 Process Systems Engineering: Volume 2: Multi-Parametric Model-Based Control
ISBN: 978-3-527-31692-2
Hardcover
275 pages
April 2007
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References.
List of Authors.
Part I Theory.
1 Linear Model Predictive Control via Multiparametric Programming.
1.1 Introduction.
1.1.1 Multiparametric Programming.
1.1.2 Model Predictive Control.
1.2 Multiparametric Quadratic Programming.
1.2.1 De.nition of CRrest.
1.3 Numerical Example.
1.4 Computational Complexity.
1.4.1 Computational Time.
1.5 Extensions to the Basic MPC Problem.
1.5.1 Reference Tracking.
1.5.2 Relaxation of Constraints.
1.5.3 The Constrained Linear Quadratic Regulator Problem.
1.6 Conclusions.
References.
2 Hybrid Parametric Model-Based Control.
2.1 Introduction.
2.2 The Explicit Control Law for Hybrid Systems via Parametric Programming.
2.2.1 General Hybrid Systems.
2.2.2 Piecewise Linear Systems.
2.3 The Explicit Control Law for Continuous Time Systems via Parametric Programming.
2.3.1 Problem Formulation.
2.3.2 Stability Requirements.
2.3.3 Solution Procedures.
2.3.4 Illustrative Process Example 2.3.
2.3.5 Illustrative Biomedical Process Example 2.3.2.
2.3.6 Illustrative Mathematical Example 2.3.3.
2.4 Conclusions.
References.
3 Robust Parametric Model-Based Control.
3.1 Introduction.
3.2 Robust Parametric Model-Based Control for Systems with Input Uncertainties.
3.2.1 Open-Loop Robust Parametric Model Predictive Controller.
3.2.2 Parametric Solution of the Inner Maximization Problem.
3.2.3 Closed-Loop Robust Parametric Model-Based Control.
3.2.4 Reference Tracking Robust Parametric Model-Based Controller.
3.2.5 Example—Two State MIMO Evaporator.
3.3 Robust Parametric Model-Based Control for Systems with Model Parametric Uncertainties.
3.3.1 MPC of Parametric Uncertain Linear Systems.
3.3.2 Uncertain Matrices.
3.3.3 The Robust Counterpart Problem.
3.3.4 Example of Two-Dimensional Linear Parametric Uncertain System.
3.4 Conclusions.
References.
4 Parametric Dynamic Optimization.
4.1 Introduction.
4.2 Solution Procedure—Theoretical Developments for mp-DO.
4.2.1 Control Vector Parametrization.
4.2.2 Parameter Representation.
4.2.3 Problems Without Path Constraints.
4.2.4 Problems with Path Constraints.
4.3 Illustrative Examples.
4.3.1 Example 1: Exothermic CSTR.
4.3.2 Example 2: Fluidized Catalytic Cracking Unit.
4.4 Software Implementation Issues.
4.5 Concluding Remarks.
Appendix A. Critical Parameter Values in Path Constraints.
Appendix B. Solution Properties of the mp-DO Algorithm.
Appendix B.1. Convergence Properties of the Direct mp-DO Algorithm.
Appendix B.2. Solution of a Semiin.nite Program.
Acknowledgment.
References.
5 Continuous-Time Parametric Model-Based Control.
5.1 Introduction.
5.1.1 Linear Continuous-Time MPC.
5.1.2 Implicit MPC.
5.2 Multiparametric Dynamic Optimization.
5.2.1 Optimality Conditions.
5.2.2 Parametric Control Profile.
5.2.3 Algorithm for Solving the mp-DO Problem.
5.3 Control Implementation.
5.4 Comparison Between Continuous-Time and Discrete-Time MPC.
5.5 Examples.
5.5.1 Example of a SISO System with One State.
5.5.2 Example of a SISO System with Two States.
5.6 Extension to Nonlinear Problem.
5.6.1 Example.
5.7 Conclusions.
References.
Part II Applications.
6 Integration of Design and Control.
6.1 Introduction.
6.1.1 Process and Control Design Using Advanced Control Schemes.
6.1.2 Simultaneous Design and Control Under Uncertainty Framework.
6.1.3 Mixed-Integer Dynamic Optimization.
6.2 Problem Formulation.
6.3 Theoretical Developments—Solution Procedure.
6.3.1 Problem Reformulation.
6.3.2 Decomposition Approach for Process and Control Design—Algorithm 6.2.
6.3.3 Modeling Aspects of the Parametric Controller.
6.3.4 Disturbance Rejection.
6.3.5 Control Structure Selection.
6.4 Process Example 6.2—Evaporation Process.
6.4.1 Objective Function.
6.4.2 Inequality Constraints.
6.4.3 Disturbances.
6.4.4 Decision Variables.
6.5 Process Example 6.3—Distillation Column.
6.5.1 Problem Formulation.
6.6 Computational Times and Software Implementation Issues.
6.7 Conclusions.
References.
7 Model-Based Control of Blood Glucose for Type 1 Diabetes.
7.1 Introduction.
7.2 Model Predictive Control for Type 1 Diabetes.
7.3 Explicit Insulin Delivery Rate.
7.4 Inter- and IntraPatient Variability.
7.5 Multiobjective Blood Glucose Control.
7.5.1 Asymmetric Objective Function.
7.5.2 Constraint Prioritization.
7.6 Concluding Remarks.
Acknowledgments.
References.
8 Control of Anesthesia.
8.1 Introduction.
8.2 Compartmental Model for Anesthesia.
8.2.1 Pharmacokinetic Modeling of Anesthesia.
8.2.2 Pharmacodynamic Modeling of Anesthesia.
8.2.3 Baroreflex.
8.3 Validation of the Compartmental Model for Anesthesia.
8.4 Model-Based and Parametric Control of Anesthesia.
8.5 Concluding Remarks.
References.
9 Model-Based Control of Pilot Plant Reactor.
9.1 Introduction.
9.2 Description of the Reactor.
9.2.1 Reactor Simulation.
9.3 Planning Experiments: Steady-State Reactor Behavior.
9.4 Derivation of the Explicit Model-Based Control Law.
9.5 Results.
9.5.1 Implementation of the Parametric Controller.
9.6 Concluding Remarks.
References.
10 MPC on a Chip.
10.1 Introduction.
10.2 Automatic Control: History and Present.
10.2.1 Proportional Integral Derivative Control.
10.2.2 Model-Based Predictive Control.
10.3 Parametric MPC.
10.3.1 Online Optimization via Off-Line Optimization.
10.4 Putting Theory into Practice.
10.4.1 A Parametric MPC Controller for the PARSEX Pilot Plant.
10.4.2 Parametric MPC for an Air Separation Unit.
10.4.3 An Automotive Example—pMPC for an Active Valve Train Actuation System.
10.5 Blood Glucose Control for Type 1 Diabetes.
10.6 Conclusions.
References.
Index.
