Distributed Model Predictive Control for Plant-Wide Systems

Table of Contents:
Preface xi About the Authors xv Acknowledgement xvii List of Figures xix List of Tables xxiii 1 Introduction 1 1.1 Plant-Wide System 1 1.2 Control System Structure of the Plant-Wide System 3 1.2.1 Centralized Control 4 1.2.2 Decentralized Control and Hierarchical Coordinated Decentralized Control 5 1.2.3 Distributed Control 6 1.3 Predictive Control 8 1.3.1 What is Predictive Control 8 1.3.2 Advantage of Predictive Control 9 1.4 Distributed Predictive Control 9 1.4.1 Why Distributed Predictive Control 9 1.4.2 What is Distributed Predictive Control 10 1.4.3 Advantage of Distributed Predictive Control 10 1.4.4 Classification of DMPC 11 1.5 About this Book 13 Part I FOUNDATION 2 Model Predictive Control 19 2.1 Introduction 19 2.2 Dynamic Matrix Control 20 2.2.1 Step Response Model 20 2.2.2 Prediction 21 2.2.3 Optimization 22 2.2.4 Feedback Correction 23 2.2.5 DMC with Constraint 24 2.3 Predictive Control with the State Space Model 26 2.3.1 System Model 27 2.3.2 Performance Index 28 2.3.3 Prediction 28 2.3.4 Closed-Loop Solution 30 2.3.5 State Space MPC with Constraint 31 2.4 Dual Mode Predictive Control 33 2.4.1 Invariant Region 33 2.4.2 MPC Formulation 34 2.4.3 Algorithms 35 2.4.4 Feasibility and Stability 36 2.5 Conclusion 37 3 Control Structure of Distributed MPC 39 3.1 Introduction 39 3.2 Centralized MPC 40 3.3 Single-Layer Distributed MPC 41 3.4 Hierarchical Distributed MPC 42 3.5 Example of the Hierarchical DMPC Structure 43 3.6 Conclusion 45 4 Structure Model and System Decomposition 47 4.1 Introduction 47 4.2 System Mathematic Model 48 4.3 Structure Model and Structure Controllability 50 4.3.1 Structure Model 50 4.3.2 Function of the Structure Model in System Decomposition 51 4.3.3 Input–Output Accessibility 53 4.3.4 General Rank of the Structure Matrix 56 4.3.5 Structure Controllability 56 4.4 Related Gain Array Decomposition 58 4.4.1 RGA Definition 59 4.4.2 RGA Interpretation 60 4.4.3 Pairing Rules 61 4.5 Conclusion 63 Part II UNCONSTRAINED DISTRIBUTED PREDICTIVE CONTROL 5 Local Cost Optimization-based Distributed Model Predictive Control 67 5.1 Introduction 67 5.2 Local Cost Optimization-based Distributed Predictive Control 68 5.2.1 Problem Description 68 5.2.2 DMPC Formulation 69 5.2.3 Closed-loop Solution 72 5.2.4 Stability Analysis 79 5.2.5 Simulation Results 79 5.3 Distributed MPC Strategy Based on Nash Optimality 82 5.3.1 Formulation 83 5.3.2 Algorithm 86 5.3.3 Computational Convergence for Linear Systems 86 5.3.4 Nominal Stability of Distributed Model Predictive Control System 88 5.3.5 Performance Analysis with Single-step Horizon Control Under Communication Failure 89 5.3.6 Simulation Results 94 5.4 Conclusion 99 Appendix 99 Appendix A. QP problem transformation 99 Appendix B. Proof of Theorem 5.1 100 6 Cooperative Distributed Predictive Control 103 6.1 Introduction 103 6.2 Noniterative Cooperative DMPC 104 6.2.1 System Description 104 6.2.2 Formulation 104 6.2.3 Closed-Form Solution 107 6.2.4 Stability and Performance Analysis 109 6.2.5 Example 113 6.3 Distributed Predictive Control based on Pareto Optimality 114 6.3.1 Formulation 118 6.3.2 Algorithm 119 6.3.3 The DMPC Algorithm Based on Plant-Wide Optimality 119 6.3.4 The Convergence Analysis of the Algorithm 121 6.4 Simulation 121 6.5 Conclusions 123 7 Networked Distributed Predictive Control with Information Structure Constraints 125 7.1 Introduction 125 7.2 Noniterative Networked DMPC 126 7.2.1 Problem Description 126 7.2.2 DMPC Formulation 127 7.2.3 Closed-Form Solution 132 7.2.4 Stability Analysis 135 7.2.5 Analysis of Performance 135 7.2.6 Numerical Validation 137 7.3 Networked DMPC with Iterative Algorithm 144 7.3.1 Problem Description 144 7.3.2 DMPC Formulation 145 7.3.3 Networked MPC Algorithm 147 7.3.4 Convergence and Optimality Analysis for Networked 150 7.3.5 Nominal Stability Analysis for Distributed Control Systems 152 7.3.6 Simulation Study 153 7.4 Conclusion 159 Appendix 159 Appendix A. Proof of Lemma 7.1 159 Appendix B. Proof of Lemma 7.2 160 Appendix C. Proof of Lemma 7.3 160 Appendix D. Proof of Theorem 7.1 161 Appendix E. Proof of Theorem 7.2 161 Appendix F. Derivation of the QP problem (7.52) 164 Part III CONSTRAINT DISTRIBUTED PREDICTIVE CONTROL 8 Local Cost Optimization Based Distributed Predictive Control with Constraints 169 8.1 Introduction 169 8.2 Problem Description 170 8.3 Stabilizing Dual Mode Noncooperative DMPC with Input Constraints 171 8.3.1 Formulation 171 8.3.2 Algorithm Design for Resolving Each Subsystem-based Predictive Control 176 8.4 Analysis 177 8.4.1 Recursive Feasibility of Each Subsystem-based Predictive Control 177 8.4.2 Stability Analysis of Entire Closed-loop System 183 8.5 Example 184 8.5.1 The System 184 8.5.2 Performance Comparison with the Centralized MPC 185 8.6 Conclusion 187 9 Cooperative Distributed Predictive Control with Constraints 189 9.1 Introduction 189 9.2 System Description 190 9.3 Stabilizing Cooperative DMPC with Input Constraints 191 9.3.1 Formulation 191 9.3.2 Constraint C-DMPC Algorithm 193 9.4 Analysis 194 9.4.1 Feasibility 194 9.4.2 Stability 199 9.5 Simulation 201 9.6 Conclusion 208 10 Networked Distributed Predictive Control with Inputs and Information Structure Constraints 209 10.1 Introduction 209 10.2 Problem Description 210 10.3 Constrained N-DMPC 212 10.3.1 Formulation 212 10.3.2 Algorithm Design for Resolving Each Subsystem-based Predictive Control 218 10.4 Analysis 219 10.4.1 Feasibility 219 10.4.2 Stability 225 10.5 Formulations Under Other Coordination Strategies 227 10.5.1 Local Cost Optimization Based DMPC 227 10.5.2 Cooperative DMPC 228 10.6 Simulation Results 229 10.6.1 The System 229 10.6.2 Performance of Closed-loop System under the N-DMPC 230 10.6.3 Performance Comparison with the Centralized MPC and the Local Cost Optimization based MPC 231 10.7 Conclusions 236 Part IV APPLICATION 11 Hot-Rolled Strip Laminar Cooling Process with Distributed Predictive Control 239 11.1 Introduction 239 11.2 Laminar Cooling of Hot-rolled Strip 240 11.2.1 Description 240 11.2.2 Thermodynamic Model 241 11.2.3 Problem Statement 242 11.3 Control Strategy of HSLC 244 11.3.1 State Space Model of Subsystems 244 11.3.2 Design of Extended Kalman Filter 247 11.3.3 Predictor 247 11.3.4 Local MPC Formulation 248 11.3.5 Iterative Algorithm 249 11.4 Numerical Experiment 251 11.4.1 Validation of Designed Model 251 11.4.2 Convergence of EKF 252 11.4.3 Performance of DMPC Comparing with Centralized MPC 252 11.4.4 Advantages of the Proposed DMPC Framework Comparing with the Existing Method 253 11.5 Experimental Results 256 11.6 Conclusion 258 12 High-Speed Train Control with Distributed Predictive Control 263 12.1 Introduction 263 12.2 System Description 264 12.3 N-DMPC for High-Speed Trains 264 12.3.1 Three Types of Force 264 12.3.2 The Force Analysis of EMUs 266 12.3.3 Model of CRH2 267 12.3.4 Performance Index 271 12.3.5 Optimization Problem 272 12.4 Simulation Results 272 12.4.1 Parameters of CRH2 273 12.4.2 Simulation Matrix 273 12.4.3 Results and Some Comments 274 12.5 Conclusion 278 13 Operation Optimization of Multitype Cooling Source System Based on DMPC 279 13.1 Introduction 279 13.2 Structure of Joint Cooling System 279 13.3 Control Strategy of Joint Cooling System 280 13.3.1 Economic Optimization Strategy 281 13.3.2 Design of Distributed Model Predictive Control in Multitype Cold Source System 283 13.4 Results and Analysis of Simulation 286 13.5 Conclusion 292 References 293 Index 299

About the Author :
SHAOYUAN LI Shanghai Jiao Tong University, China YI ZHENG Shanghai Jiao Tong University, China