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Proquest Dissertations ROBUST MODEL PREDICTIVE CONTROL FOR PROCESS CONTROL AND SUPPLY CHAIN OPTIMIZATION By XIANG LI, B.Eng., M.Eng. A Thesis Submitted to the School of Graduate Studies in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy McMaster University © Copyright by Xiang Li, September 2009 Library and Archives Bibliotheque et 1*1 Canada Archives Canada Published Heritage Direction du Branch Patrimoine de I'edition 395 Wellington Street 395, rue Wellington OttawaONK1A0N4 Ottawa ON K1A 0N4 Canada Canada Your file Votre reference ISBN: 978-0-494-64703-5 Our file Notre reference ISBN: 978-0-494-64703-5 NOTICE: AVIS: The author has granted a non­ L'auteur a accorde une licence non exclusive exclusive license allowing Library and permettant a la Bibliotheque et Archives Archives Canada to reproduce, Canada de reproduire, publier, archiver, publish, archive, preserve, conserve, sauvegarder, conserver, transmettre au public communicate to the public by par telecommunication ou par Nnternet, preter, telecommunication or on the Internet, distribuer et vendre des theses partout dans le loan, distribute and sell theses monde, a des fins commerciales ou autres, sur worldwide, for commercial or non­ support microforme, papier, electronique et/ou commercial purposes, in microform, autres formats. paper, electronic and/or any other formats. The author retains copyright L'auteur conserve la propriete du droit d'auteur ownership and moral rights in this et des droits moraux qui protege cette these. Ni thesis. Neither the thesis nor la these ni des extraits substantiels de celle-ci substantial extracts from it may be ne doivent etre imprimes ou autrement printed or otherwise reproduced reproduits sans son autorisation. without the author's permission. In compliance with the Canadian Conformement a la loi canadienne sur la Privacy Act some supporting forms protection de la vie privee, quelques may have been removed from this formulaires secondaires ont ete enleves de thesis. cette these. While these forms may be included Bien que ces formulaires aient inclus dans in the document page count, their la pagination, il n'y aura aucun contenu removal does not represent any loss manquant. of content from the thesis. 1+1 Canada DOCTOR OF PHILOSOPHY (2009) McMaster University (Chemical Engineering) Hamilton, Ontario TITLE: Robust Model Predictive Control for Process Control and Supply Chain Optimization AUTHOR: Xiang Li, B.Eng., M.Eng. (Zhejiang University, P. R. China) SUPERVISOR: Professor T. E. Marlin NUMBER OF PAGES: x, 295 ii Abstract Model Predictive Control (MPC) is traditionally designed assuming no model mismatch and tuned to provide acceptable behavior when mismatch occurs. This thesis extends the MPC design to account for explicit mismatch in the control and optimization of a wide range of uncertain dynamic systems with feedback, such as in process control and supply chain optimization. The major contribution of the thesis is the development of a new MPC method for robust performance, which offers a general framework to optimize the uncertain system behavior in the closed-loop subject to hard bounds on manipulated variables and soft bounds on controlled variables. This framework includes the explicit handling of correlated, time-varying or time-invariant, parametric uncertainty appearing externally (in demands and disturbances) and internally (in plant/model mismatch) to the control system. In addition, the uncertainty in state estimation is accounted for in the controller. For efficient and reliable real-time solution, the bilevel stochastic optimization formulation of the robust MPC method is approximated by a limited number of (convex) Second Order Cone Programming (SOCP) problems with an industry-proven heuristic and the classical chance-constrained programming technique. A closed-loop uncertainty characterization method is also developed which improves real-time tractability by performing intensive calculations off-line. The new robust MPC method is extended for process control problems by integrating a robust steady-state optimization method addressing closed-loop uncertainty. In addition, the objective function for trajectory optimization can be formulated as nominal or expected dynamic performance. Finally, the method is formulated in deviation variables to correctly estimate time-invariant uncertainty. iii The new robust MPC method is also tailored for supply chain optimization, which is demonstrated through a typical industrial supply chain optimization problem. The robust MPC optimizes scenario-specific safety stock levels while satisfying customer demands for time-varying systems with uncertainty in demand, manufacturing and transportation. Complexity analysis and computational study results demonstrate that the robust MPC solution times increase with system scale moderately, and the method does not suffer from the curse of dimensionality. iv Acknowledgements First and foremost, I would like to express my sincere gratitude to my supervisor, Dr. Thomas Marlin, for his patient and insightful guidance, which not only has helped out this thesis, but also will be beneficial to my future career. I also thank him for giving me ample freedom to carry out my own idea, especially at the early stage of the research. Besides my supervisor, I would like to thank other members of my research committee, Dr. Chris Swartz, Dr. Tamas Terlaky and Dr. Tim Davidson, for their valuable suggestions as well as hard questions that boost the progress of this research. My sincere thanks also go to all the fellow graduate students in the MACC, for their friendship that make my life during the Ph.D. study warm and colorful. In particular, I would like to thank Yongsong, Zhiwen, Adam, Alberto, Zheng, Honglu, Jesus, Kevin, Danielle, Alexei, Rhoda, Rahul, Benoit. I would especially thank Weitao for helping me settle down and get familiar with Canadian life quickly during my early time in Hamilton. In addition, I am grateful to a confidential industrial collaborator, for their offering important industrial data to facilitate the supply chain optimization research in this thesis. Last but not the least, I would like to thank my parents, Bingrui and Zhijiang, for bringing me to this world, raising me up and always giving me unconditional support, and my wife, Hui, for her understanding and encouragement during the course of my Ph.D. research. v Table of Contents Chapter 1 Introduction 1 1.1 Model Predictive Control 2 1.1.1 Conventional, nominal MPC 2 1.1.2 Robust MPC, nonlinear MPC and adaptive MPC 3 1.2 Process Control 5 1.3 Supply Chain Optimization 6 1.4 Goal and Scope of the Research 8 1.5 Thesis Outline 10 1.6 Terminology and Conventions 12 Chapter 2 Literature Review 14 2.1 The State-of-the-art Robust MPC Methods 14 2.1.1 Different approaches for formulating uncertain model 15 2.1.2 Approaches for other aspects of robust MPC 20 2.1.3 Summary of the "representative" robust MPC methods 25 2.1.4 Robust steady-state optimization 28 2.2 Supply Chain Optimization Under Uncertainty 29 2.2.1 Methods for optimization under uncertainty 29 2.2.2 Control strategies for the uncertain system with feedback 31 2.3 Summary 33 vi Chapter 3 A General Framework for Robust MPC 36 3.1 Nominal MPC formulation - Basis of the Robust MPC 38 3.2 The New Robust MPC Formulation 44 3.2.1 Robust MPC with closed-loop model 44 3.2.2 The reformulation to single level problem 50 3.2.3 The reformulation with known saturated manipulated variables 52 3.2.4 The active set heuristic to obtain the active bounds 56 3.2.5 The deviation model enhanced for time-invariant uncertainty 59 3.3 The Solution Techniques 63 3.3.1 Solution with chance-constraints 63 3.3.2 Efficient uncertainty characterization 67 3.4 Uncertainties in State-Estimation 72 3.5 Summary of the Robust MPC Algorithm 76 3.6 Case Study Results and Discussion 78 3.6.1 The control methods evaluated in the case studies 78 3.6.2 CSTR control system 1 79 3.6.3 CSTR control system 2 89 3.7 Conclusions 101 Chapter 4 Robust MPC for Process Control 103 4.1 Robust Steady-State Optimization 104 4.1.1 Steady-state optimization in industrial MPC control system 104 4.1.2 The robust steady-state optimization with closed-loop uncertainty 107 4.1.3 The reformulation to convex optimization 110 4.1.4 The deviation model to exploit the feedback information 116 vii 4.1.5 Summary of the Robust Steady-State Optimization Method 119 4.2 Optimization of Robust Dynamic Performance 121 4.3 Case Study Results and Discussion 126 4.3.1 The control and optimization methods used in the case studies 127 4.3.2 Binary distillation control system 1 128 4.3.3 Binary distillation control system 2 141 4.3.4 Advantages of robust MPC minimizing robust performance 145 4.4 Conclusions 161 Chapter 5 Robust MPC for Supply Chain Optimization 163 5.1 The Industrial Supply Chain Optimization Problem 164 5.2 The Nominal MPC Formulation 167 5.2.1 The discrete-time nominal state-space model 167 5.2.2 The economic objective and the constraints 171 5.2.3 The nominal MPC formulation 174 5.3 The Robust MPC Formulation 175 5.3.1 Description of uncertainties with uncertain parameters 175 5.3.2 Closed-loop optimization with approximating inner QP problems 179 5.3.3 SOCP formulation with tailored chance-constrained program 183 5.4 The Model for Supply Chain Simulation 186 5.5 Case Study Results and Discussion 187 5.5.1 Case study with 1IP/SKU type and 1 RDC 189 5.5.2 Case study with 2 IP/SKU types and 2 RDCs 205 5.5.3 Computational complexity 210 5.6 Conclusions 213 viii Chapter
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