Multi-Parametric Model-Based Control Theory

This volume covers theoretical advances and developments, computational challenges and tools as well as applications in the area of multi-parametric model based control.Part I is concerned with the presentation of algorithms for parametric model based control focusing on: novel frameworks for the derivation of explicit optimal control policies for continuous time-linear dynamic systems new theoretical developments on hybrid model based control methods for obtaining the explicit robust model-based tracking control theoretical frameworks for parametric dynamic optimization and recent developments for continuous-time systemsPart II presents a series of application in the following areas: the incorporation of advanced model based controllers in a simultaneous process design and control framework for complex separation systems the development of advanced model based control techniques for regulating the blood glucose for patients with Type 1 diabetes the design of model predictive and parametric controllers for anesthesia. the development of optimal control policies in a pilot plant exothermic reactorThe volume is intended for academics and researchers that carry out model based control research, industrial practitioners involved in the control of new and existing processes and products, policy makers, as well as for educational purposes both in academia and industry.

Efstratios N. Pistikopoulos is a Professor of Chemical Engineering at Imperial College London and the Director of its Centre for Process Systems Engineering (CPSE). He holds a first degree in Chemical Engineering from Aristotle University of Thessaloniki, Greece and a PhD from Carnegie Mellon University, USA. He has supervised more than twenty PhD students, authored/ co-authored over 150 major research journal publications and been involved in over 50 major research projects and contracts. A co-founder and Director of two successful spin-off companies from Imperial, Process Systems Enterprise (PSE) Limited and Parametric Optimization Solutions (PAROS) Limited, he consults widely to a large number of process industry companies.

Michael C. Georgiadis is a senior researcher in the Centre for Process Systems Engineering at Imperial College London and the manager of academic business development of Process Systems Enterprise Ltd in Thessaloniki, Greece. He holds a first degree in Chemical Engineering from Aristotle University of Thessaloniki and a MSc and PhD from Imperial College. He has authored/ co-authored over 40 journal publications and two books. He has a long experience in the management and participation of more than 20 collaborative research contracts and projects.

Dr. Vivek Dua is a Lecturer in the Department of Chemical Engineering at University College London. He obtained his first degree in Chemical Engineering from Panjab University, Chandigarh, India and MTech in chemical engineering from the Indian Institute of Technology, Kanpur. He joined Kinetics Technology India Ltd. as a Process Engineer before moving to Imperial College London, where he obtained his PhD in Chemical Engineering. He was an Assistant Professor in the Department of Chemical Engineering at Indian Institute of Technology, Delhi before joining University College London. He is a co-founder of Parametric Optimization Solutions (PAROS) Ltd.

Preface—Volume 2: Muliparametric Model-Based Control
References
List of Authors
Theory
Linear Model Predictive Control via Multiparametric Programming
Introduction
Multiparametric Programming
Model Predictive Control
Multiparametric Quadratic Programming
De.nition of CRrest
Numerical Example
Computational Complexity
Computational Time
Extensions to the Basic MPC Problem
Reference Tracking
Relaxation of Constraints
The Constrained Linear Quadratic Regulator Problem
Conclusions
References
Hybrid Parametric Model-Based Control
Introduction
The Explicit Control Law for Hybrid Systems via Parametric Programming
General Hybrid Systems
Piecewise Linear Systems
The Explicit Control Law for Continuous Time Systems via Parametric Programming
Problem Formulation
Stability Requirements
Solution Procedures
Illustrative Process Example 2.3
Illustrative Biomedical Process Example 2.3.2
Illustrative Mathematical Example 2.3.3
Conclusions
References
Robust Parametric Model-Based Control
Introduction
Robust Parametric Model-Based Control for Systems with Input Uncertainties
Open-Loop Robust Parametric Model Predictive Controller
Parametric Solution of the Inner Maximization Problem
Closed-Loop Robust Parametric Model-Based Control
Reference Tracking Robust Parametric Model-Based Controller
Example—Two State MIMO Evaporator
Robust Parametric Model-Based Control for Systems with Model Parametric Uncertainties
MPC of Parametric Uncertain Linear Systems
Uncertain Matrices
The Robust Counterpart Problem
Example of Two-Dimensional Linear Parametric Uncertain System
Conclusions
References
Parametric Dynamic Optimization
Introduction
Solution Procedure—Theoretical Developments for mp-DO
Control Vector Parametrization
Parameter Representation
Problems Without Path Constraints
Problems with Path Constraints
Illustrative Examples
Example 1: Exothermic CSTR
Example 2: Fluidized Catalytic Cracking Unit
Software Implementation Issues
Concluding Remarks
Critical Parameter Values in Path Constraints
Solution Properties of the mp-DO Algorithm
Convergence Properties of the Direct mp-DO Algorithm
Solution of a Semiin.nite Program
Acknowledgment
References
Continuous-Time Parametric Model-Based Control
Introduction
Linear Continuous-Time MPC
Implicit MPC
Multiparametric Dynamic Optimization
Optimality Conditions
Parametric Control Profile
Algorithm for Solving the mp-DO Problem
Control Implementation
Comparison Between Continuous-Time and Discrete-Time MPC
Examples
Example of a SISO System with One State
Example of a SISO System with Two States
Exten
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Multi-Parametric Model-Based Control Theory and Applications

Summary

Author Biography

Table of Contents

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