 149

8.3.3 Numerical Example 150

8.4 Two-Step Output Feedback Model Predictive Control 153

8.5 Generalized Predictive Control: Basics 159

8.5.1 Output Prediction 159

8.5.2 Receding Horizon Optimization 161

8.5.3 Dead-Beat Property of Generalized Predictive Control 164

8.5.4 On-line Identification and Feedback Correction 167

8.6 Two-Step Generalized Predictive Control 167

8.6.1 Unconstrained Algorithm 168

8.6.2 Algorithm with Input Saturation 168

8.6.3 Stability Results Based on Popov's Theorem 170

8.7 Region of Attraction for Two-Step Generalized Predictive Control 173

8.7.1 State Space Description 173

8.7.2 Stability with Region of Attraction 174

8.7.3 Computation of Region of Attraction 175

8.7.4 Numerical Example 177

9 Heuristic Model Predictive Control for LPV Model 179

9.1 A Heuristic Approach Based on Open-Loop Optimization 180

9.2 Open-Loop MPC for Unmeasurable State 186

10 Robust Model Predictive Control 195

10.1 A Cornerstone Method 195

10.1.1 KBM Formula 195

10.1.2 KBM Controller 197

10.1.3 Example: Generalizing to Networked Control 199

10.1.3.1 Closed-Loop Model for Double-Sided, Finite-Bounded, Arbitrary Packet Loss 199

10.1.3.2 MPC for Double-Sided, Arbitrary Packet Loss 200

10.1.3.3 Solution of MPC for Double-Sided Packet Loss 201

10.2 Invariant Set Trap 204

10.3 Prediction Horizon: Zero or One 211

10.3.1 One Over Zero 211

10.3.2 One: Generalizing to Networked Control 214

10.3.2.1 Algorithm 215

10.3.2.2 A Numerical Example 218

10.4 Variant Feedback MPC 219

10.5 About Optimality 226

10.5.1 Constrained Linear Time-Varying Quadratic Regulation with Near-Optimal Solution 227

10.5.1.1 Solving KBM Controller 228

10.5.1.2 Solving Problem Without Terminal Cost 229

10.5.1.3 Solving Problem with Terminal Cost 230

10.5.1.4 Overall Algorithm and Analysis 230

10.5.1.5 Numerical Example 231

10.5.2 Alternatives with Nominal Performance Cost 232

10.5.2.1 Problem Formulation 232

10.5.2.2 Robust MPC Based on Partial Feedback Control 233

10.5.2.3 Introducing Vertex Control Moves 235

10.5.2.4 Numerical Example 236

10.5.3 More Discussions 236

11 Output Feedback Robust Model Predictive Control 239

11.1 Model and Controller Descriptions 245

11.1.1 Controller for LPV Model 247

11.1.2 Controller for Quasi-LPV Model 248

11.2 Characterization of Stability and Optimality 249

11.2.1 Review of Quadratic Boundedness 249

11.2.2 Stability Condition 251

11.2.3 Optimality Condition 252

11.2.4 A Paradox for State Convergence 254

11.3 General Optimization Problem 255

11.3.1 Handling Physical Constraints 255

11.3.2 Current Augmented State 256

11.3.3 Some Usual Transformations 258

11.3.4 Handling Double Convex Combinations 259

11.4 Solutions to Output Feedback MPC 260

11.4.1 Full Online Method for LPV 261

11.4.2 Partial Online Method for LPV 262

11.4.3 Relaxed Variables in Optimization Problem 264

11.4.4 Alternative Forms Based on Congruence Transformation 265

11.4.5 Description of Bound on True State 271

References 273

Index 279

Yuanqing Yang, PhD, teaches MPC to both undergraduate and graduate students in the School of Automation, Chongqing University of Posts and Telecommunications, China. His research interests include model predictive control, fuzzy control, networked control, and distributed control systems.