Model Predictive Control in the Process Industry

1 Introduction to Model Based Predictive Control.- 1.1 MPC Strategy.- 1.2 Historical Perspective.- 1.3 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 MPC Based on the Impulse Response.- 2.3.1 Process Model and Prediction.- 2.3.2 Control Law.- 2.4 Generalized Predictive Control.- 2.4.1 Formulation of Generalized Predictive Control.- 2.4.2 The Coloured Noise Case.- 2.4.3 An example.- 2.5 Constrained Receding-Horizon Predictive Control.- 2.5.1 Computation of the Control Law.- 2.5.2 Properties.- 2.6 Stable GPC.- 2.6.1 Formulation of the control law.- 2.7 Filter Polynomials for Improving Robustness.- 2.7.1 Selection of the T polynomial.- 2.7.2 Relation with other Formulations.- 3 Simple Implementation of GPC for Industrial Processes.- 3.1 Plant Model.- 3.1.1 Plant Identification: The Reaction Curve Method.- 3.2 The Dead Time Multiple of Sampling Time Case.- 3.2.1 Discrete Plant Model.- 3.2.2 Problem Formulation.- 3.2.3 Computation of the Controller Parameters.- 3.2.4 Role of the Control-Weighting Factor.- 3.2.5 Implementation Algorithm.- 3.2.6 An Implementation Example.- 3.3 The Dead Time non Multiple of the Sampling Time Case.- 3.3.1 Discrete Model of the Plant.- 3.3.2 Controller Parameters.- 3.3.3 Example.- 3.4 Integrating Processes.- 3.4.1 Derivation of the Control Law.- 3.4.2 Controller parameters.- 3.4.3 Example.- 3.5 Consideration of Ramp Setpoints.- 3.5.1 Example.- 4 Robustness Analysis in Precomputed GPC.- 4.1 Structured Uncertainties.- 4.1.1 Parametric Uncertainties.- 4.1.2 Unmodelled Dynamics.- 4.1.3 Both Types of Uncertainties.- 4.2 Stability Limits with Structured Uncertainties.- 4.2.1 Influence of Parametric Uncertainties.- 4.2.2 Influence of Unmodelled Dynamics.- 4.2.3 Combined Effect.- 4.2.4 Influence of the Control Effort.- 4.3 Unstructured Uncertainties.- 4.3.1 Process Description.- 4.3.2 Measurement of the Robustness of the GPC.- 4.3.3 Robustness Limits.- 4.4 Relationship between the two Types of Uncertainties.- 4.4.1 Uncertainty in the Gain.- 4.4.2 Uncertainty in the Delay.- 4.5 General Comments.- 5 Multivariate GPC.- 5.1 Derivation of Multivariable GPC.- 5.1.1 White Noise Case.- 5.1.2 Coloured noise case.- 5.2 Obtaining a Matrix Fraction Description.- 5.2.1 Transfer Matrix Representation.- 5.2.2 Parametric Identification.- 5.3 State Space Formulation.- 5.3.1 Matrix Fraction and State Space Equivalences.- 5.4 Dead Time Problems.- 5.5 Example: Distillation Column.- 6 Constrained MPC.- 6.1 Constraints and GPC.- 6.1.1 Illustrative Examples.- 6.2 Revision of Main Quadratic Programming Algorithms.- 6.2.1 The Active Set Methods.- 6.2.2 Feasible Directions Methods.- 6.2.3 Initial Feasible Point.- 6.2.4 Pivoting Methods.- 6.3 Constraints Handling.- 6.3.1 Slew Rate Constraints.- 6.3.2 Amplitude Constraints.- 6.3.3 Output Constraints.- 6.3.4 Constraints Reduction.- 6.4 1-norm.- 6.5 Constrained MPC and Stability.- 7 Robust MPC.- 7.1 Process Models and Uncertainties.- 7.1.1 Truncated Impulse Response Uncertainties.- 7.1.2 Matrix Fraction Description Uncertainties.- 7.1.3 Global Uncertainties.- 7.2 Objective Functions.- 7.2.1 Quadratic Norm.- 7.2.2 ? — ? norm.- 7.2.3 1-norm.- 7.3 Illustrative Examples.- 7.3.1 Bounds on the Output.- 7.3.2 Uncertainties in the Gain.- 8 Applications.- 8.1 Solar Power Plant.- 8.1.1 Control Strategy.- 8.1.2 Plant Results.- 8.2 Composition Control in an Evaporator.- 8.2.1 Description of the Process.- 8.2.2 Obtaining the Linear Model.- 8.2.3 Controller Design.- 8.2.4 Results.- 8.3 Pilot Plant.- 8.3.1 Plant Description.- 8.3.2 Plant Control.- 8.3.3 Flow Control.- 8.3.4 Temperature Control at the Exchanger Output.- 8.3.5 Temperature Control in the Tank.- 8.3.6 Level Control.- 8.3.7 Remarks.- A Revision of the Simplex method.- A.1 Equality Constraints.- A.2 Finding an Initial Solution.- A.3 Inequality Constraints.- B Model Predictive Control Simulation Program.- References.