Model Predictive Control

1 Introduction to Model Based Predictive Control.- 1.1 MPC Strategy.- 1.2 Historical Perspective.- 1.3 Industrial Technology.- 1.4 Outline of the Chapters.- 2 Model Based Predictive Controllers.- 2.1 MPC Elements.- 2.1.1 Prediction Model.- 2.1.2 Objective Function.- 2.1.3 Obtaining the Control Law.- 2.2 Review of some MPC Algorithms.- 2.3 Nonlinear Predictive Control.- 2.3.1 Nonlinear Models.- 2.3.2 Techniques for Nonlinear Predictive Control.- 3 Commercial Model Predictive Control Schemes.- 3.1 Dynamic Matrix Control.- 3.1.1 Prediction.- 3.1.2 Measurable Disturbances.- 3.1.3 Control Algorithm.- 3.2 Model Algorithmic Control.- 3.2.1 Process Model and Prediction.- 3.2.2 Control Law.- 3.2.3 Multivariable Processes.- 3.3 Predictive Functional Control.- 3.3.1 Formulation.- 3.4 Case Study: a Water Heater.- 4 Generalized Predictive Control.- 4.1 Introduction.- 4.2 Formulation of Generalized Predictive Control.- 4.3 The Coloured Noise Case.- 4.4 An Example.- 4.5 Closed Loop Relationships.- 4.6 The Role of the T polynomial.- 4.6.1 Selection of the T Polynomial.- 4.6.2 Relationships with other Formulations.- 4.7 The P Polynomial.- 4.8 Consideration of Measurable Disturbances.- 4.9 Use of a Different Predictor in GPC.- 4.9.1 Equivalent Structure.- 4.9.2 A Comparative Example.- 4.10 Constrained Receding-Horizon Predictive Control.- 4.10.1 Computation of the Control Law.- 4.10.2 Properties.- 4.11 Stable GPC.- 4.11.1 Formulation of the Control Law.- 5 Simple Implementation of GPC for Industrial Processes.- 5.1 Plant Model.- 5.1.1 Plant Identification: The Reaction Curve Method.- 5.2 The Dead Time Multiple of Sampling Time Case.- 5.2.1 Discrete Plant Model.- 5.2.2 Problem Formulation.- 5.2.3 Computation of the Controller Parameters.- 5.2.4 Role of the Control-Weighting Factor.- 5.2.5 Implementation Algorithm.- 5.2.6 An Implementation Example.- 5.3 The Dead Time non Multiple of the Sampling Time Case.- 5.3.1 Discrete Model of the Plant.- 5.3.2 Controller Parameters.- 5.3.3 Example.- 5.4 Integrating Processes.- 5.4.1 Derivation of the Control Law.- 5.4.2 Controller Parameters.- 5.4.3 Example.- 5.5 Consideration of Ramp Setpoints.- 5.5.1 Example.- 5.6 Comparison with Standard GPC.- 5.7 Stability Robustness Analysis.- 5.7.1 Structured Uncertainties.- 5.7.2 Unstructured Uncertainties.- 5.7.3 General Comments.- 5.8 Composition Control in an Evaporator.- 5.8.1 Description of the Process.- 5.8.2 Obtaining the Linear Model.- 5.8.3 Controller Design.- 5.8.4 Results.- 6 Multivariable MPC.- 6.1 Derivation of Multivariable GPC.- 6.1.1 White Noise Case.- 6.1.2 Coloured Noise Case.- 6.1.3 Measurable Disturbances.- 6.2 Obtaining a Matrix Fraction Description.- 6.2.1 Transfer Matrix Representation.- 6.2.2 Parametric Identification.- 6.3 State Space Formulation.- 6.3.1 Matrix Fraction and State Space Equivalences.- 6.4 Dead Time Problems.- 6.5 Example: Distillation Column.- 6.6 Application of DMC to a Chemical Reactor.- 6.6.1 Plant Description.- 6.6.2 Obtaining the Plant Model.- 6.6.3 Control Law.- 6.6.4 Simulation Results.- 7 Constrained MPC.- 7.1 Constraints and MPC.- 7.1.1 Illustrative Examples.- 7.2 Constraints and optimization.- 7.3 Revision of Main Quadratic Programming Algorithms.- 7.3.1 The Active Set Methods.- 7.3.2 Feasible Directions Methods.- 7.3.3 Initial Feasible Point.- 7.3.4 Pivoting Methods.- 7.4 Constraints Handling.- 7.4.1 Slew Rate Constraints.- 7.4.2 Amplitude Constraints.- 7.4.3 Output Constraints.- 7.4.4 Constraints Reduction.- 7.5 1-norm.- 7.6 Case study : a Compressor.- 7.7 Constraint Management.- 7.7.1 Feasibility.- 7.7.2 Techniques for Improving Feasibility.- 7.8 Constrained MPC and Stability.- 7.9 Multiobjective MPC.- 7.9.1 Priorization of Objectives.- 8 Robust MPC.- 8.1 Process Models and Uncertainties.- 8.1.1 Truncated Impulse Response Uncertainties.- 8.1.2 Matrix Fraction Description Uncertainties.- 8.1.3 Global Uncertainties.- 8.2 Objective Functions.- 8.2.1 Quadratic Norm.- 8.2.2 ? — ? norm.- 8.2.3 1-norm.- 8.3 Illustrative Examples.- 8.3.1 Bounds on the Output.- 8.3.2 Uncertainties in the Gain.- 8.4 Robust MPC and Linear Matrix Inequalities.- 9 Applications.- 9.1 Solar Power Plant.- 9.1.1 Self tuning GPC Control Strategy.- 9.1.2 Gain scheduling Generalized Predictive Control.- 9.2 Pilot Plant.- 9.2.1 Plant Description.- 9.2.2 Plant Control.- 9.2.3 Flow Control.- 9.2.4 Temperature Control at the Exchanger Output.- 9.2.5 Temperature Control in the Tank.- 9.2.6 Level Control.- 9.2.7 Remarks.- 9.3 Model Predictive Control in a Sugar Refinery.- A Revision of the Simplex method.- A.1 Equality Constraints.- A.2 Finding an Initial Solution.- A.3 Inequality Constraints.- References.