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Model predictive control
About: Model predictive control is a research topic. Over the lifetime, 39662 publications have been published within this topic receiving 660470 citations.
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TL;DR: This review focuses on model predictive control of constrained systems, both linear and nonlinear, and distill from an extensive literature essential principles that ensure stability to present a concise characterization of most of the model predictive controllers that have been proposed in the literature.
8,064 citations
Book•
01 Dec 2001
TL;DR: A standard formulation of Predictive Control is presented, with examples of step response and transfer function formulations, and a case study of robust predictive control in the context of MATLAB.
Abstract: 1. Introduction to Predictive Control. 2. A Standard Formulation of Predictive Control. 3. Solving Predictive Control Problems. 4. Step Response and Transfer Function Formulations. 5. Tuning. 6. Stability. 7. Robust Predictive Control. 8. Perspectives. 9. Case Studies. 10. The Model Predictive Control Toolbox. References Appendices A. Some Commercial MPC Products B. MATLAB Program basicmpc C. The MPC Toolbox D. Solutions to Problems
5,468 citations
TL;DR: The flexible constraint handling capabilities of MPC are shown to be a significant advantage in the context of the overall operating objectives of the process industries and the 1-, 2-, and ∞-norm formulations of the performance objective are discussed.
5,188 citations
TL;DR: An overview of commercially available model predictive control (MPC) technology, both linear and nonlinear, based primarily on data provided by MPC vendors, is provided in this article, where a brief history of industrial MPC technology is presented first, followed by results of our vendor survey of MPC control and identification technology.
4,819 citations
Book•
26 Jan 2012
TL;DR: In this article, the authors present a model predictive controller for a water heating system, which is based on the T Polynomial Process (TOP) model of the MPC.
Abstract: 1 Introduction to Model Predictive Control.- 1.1 MPC Strategy.- 1.2 Historical Perspective.- 1.3 Industrial Technology.- 1.4 Outline of the Chapters.- 2 Model 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 State Space Formulation.- 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.- 3.3 Predictive Functional Control.- 3.3.1 Formulation.- 3.4 Case Study: A Water Heater.- 3.5 Exercises.- 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.- 4.12 Exercises.- 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 the 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 Nonmultiple 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.- 5.9 Exercises.- 6 Multivariable Model Predictive Control.- 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 Case Study: Flight Control.- 6.5 Convolution Models Formulation.- 6.6 Case Study: Chemical Reactor.- 6.6.1 Plant Description.- 6.6.2 Obtaining the Plant Model.- 6.6.3 Control Law.- 6.6.4 Simulation Results.- 6.7 Dead Time Problems.- 6.8 Case Study: Distillation Column.- 6.9 Multivariable MPC and Transmission Zeros.- 6.9.1 Simulation Example.- 6.9.2 Tuning MPC for Processes with OUD Zeros.- 6.10 Exercises.- 7 Constrained Model Predictive Control.- 7.1 Constraints and MPC.- 7.1.1 Constraint General Form.- 7.1.2 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 Direction 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 Constraint 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.- 7.10 Exercises.- 8 Robust Model Predictive Control.- 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 Cost Function.- 8.2.2 ?-? norm.- 8.2.3 1-norm.- 8.3 Robustness by Imposing Constraints.- 8.4 Constraint Handling.- 8.5 Illustrative Examples.- 8.5.1 Bounds on the Output.- 8.5.2 Uncertainties in the Gain.- 8.6 Robust MPC and Linear Matrix Inequalities.- 8.7 Closed-Loop Predictions.- 8.7.1 An Illustrative Example.- 8.7.2 Increasing the Number of Decision Variables.- 8.7.3 Dynamic Programming Approach.- 8.7.4 Linear Feedback.- 8.7.5 An Illustrative Example.- 8.8 Exercises.- 9 Nonlinear Model Predictive Control.- 9.1 Nonlinear MPC Versus Linear MPC.- 9.2 Nonlinear Models.- 9.2.1 Empirical Models.- 9.2.2 Fundamental Models.- 9.2.3 Grey-box Models.- 9.2.4 Modelling Example.- 9.3 Solution of the NMPC Problem.- 9.3.1 Problem Formulation.- 9.3.2 Solution.- 9.4 Techniques for Nonlinear Predictive Control.- 9.4.1 Extended Linear MPC.- 9.4.2 Local Models.- 9.4.3 Suboptimal NPMC.- 9.4.4 Use of Short Horizons.- 9.4.5 Decomposition of the Control Sequence.- 9.4.6 Feedback Linearization.- 9.4.7 MPC Based on Volterra Models.- 9.4.8 Neural Networks.- 9.4.9 Commercial Products.- 9.5 Stability and Nonlinear MPC.- 9.6 Case Study: pH Neutralization Process.- 9.6.1 Process Model.- 9.6.2 Results.- 9.7 Exercises.- 10 Model Predictive Control and Hybrid Systems.- 10.1 Hybrid System Modelling.- 10.2 Example: A Jacket Cooled Batch Reactor.- 10.2.1 Mixed Logical Dynamical Systems.- 10.2.2 Example.- 10.3 Model Predictive Control of MLD Systems.- 10.3.1 Branch and Bound Mixed Integer Programming.- 10.3.2 An Illustrative Example.- 10.4 Piecewise Affine Systems.- 10.4.1 Example: Tankwith Different Area Sections.- 10.4.2 Reach Set, Controllable Set, and STG Algorithm.- 10.5 Exercises.- 11 Fast Methods for Implementing Model Predictive Control.- 11.1 Piecewise Affinity of MPC.- 11.2 MPC and Multiparametric Programming.- 11.3 Piecewise Implementation of MPC.- 11.3.1 Illustrative Example: The Double Integrator.- 11.3.2 Nonconstant References and Measurable Disturbances.- 11.3.3 Example.- 11.3.4 The 1-norm and ?-norm Cases.- 11.4 Fast Implementation of MPC forUncertain Systems.- 11.4.1 Example.- 11.4.2 The Closed-Loop Min-max MPC.- 11.5 Approximated Implementation for MPC.- 11.6 Fast Implementation of MPC and Dead Time Considerations.- 11.7 Exercises.- 12 Applications.- 12.1 Solar Power Plant.- 12.1.1 Selftuning GPC Control Strategy.- 12.1.2 Gain Scheduling Generalized Predictive Control.- 12.2 Pilot Plant.- 12.2.1 Plant Description.- 12.2.2 Plant Control.- 12.2.3 Flow Control.- 12.2.4 Temperature Control at the Exchanger Output.- 12.2.5 Temperature Control in the Tank.- 12.2.6 Level Control.- 12.2.7 Remarks.- 12.3 Model Predictive Control in a Sugar Refinery.- 12.4 Olive Oil Mill.- 12.4.1 Plant Description.- 12.4.2 Process Modelling and Validation.- 12.4.3 Controller Synthesis.- 12.4.4 Experimental Results.- 12.5 Mobile Robot.- 12.5.1 Problem Definition.- 12.5.2 Prediction Model.- 12.5.3 Parametrization of the Desired Path.- 12.5.4 Potential Function for Considering Fixed Obstacles.- 12.5.5 The Neural Network Approach.- 12.5.6 Training Phase.- 12.5.7 Results.- A Revision of the Simplex Method.- A.1 Equality Constraints.- A.2 Finding an Initial Solution.- A.3 Inequality Constraints.- B Dynamic Programming and Linear Quadratic Optimal Control.- B.1 LinearQuadratic Problem.- B.2 InfiniteHorizon.- References.
3,913 citations