Modeling and Intelligent Control of a Distillation Column Joao˜ Rodrigo Camelo Barroso Dissertac¸ao˜ para obtenc¸ao˜ do Grau de Mestre em Engenharia Mecanicaˆ J ´uri Presidente: Prof. Joao˜ Rogerio´ Caldas Pinto Orientador: Prof. Jose´ Alberto de Jesus Borges Co-Orientador: Profa Carla Isabel Costa Pinheiro Vogal: Prof. Joao˜ Miguel Alves da Silva Outubro - 2009 Este trabalho reflecte as ideias dos seus autores que, eventualmente, poderao˜ nao˜ coincidir com as do Instituto Superior Tecnico.´ Abstract The aim of the present work is to develop models and design controllers for an experimental pilot- scale continuous distillation process. Distillation columns are highly complex systems characterized by nonlinear dynamics, multiple equi- librium points and operational modes, therefore require suitable modeling techniques.These models are used to design controllers that are suitable for reference tracking, Fault Detection and Isolation and Fault Tolerant Control. The objective of such controllers is to enhance productivity throughout the distillation process. Two main types of black box models are derived: Linear State-Space Models and Nonlinear Models, namely Fuzzy Models, Composite Local Linear Models and Artificial Neural Networks. All these models will be estimated and compared using both experimental and simulated data, with the last being provided by a First Principles Model. The resulting models can be used to predict system outputs, therefore are suitable for integration into optimal control schemes, such as Model Based Predictive Control. The optimization problem in the nonlinear controller case is addressed using either Branch and Bound and a composition of multiple local linear optimal solutions. These controllers are then compared with respect to tracking error and computational load. The integration of fault tolerant control allows reducing the impact of abrupt faults in the control vari- ables. The system is normally operating in nominal conditions and if a known fault occurs the controller is modified in order to accommodate this new state. Keywords: Continuous Distillation Process, Nonlinear Modeling, Nonlinear Model Based Predictive Control, Fault Detection and Isolation, Fault Tolerant Control v vi Resumo O objectivo deste trabalho e´ desenvolver modelos e projectar controladores para um processo cont´ınuo de destilac¸ao˜ a` escala piloto. As colunas de destilac¸ao˜ sao˜ sistemas altamente complexos caracterizados por dinamicasˆ nao-˜ lineares, multiplos´ pontos de equil´ıbrio e modos operacionais, exigindo assim tecnicas´ de modelac¸ao˜ adequadas. Estes modelos sao˜ utilizados para projectar controladores para o seguimento de re- ferenciasˆ e detecc¸ao,˜ isolamento e controlo tolerante a falhas. O objectivo e´ aumentar a produtividade no processo de destilac¸ao.˜ Sao˜ desenvolvidos dois tipos de modelos: modelos lineares em espac¸o de estados e modelos nao-˜ lineares, nomeadamente Modelos Fuzzy, Composic¸ao˜ de Modelos Locais Lineares e Redes Neuronais Artificiais. Todos estes modelos sao˜ estimados e comparados com dados experimentais e de simulac¸ao,˜ sendo estes ultimos´ obtidos a partir de um modelo de primeiros princ´ıpios. Os modelos resultantes podem ser usados para prever as sa´ıdas futuras do sistema, logo sao˜ adequados para integrac¸ao˜ em esquemas de controlo optimo,´ nomeadamente Controlo Preditivo. As abordagens para a resoluc¸ao˜ do problema de optimizac¸ao˜ nos casos em que se utilizam modelos nao-˜ lineares sao:˜ Branch and Bound e composic¸ao˜ de soluc¸oes˜ lineares locais optimas.´ Estes controladores sao˜ comparados utilizando o erro de seguimento e o esforc¸o computacional. A integrac¸ao˜ do controlo tolerante a falhas permite reduzir o impacto destas nas variaveis´ de controlo e deste modo aumentar a produtividade no processo de destilac¸ao.˜ O processo funciona normalmente em condic¸oes˜ nominais e quando uma falha conhecida ocorrer o controlador e´ alterado de forma a lidar com este novo estado. Palavras chave: Processo de Destilac¸ao˜ Cont´ınuo, Modelac¸ao˜ Nao-Linear˜ , Controlador Preditivo Baseado em Modelo Nao-Linear,˜ Detecc¸ao˜ e Isolamento de Falhas, Controlo Tolerante a Falhas vii viii Acknowledgments My first words of appreciation are undoubtedly to my supervisors Professor Jose´ Borges and Pro- fessor Carla Pinheiro. I would like to thank them for their invaluable support and patience, and for the advice and orientation provided throughout this work. I also want to thank Prof. Joao˜ Miguel Silva, Prof. Ana Pires and Taniaˆ Pinto for their help regarding the distillation column and its experimental tests. My colleagues also deserve a special acknowledgment due to all the advice, support and information they provided, through all the course and specially in these last intensive months. I’d also like to thank my family for being there in the hardest times, when I needed them most. Finally, I would like to thank the financial support granted by the project POCI/EME/59522/2004 Fault-Tolerant control based on multi-agents systems from Fundac¸ao˜ para a Cienciaˆ e Tecnologia. ix x Contents Abstract v Resumo vii Contents xi List of Figures xv List of Tables xix Notation xxi 1 Introduction 1 1.1 Distillationanditsbackground. .............. 1 1.2 Motivation...................................... ....... 2 1.3 Stateoftheart ................................... ....... 3 1.3.1 Black-BoxModels ............................... ..... 3 1.3.2 Control ....................................... ... 4 1.4 Contributionofthiswork . ........... 4 1.5 Outlineofthiswork............................... ......... 5 2 Description of the computer aided tools 7 2.1 Introduction to Nonlinear Systems . ............. 7 2.2 FuzzySystems.................................... ...... 8 2.2.1 Fuzzy Inference Systems . ....... 8 2.2.2 DynamicFuzzySystems . ..... 10 2.2.3 FuzzyClustering ............................... ...... 11 2.3 Composite Local Linear Models . ........... 11 2.4 ArtificialNeuralNetworks . ........... 12 2.4.1 ArtificialNeuron ............................... ...... 12 2.4.2 Neural Network Architecture . ......... 13 2.4.3 Learning ...................................... 13 2.5 ModelPredictiveControl. ........... 14 xi 2.6 NonlinearPredictiveControl. ............. 15 2.6.1 Branch-and-Bound. ...... 16 2.7 FaultTolerantControl . .......... 17 2.7.1 Disturbances .................................. ..... 17 2.7.2 Classificationoffaults . ......... 17 2.8 PerformanceCriteria. .......... 18 3 Distillation Columns 19 3.1 Introduction.................................... ........ 19 3.2 Columnsinternals ................................ ........ 19 3.3 Vapor-Liquid-Equilibrium (VLE) . .............. 20 3.4 ColumnDesign.................................... ...... 21 3.4.1 McCabe-ThieleMethod . ...... 22 3.4.2 FenskeEquation ................................ ..... 23 3.5 Properties of the experimental distillation column . .................... 23 4 Distillation Column Modeling 25 4.1 FirstPrinciplesModel . .......... 25 4.2 Input/Output data preprocessing . ............. 27 4.2.1 Persistencyofexcitation . .......... 27 4.2.2 Normalizationofvariables . .......... 28 4.3 Linearmodels.................................... ....... 29 4.3.1 Linear models based in simulated data . ........... 30 4.3.2 Linear models based in real data . ......... 31 4.4 Nonlinear models based in simulated data . .............. 32 4.4.1 FuzzyModels................................... 32 4.4.2 Composite Local Linear Models . ......... 35 4.4.3 ArtificialNeuralNetworks . ......... 39 4.5 Nonlinear Models based in real data . ............ 41 4.5.1 FuzzyModels................................... 41 4.5.2 Composite Local Linear Models . ......... 43 4.6 Discussionofresults . .......... 45 5 Model Based Control 51 5.1 Problem description and assumptions . ............. 51 5.2 MPCbasedinlinearmodel . ........ 53 5.3 NMPCwithB&B ..................................... 55 5.3.1 B&BusingFMmodels.............................. 56 5.3.2 B&BusingCLLMmodels .. ..... ..... ..... ...... ..... 58 5.3.3 Time comparison between models used by B&B . ......... 60 xii 5.4 NMPC with a composition of MPC’s . ......... 60 5.5 Discussionofresults . .......... 64 5.5.1 Computationaltime ............................. ...... 66 6 Fault Tolerant Control 69 6.1 Problemdescription .............................. ......... 69 6.1.1 FaultDetection ................................ ...... 70 6.1.2 FaultIdentification . ........ 70 6.1.3 Control Reconfiguration Mechanism . .......... 71 6.2 Results ......................................... ..... 72 6.2.1 Tuning of Model Based Controller in case of Tebul ................... 73 6.2.2 Tuning of Model Based Controller in case of Tvap ................... 74 7 Conclusions 75 7.1 Modeling ........................................ ..... 75 7.2 Control ......................................... ..... 75 7.3 Fault Identification and Control . ............. 76 7.4 Futurework...................................... ...... 76 Bibliography 77 Appendix 81 A Fuzzy models Properties 83 A.1 Modelbasedinsimulations . .......... 83 A.2 Modelbasedinrealdata. ......... 85 B Modifications implemented to the Branch and Bound MPC scheme 87 B.1 IntegrationinSimulink . ........... 87 xiii xiv List of Figures 1.1 Alembic used to distillate beverages . .............. 1 2.1 Fuzzy Inference System block diagram . ............. 9 2.2 ArtificialNeuralNetwork . ........... 12 2.3 ArtificialNeuron ................................. ........ 13 2.4 RecurrentNeuralNetwork. .......... 14 2.5