Model Predictive Control

Baocang Ding, 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, control of power network, process control, and control software development. 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.

• About the Authors xiPreface xiiiAcronyms xvIntroduction xvii1 Concepts 11.1 PID and Model Predictive Control 11.2 Two-Layered Model Predictive Control 41.3 Hierarchical Model Predictive Control 72 Parameter Estimation and Output Prediction 112.1 Test Signal for Model Identification 112.1.1 Step Test 112.1.2 White Noise 112.1.3 Pseudo-Random Binary Sequence 132.1.4 Generalized Binary Noise 142.2 Step Response Model Identification 152.2.1 Model 152.2.2 Data Processing 172.2.2.1 Marking or Interpolation of Bad Data 172.2.2.2 Smoothing Data 182.2.3 Model Identification 192.2.3.1 Case Grouping 192.2.3.2 Cased Data Preparation for Stable Dependent Variables 192.2.3.3 Cased Data Preparation for Integral Dependent Variables 212.2.3.4 Least Square Solution to Parameter Regression 222.2.3.5 Least Square Solution by SVD Decomposition 242.2.3.6 Filtering Pulse Response Coefficients 242.2.4 Numerical Example 272.3 Prediction Based on Step Response Model and Kalman Filter 302.3.1 Steady-State Kalman Filter and Predictor 312.3.2 Steady-State Kalman Filter and Predictor Based on Step Response Model 322.3.2.1 Open-Loop Prediction of Stable CV 332.3.2.2 Open-Loop Prediction of Integral CV 363 Steady-State Target Calculation 393.1 RTO and External Target 393.2 Economic Optimization and Target Tracking Problem 403.2.1 Economic Optimization 413.2.1.1 Optimization Problem 413.2.1.2 Minimum-Move Problem 423.2.2 Target Tracking Problem 463.3 Judging Feasibility and Adjusting Soft Constraint 463.3.1 Weight Method 473.3.1.1 An Illustrative Example 473.3.1.2 Weight Method 503.3.2 Priority-Rank Method 513.3.2.1 Ascending-Number Method 523.3.2.2 Descending-Number Method 523.3.3 Compromise Between Adjusting Soft Constraints and Economic Optimization 554 Two-Layered DMC for Stable Processes 574.1 Open-Loop Prediction Module 594.2 Steady-State Target Calculation Module 614.2.1 Hard and Soft Constraints 614.2.2 Priority Rank of Soft Constraints 634.2.3 Feasibility Stage 644.2.4 Economic Stage 664.3 Dynamic Calculation Module 674.4 Numerical Example 705 Two-Layered DMC for Stable and Integral Processes 735.1 Open-Loop Prediction Module 745.2 Steady-State Target Calculation Module 775.2.1 Hard and Soft Constraints 785.2.2 Priority Rank of Soft Constraints 805.2.3 Feasibility Stage 815.2.4 Economic Stage 835.3 Dynamic Calculation Module 855.4 Numerical Example 876 Two-Layered DMC for State-Space Model 956.1 Artificial Disturbance Model 956.1.1 Basic Model 966.1.2 Controlled Variable as Additional State 976.1.3 Manipulated Variable as Additional State 986.1.4 Kalman Filter 1006.2 Open-Loop Prediction Module 1036.3 Steady-State Target Calculation Module 1046.3.1 Constraints on Steady-State Perturbation Increment 1046.3.2 Feasibility Stage 1066.3.3 Economic Stage Without Soft Constraint 1076.4 Dynamic Calculation Module 1086.5 Numerical Example 1107 Offset-Free, Nonlinearity and Variable Structure in Two-Layered MPC 1157.1 State Space Steady-State Target Calculation with Target Tracking 1157.1.1 Case all External Targets Having Equal Importance 1177.1.2 Case CV External Target Being More Important Than MV External Target 1177.2 QP-Based Dynamic Control and Offset-Free 1197.3 Static Nonlinear Transformation 1257.3.1 Principle of Nonlinear Transformation 1257.3.2 Usual Nonlinear Transformations 1277.3.2.1 Nonlinear Transformation of Valve Output 1277.3.2.2 Piecewise Linear Transformation 1287.4 Two-Layered MPC with Varying Degree of Freedom 1297.4.1 Numerical Example Without Varying Structure 1307.4.2 Numerical Example with Varying Number of Manipulated Variables 1317.5 Numerical Example with Output Collinearity 1358 Two-Step Model Predictive Control for Hammerstein Model 1418.1 Two-Step State Feedback MPC 1428.2 Stability of Two-Step State Feedback MPC 1448.3 Region of Attraction for Two-Step MPC: Semi-Global Stability 1478.3.1 System Matrix Having No Eigenvalue Outside of Unit Circle 1478.3.2 System Matrix Having Eigenvalues Outside of Unit Circle 1498.3.3 Numerical Example 1508.4 Two-Step Output Feedback Model Predictive Control 1538.5 Generalized Predictive Control: Basics 1598.5.1 Output Prediction 1598.5.2 Receding Horizon Optimization 1618.5.3 Dead-Beat Property of Generalized Predictive Control 1648.5.4 On-line Identification and Feedback Correction 1678.6 Two-Step Generalized Predictive Control 1678.6.1 Unconstrained Algorithm 1688.6.2 Algorithm with Input Saturation 1688.6.3 Stability Results Based on Popov’s Theorem 1708.7 Region of Attraction for Two-Step Generalized Predictive Control 1738.7.1 State Space Description 1738.7.2 Stability with Region of Attraction 1748.7.3 Computation of Region of Attraction 1758.7.4 Numerical Example 1779 Heuristic Model Predictive Control for LPV Model 1799.1 A Heuristic Approach Based on Open-Loop Optimization 1809.2 Open-Loop MPC for Unmeasurable State 18610 Robust Model Predictive Control 19510.1 A Cornerstone Method 19510.1.1 KBM Formula 19510.1.2 KBM Controller 19710.1.3 Example: Generalizing to Networked Control 19910.1.3.1 Closed-Loop Model for Double-Sided, Finite-Bounded, Arbitrary Packet Loss 19910.1.3.2 MPC for Double-Sided, Arbitrary Packet Loss 20010.1.3.3 Solution of MPC for Double-Sided Packet Loss 20110.2 Invariant Set Trap 20410.3 Prediction Horizon: Zero or One 21110.3.1 One Over Zero 21110.3.2 One: Generalizing to Networked Control 21410.3.2.1 Algorithm 21510.3.2.2 A Numerical Example 21810.4 Variant Feedback MPC 21910.5 About Optimality 22610.5.1 Constrained Linear Time-Varying Quadratic Regulation with Near-Optimal Solution 22710.5.1.1 Solving KBM Controller 22810.5.1.2 Solving Problem Without Terminal Cost 22910.5.1.3 Solving Problem with Terminal Cost 23010.5.1.4 Overall Algorithm and Analysis 23010.5.1.5 Numerical Example 23110.5.2 Alternatives with Nominal Performance Cost 23210.5.2.1 Problem Formulation 23210.5.2.2 Robust MPC Based on Partial Feedback Control 23310.5.2.3 Introducing Vertex Control Moves 23510.5.2.4 Numerical Example 23610.5.3 More Discussions 23611 Output Feedback Robust Model Predictive Control 23911.1 Model and Controller Descriptions 24511.1.1 Controller for LPV Model 24711.1.2 Controller for Quasi-LPV Model 24811.2 Characterization of Stability and Optimality 24911.2.1 Review of Quadratic Boundedness 24911.2.2 Stability Condition 25111.2.3 Optimality Condition 25211.2.4 A Paradox for State Convergence 25411.3 General Optimization Problem 25511.3.1 Handling Physical Constraints 25511.3.2 Current Augmented State 25611.3.3 Some Usual Transformations 25811.3.4 Handling Double Convex Combinations 25911.4 Solutions to Output Feedback MPC 26011.4.1 Full Online Method for LPV 26111.4.2 Partial Online Method for LPV 26211.4.3 Relaxed Variables in Optimization Problem 26411.4.4 Alternative Forms Based on Congruence Transformation 26511.4.5 Description of Bound on True State 271References 273Index 279